Carl Ollivier-Gooch


Research Interests

Algorithm Development for Computational Fluid Dynamics
Applied Aerodynamics
Numerical analysis
Unstructured Mesh Generation
Error and Stability Analysis for Unstructured Mesh Methods
Computer Sciences and Mathematical Tools
Fluid mechanics

Relevant Thesis-Based Degree Programs

Research Options

I am available and interested in collaborations (e.g. clusters, grants).

Research Methodology

Development of software for numerical simulation of PDE's
Unstructured mesh generation
Machine learning applications in computational aerodynamics


Master's students
Doctoral students
Postdoctoral Fellows
  • Simulation of high-lift aerodynamic configurations, including extending my group's existing tools as needed for these problems.
  • Developing tools to identify whether there are unresolved features in a flow.
  • Combine and extend my group's existing tools to produce a complete toolchain for mesh generation for complex aerodynamic configurations.

Students working in my group come from a variety of backgrounds.  The characteristics I look for, roughly in order of importance are:

  • Intelligence
  • Problem-solving ability
  • Ability to carry tasks to completion
  • Ability and interest in programming
  • Attention to detail

For PhD positions, I strongly prefer students whose master's projects included writing CFD code (preferably using unstructured meshes).  Experience has taught me that there's a small risk of a student discovering they're not as interested in this sort of research as they thought.  For a master's degree, it's possible to power through the last few months if this happens.  For a PhD, that would be the last few years, and that's really bad for everyone.  Hence my preference.

Beyond these characteristics, I'm open to applicants from a wide range of backgrounds, both academically and personally.  Women and other applicants whose backgrounds are underrepresented in STEM are particularly encouraged to apply.

I support experiential learning experiences, such as internships and work placements, for my graduate students and Postdocs.

Complete these steps before you reach out to a faculty member!

Check requirements
  • Familiarize yourself with program requirements. You want to learn as much as possible from the information available to you before you reach out to a faculty member. Be sure to visit the graduate degree program listing and program-specific websites.
  • Check whether the program requires you to seek commitment from a supervisor prior to submitting an application. For some programs this is an essential step while others match successful applicants with faculty members within the first year of study. This is either indicated in the program profile under "Admission Information & Requirements" - "Prepare Application" - "Supervision" or on the program website.
Focus your search
  • Identify specific faculty members who are conducting research in your specific area of interest.
  • Establish that your research interests align with the faculty member’s research interests.
    • Read up on the faculty members in the program and the research being conducted in the department.
    • Familiarize yourself with their work, read their recent publications and past theses/dissertations that they supervised. Be certain that their research is indeed what you are hoping to study.
Make a good impression
  • Compose an error-free and grammatically correct email addressed to your specifically targeted faculty member, and remember to use their correct titles.
    • Do not send non-specific, mass emails to everyone in the department hoping for a match.
    • Address the faculty members by name. Your contact should be genuine rather than generic.
  • Include a brief outline of your academic background, why you are interested in working with the faculty member, and what experience you could bring to the department. The supervision enquiry form guides you with targeted questions. Ensure to craft compelling answers to these questions.
  • Highlight your achievements and why you are a top student. Faculty members receive dozens of requests from prospective students and you may have less than 30 seconds to pique someone’s interest.
  • Demonstrate that you are familiar with their research:
    • Convey the specific ways you are a good fit for the program.
    • Convey the specific ways the program/lab/faculty member is a good fit for the research you are interested in/already conducting.
  • Be enthusiastic, but don’t overdo it.
Attend an information session

G+PS regularly provides virtual sessions that focus on admission requirements and procedures and tips how to improve your application.



These videos contain some general advice from faculty across UBC on finding and reaching out to a potential thesis supervisor.

Graduate Student Supervision

Doctoral Student Supervision

Dissertations completed in 2010 or later are listed below. Please note that there is a 6-12 month delay to add the latest dissertations.

Application of conditional filtering to simulation of turbulence, chemistry, and their interactions (2019)

Combustion technology has been applied in human society for millennia and, since the industrial revolution, has become an integral part of most energy supply chains. Simulation is an important tool in modern combustor design; this thesis aims to improve the quality of combustion simulation tools, and thereby facilitate the design of improved combustors. More specifically, it aims to examine how generalizing and/or relaxing the definition of conditional filtering – a common technique in turbulence-chemistry interaction modelling – can produce novel turbulence and combustion models. The work begins with an extension of the Conditional Source-term Estimation (CSE) model for turbulence-chemistry interaction modelling. A novel variation of the algorithm, termed CSE with Geometric Conditioning Variables (CSE-GCV) is proposed as a method of circumventing the theoretical and practical issues associated with traditional CSE ensemble division. In CSE-GCV, the concept of the conditional filter is generalized by introducing geometric (position-based) variables as conditioning variables. CSE-GCV is tested and found to be workable; a theoretical analysis demonstrates that CSE-GCV also generally has the advantage of reduced computational complexity compared to traditional CSE. In a separate study, the stabilization procedure employed in traditional dynamic sub-filter modelling for Large Eddy Simulation (LES) is re-interpreted as a form of conditional filtering based on position. This re-interpretation is used as the starting point for a "conditional dynamic" sub-filter model in which the stabilization procedure is based on filtering conditionally on scalar fields. Both the traditional and conditional models are applied to a turbulent flame; results suggest that the two models perform similarly, although performance of both is sub-optimal in the case considered. The final, two-part, study is based around the suggestion that, with sufficient conditioning, conditionally-filtered fields should be independent of position. It is found that assuming this uniformity produces a novel turbulence-chemistry interaction model, termed the Uniform Conditional State (UCS) model, in which the conditional scalar dissipation model is the key un-closed parameter. The UCS model is applied to a series of turbulent non-premixed flames, and is found to predict their properties to good accuracy, with details showing some sensitivity to the conditional scalar dissipation model.

View record

Numerical stability analyses and improvement of cell-centered finite volume methods on unstructured meshes (2019)

The purpose of this thesis is to develop a framework in which one can detect and automatically improve the numerical stability of cell-centered finite-volume calculations on unstructured meshes through optimization schemes that modify the mesh, the solution reconstruction, or the boundary conditions. In this process, eigenanalysis and the gradients of the eigenvalues with respect to different parameters are used to ensure energy stability of the system, consequently resulting in convergence. First, gradients of eigenvalues with respect to the local changes in the mesh are calculated to find directions and magnitudes of mesh movements that will make the Jacobian of a semi-discrete system of equations negative semi-definite. These mesh movement vectors are used to modify the mesh locally. The numerical results show that the proposed methods are able to locate the problematic parts of the mesh responsible for instabilities for several physical problems and to correct the instability. Secondly, I develop a mathematical method, introduced by Haider et al., to measure the stability impact of the reconstruction for high order and nonlinear problems, regardless of the solution. Second order and third order accurate advection and Burgers and Euler problems are used to present detailed practical results and discussion around the use of the local reconstruction map for stability analysis. This method shows that increasing the stencil size will lead to more stable problems. An empirical study is performed which sheds light on connections between the mesh properties and the stability of the reconstruction. I also propose a systematic approach to optimize both the shape and the size of the reconstruction stencil for better numerical stability through eigenvalue analysis. In this approach, one can directly optimize the solution reconstruction stencil for every control volume to obtain better numerical stability and convergence properties for steady state problems.The rightmost eigenpairs of the spatially discretized system of equations are used to obtain an optimized boundary condition which will ensure the energy stability of the system. Lastly, the sensitivity of the rightmost eigenvalues to the solution is measured to investigate the effect of using surrogate solutions for the purpose of linearizing the semi-discretized Jacobian.

View record

Numerical estimation of discretization error on unstructured meshes (2018)

A numerical estimation of discretization error is performed for solutions to steady and unsteady models for compressible flow. An accurate and reliable estimate of discretization error is useful in obtaining a more accurate defect corrected solution, as well as a tight uncertainty bound as error bars. The error estimation procedure is performed by solving an auxiliary problem, known as the error transport equation (ETE), solved on the same mesh as the original model equations. Unlike unsteady adjoint methods for error in functionals, the ETE requires only one other set of equations to be solved, agnostic to the choice and number of output functionals, including common aerodynamic quantities such as lift or drag. Furthermore, co-advancing the ETE in time only requires the storage of local solutions in time and not the entire history, reducing memory requirements. This method of error estimation is performed in the context of higher order finite-volume methods on unstructured meshes. Approaches based on solving the ETE can be found in the literature for uniform or smooth meshes, but this has not been well studied for unstructured meshes. Such meshes necessarily have nonsmooth geometric features, which create many difficulties in accurate error estimation. These difficulties in accurate discretizations of the ETE are investigated, including the discretization of the ETE source term, which is critical to error estimate accuracy. It was found that the proposed schemes by the ETE approach can be more efficient and robust compared to solving the higher order problem. The choices of discretization schemes need to be made carefully, and these results demonstrate how it is possible, along with justification, to obtain asymptotically accurate, efficient, and robust error estimates that can be used with vast possibilities of model equations in practice.

View record

An Adaptive Higher-Order Unstructured Finite Volume Solver for Turbulent Compressible Flows (2017)

The design of aircraft depends increasingly on the use of Computational Fluid Dynamics (CFD) in which numerical methods are employed to obtain approximate solutions for fluid flows. One route to improve the numerical accuracy of CFD simulations is higher-order discretization methods. Moreover, finite volume discretizations are the method of choice in commercial CFD solvers and also in computational aerodynamics because of intrinsic conservative and shock-capturing properties. Considering that nearly all practical flows with aerodynamic applications are classified as turbulent, we develop a higher-order finite volume solver for the Reynolds Averaged Navier-Stokes (RANS) solution of turbulent compressible flows on unstructured meshes. Higher-order flow solvers must account for boundary curvature. Since turbulent flow simulations require anisotropic cells in shear layers, we use an elasticity analogy to project the boundary curvature into the interior faces and prevent faces from intersecting near curved boundaries. Furthermore, we improve the accuracy of solution reconstruction and output quantities on highly anisotropic cells with curvature using a local curvilinear coordinate system. A robust turbulence model for higher-order discretizations is fully coupled to the system of RANS equations and an efficient solution strategy is adopted for the convergence to the steady-state solution. We present our higher-order results for simple and complicated configurations in two dimensions. These results are verified by comparison against well-established numerical and experimental values in the literature. Our results show the advantages of higher-order methods in obtaining a more accurate solution with fewer degrees of freedom and also fast and efficient convergence to the steady-state solutions. Moreover, we propose an hp-adaptation algorithm for the unstructured finite volume solver based on residual-based and adjoint-based error indicators. In this approach, we enhance the local accuracy of the discretization via h-refinement or p-enrichment based on the smoothness of the solution. Mesh refinement is carried out by local cell division and introducing non-conforming interfaces in the mesh while order enrichment is obtained by local increase of the polynomial order in the reconstruction process. Our results show that this strategy leads to accuracy and efficiencyimprovements for several types of compressible flow problems.

View record

Error Estimation and Mesh Adaptation Paradigm for Unstructured Mesh Finite Volume Methods (2017)

Error quantification for industrial CFD requires a new paradigm in which a robust flow solver with error quantification capabilities reliably produces solutions with known error bounds. Error quantification hinges on the ability to accurately estimate and efficiently exploit the local truncation error. The goal of this thesis is to develop a reliable truncation error estimator for finite-volume schemes and to use this truncation error estimate to improve flow solutions through defect correction, to correct the output functional, and to adapt the mesh. We use a higher-order flux integral based on lower order solution as an estimation of the truncation error which includes the leading term in the truncation error. Our results show that using this original truncation error estimate is dominated by rough modes and fails to provide the desired convergence for the applications of defect correction, output error estimation and mesh adaptation. So, we tried to obtain an estimate of the truncation error based on the continuous interpolated solution to improve their performance. Two different methods for interpolating were proposed: CGM's 3D surfaces and C¹ interpolation of the solution. We compared the effectiveness of these two interpolating schemes for defect correction and using C¹ interpolation of the solution for interpolating is more helpful compared to CGM, so we continued using C¹ interpolation for other purposes. For defect correction, although using the modified truncation error does not improve the order of accuracy, significant quantitative improvements are obtained. Output functional correction is based on the truncation error and the adjoint solution. Both discrete and continuous adjoint solutions can be used for functional correction. Our results for a variety of governing equations suggest that the interpolating scheme can improve the correction process significantly and improve accuracy asymptotically. Different adaptation indicators were considered for mesh adaptation and our results show that the estimate of the truncation error based on the interpolated solution is a more accurate indicator compared to the original truncation error. Adjoint-based mesh adaptation combined with modified truncation error provides even faster convergence of the output functional.

View record

Aerodynamic optimization using high-order finite-volume CFD simulations (2011)

The growth of computer power and storage capacity allowed engineers to tackle engineering design as an optimization problem. For transport aircraft, drag minimization is critical to increase range and reduce operating costs. Lift and geometric constraints are added to the optimization problem to meet payload and rigidity constraints of the aircraft. Higher order methods in CFD simulations have proved to be a valuable tool and are expected to replace current second order CFD methods in the near future; therefore, exploring the use of higher order CFD methods in aerodynamic optimization is of great research interest and is one goal of this thesis.Gradient-based optimization techniques are well known for fast convergence, but they are only local minimizers; therefore their results depend on the starting point in the design space. The gradient-independent optimization techniques can find the global minimum of an objective function but require vast computational effort; therefore, for global optimization with reasonable computational cost, a hybrid optimization strategy is needed.A new least-squares based geometry parametrization is used to describe airfoil shapes and a semi-torsional spring analogy mesh morphing tool updates the grid everywhere when the airfoil geometry changes during shape optimization.For the gradient based optimization scheme, both second and fourth order simulations have been used to compute the objective function; the adjoint approach, well known for its low computational cost, has been used for gradient computation and matches well with finite difference gradient. The gradient based optimizer have been tested for subsonic and transonic inverse design problems and for drag minimization without and with lift constraint to validate the developed optimizer. The optimization scheme used is Sequential Quadratic Programming (SQP) with the BFGS approximation of the Hessian matrix. A mesh refinement study is presented for an aerodynamically constrained drag minimization problem to show how second and fourth order optimal results behave with mesh refinement.A hybrid particle swarm / BFGS scheme has been developed for use as a global optimizer. It has been tested on a drag minimization problem with lift constraint; the hybrid scheme obtained a shock free profiles, while gradient-based optimization could not in general.

View record

Delaunay refinement mesh generation of curve-bounded domains (2009)

Delaunay refinement is a mesh generation paradigm noted for offering theoretical guarantees regarding the quality of its output. As such, the meshes it produces are a good choice for numerical methods. This thesis studies the practical application of Delaunay refinement mesh generation to geometric domains whose boundaries are curved, in both two and three dimensions. It is subdivided into three manuscripts, each of them addressing a specific problem or a previous limitation of the method. The first manuscript is concerned with the problem in two dimensions. It proposes a technique to sample the boundary with the objective of improving its recoverability. The treatment of small input angles is also improved. The quality guarantees offered by previous algorithms are shown to apply in the presence of curves. The second manuscript presents an algorithm to construct constrained Delaunay tetrahedralizations of domains bounded by piecewise smooth surfaces. The boundary conforming meshes thus obtained are typically coarser than those output by other algorithms. These meshes are a perfect starting point for the experimental study presented in the final manuscript. Therein, Delaunay refinement is shown to eliminate slivers when run using non-standard quality measures, albeit without termination guarantees. The combined results of the last two manuscripts are a major stepping stone towards combining Delaunay refinement mesh generation with CAD modelers. Some algorithms presented in this thesis have already found application in high-order finite-volume methods. These algorithms have the potential to dramatically reduce the computational time needed for numerical simulations.

View record

Efficient high-order accurate unstructured finite-volume algorithms for viscous and inviscid compressible flows (2009)

High-order accurate methods have the potential to dramatically reduce the computational time needed for aerodynamics simulations. This thesis studies the discretization and efficient convergence to steady state of the high-order accurate finite-volume method applied to the simplified problem of inviscid and laminar viscous two-dimensional flow equations. Each of the three manuscript chapters addresses a specific problem or limitation previously experienced with these schemes. The first manuscript addresses the absence of a method to maintain monotonicity of the solution at discontinuities while maintaining high-order accuracy in smooth regions. To resolve this, a slope limiter is carefully developed which meets these requirements while also maintaining the good convergence properties and computational efficiency of the least-squares reconstruction scheme. The second manuscript addresses the relatively poor convergence properties of Newton-GMRES methods applied to high-order accurate schemes. The globalization of the Newton method is improved through the use of an adaptive local timestep and of a line search algorithm. The poor convergence of the linear solver is improved through the efficient assembly of the exact flux Jacobian for use in preconditioning and to eliminate the additional residual evaluations needed by a matrix-free method. The third manuscript extends the discretization method to the viscous fluxes and boundary conditions. The discretization is demonstrated to achieve the expected order of accuracy. The fourth-order scheme is also shown to be more computationally efficient than the second-order scheme at achieving grid-converged values of drag for two-dimensional laminar flow over an airfoil.

View record

Master's Student Supervision

Theses completed in 2010 or later are listed below. Please note that there is a 6-12 month delay to add the latest theses.

Convergence acceleration of flow solvers using modal decomposition schemes (2023)

Convergence acceleration is a crucial tool for enhancing the efficiency and accuracy of numerical algorithms. Although many numerical flow solvers yield accurate solutions, they may take a long time to converge to the desired tolerance. To address this issue, this thesis proposes a convergence acceleration scheme that employs dynamic mode decomposition (DMD) to generate an over-relaxation update for flow solvers. The DMD analysis identifies the dominant solution modes causing the slow convergence of the flow solver and relaxes them towards their steady-state by extrapolating these modes to infinity and constructing a linear combination of extrapolated sums.The thesis also proposes an automation framework that leverages a machine learning pipeline to automate the application of this DMD acceleration scheme. The pipeline evaluates the DMD-generated over-relaxation updates and assesses whether they will result in convergence acceleration or not, thus ensuring a more robust convergence acceleration framework.We demonstrate that our technique accelerates the convergence of finite-volume computations and that it can achieve instantaneous convergence for linear problems and two to five orders of magnitude reduction in residual for laminar and turbulent problems. Also we show that the automation framework can successfully automate this process and eliminate the need for any input or control of the algorithm. We also demonstrate that the automation framework can apply this technique without any user intervention.The proposed convergence acceleration framework is entirely data-driven and can be integrated into a flow solver as a module which only needs a few solution updates as its input. This scheme is particularly useful for researchers who are satisfied with their flow solver's performance but seek to accelerate it without altering their code implementation by adopting more complex time-advance schemes and time stepping methods.

View record

Detecting missing flow separation and predicting error in drag using supervised machine learning (2022)

Accuracy of flow simulations is a major concern in Computational Fluid Dynamics (CFD) applications. A possible outcome of inaccuracy in CFD results is missing a major feature in the flow field. Many methods have been proposed to reduce numerical errors and increase overall accuracy, but these are not always efficient or even feasible. In this study, a purely data-driven approach is proposed to assess flow simulations both in a qualitative and a quantitative manner. In this regard, Principal Component Analysis (PCA) has been performed on compressible flow simulations around an airfoil to map the high-dimensional CFD data to a lower-dimensional PCA subspace. A machine learning classifier based on the extracted principal components has been developed to detect the simulations that miss the separation bubble behind the airfoil. The evaluative measures indicate that the model is able to detect most of the simulations where the separation region is poorly resolved. Besides the classifier, a machine learning regressor has been trained on the same PCA subspace to predict the error in the output drag coefficient. The predictions reveal that the regression model estimates accurate errors with a tight uncertainty bound. Further, more efficient models built on top of fewer PCA modes have been implemented that show similar performance. In addition, the developed models were used to inspect simulations solved on a different mesh configuration from the one the models were trained on. This generalization framework gives rise to some challenges that are thoroughly discussed. Overall, the results demonstrate that machine learning models based on the principal components of the data set are promising tools to detect possible missing flow features and predict numerical errors in CFD.

View record

Anisotropic advancing layer mesh generation (2021)

The use of computational fluid dynamics (CFD) is now a ubiquitous part of of the engineering design process, especially in aerodynamic applications. The CFD process requires a high-quality volume mesh on which to perform the simulation. However, mesh generation is typically a choke point for the process, and is often the most time-consuming step. This emphasizes the need for robust, automatic mesh generation tools that can reliably produce high-quality meshes. Advancing layer (AL) meshing is one method of mesh generation in which mesh elements are extruded off of the surface mesh one layer at a time. AL meshes are preferred for their unmatched cell alignment, orthogonality, and fraction of prismatic elements. However, two limitations of a standard AL scheme are the handling of complex corners and highly anisotropic surface meshes. This thesis, first, presents a solution to the problem of complex corners, where extruding a single vertex is inadequate. The solution presented is a robust method that essentially modifies the surface mesh by extruding in multiple directions at the corner, then creating adjacent cells, and filling holes. From here it is possible to extrude the mesh as usual. Second, an extension of the AL method is presented which enables extrusion from highly anisotropic surface meshes. Anisotropy is characterized by the use of highly stretched cells in specific areas where the flow physics produce large gradients in one direction but not in one or both of the others, a wing for example. Anisotropic cells allow for the desired mesh resolution but at a fraction of the cell count. The method presented extrudes layers while maintaining the anisotropic pseudo-structure and aspect ratio of the surface mesh and allows for a smooth transition back to regular isotropic extrusion. It is accomplished by exploiting the anisotropic pseudo-structure to decimate entire lines of vertices at once and adjusting the smoothing algorithm to maintain distance ratios between neighbouring vertices. This method demonstrates AL's ability to produce high-quality anisotropic meshes, opening a wide array of meshing possibilities.

View record

Entire domain advancing layer surface mesh (EDAMSurf) generation (2020)

The use of unstructured meshes in the simulation of a computational field to solve a real world problem is ubiquitous. To resolve the flow near viscous boundaries of a geometry, we need to have good resolution in thin shear layers close to the surface. Having a structured mesh along the boundary is an option. However, we lose the ability to tackle arbitrary geometries that way. Hence, we develop techniques to get a nearly-structured mesh near the boundary where it's needed while retaining topological flexibility by being unstructured.A plethora of 3D boundary layer mesh generation techniques start off from a discretization of the surface. A majority of these techniques either use surface inflation or iterative point placement normal to the surface to generate the advancing layer 3D mesh. Generating good boundary layer meshes in 3D depends on the quality of the underlying surface discretization. We introduce a technique to generate advancing layer surface meshes, which will provide a better starting point for 3D anisotropic mesh generation. The technique takes an input triangulation of the surface, which is fairly easy to get, even for complex geometries. Surface segments are identified and these segments are meshed independently using an advancing-layer methodology. For each surface segment, a mesh is generated by advancing layers from the identified boundaries to the surface interior while deforming the existing triangulation. As the mesh generation technique introduced here is a closed advancing layer method, we have a valid surface mesh throughout the meshing process.The method introduced to generate advancing layer meshes produces semi-structured quad-dominant meshes with the ability to have local control over the aspect ratio of mesh elements at the boundary curves of the surface. Semi-structured 2D anisotropic meshes in the boundary layer regions have been shown to have superior fluid flow simulation results. Point placement in layers, local reconnection, front recovery, front collision handling and smoothing techniques used in the study help produce a valid surface mesh at each step of mesh generation. We demonstrate the ability of the meshing algorithm to tackle fairly complex geometries and coarse initial surface discretization.

View record

A higher-order unstructured finite volume solver for three-dimensional compressible flows (2017)

High-order accurate numerical discretization methods are attractive for their potential to significantly reduce the computational costs compared to the traditional second-order methods. Among the various unstructured higher-order discretization schemes, the k-exact reconstruction finite volume method is of interest for its straightforward mathematical formulation, and its compatibility with the current lower-order industrial solvers. However, current three-dimensional finite volume solvers are limited to the solution of inviscid and laminar viscous flow problems. Since three-dimensional turbulent flows appear in many industrial applications, the current thesis takes the first step towards the development of a three-dimensional higher-order finite volume solver for the solution of both inviscid and viscous turbulent steady-state flow problems. The k-exact finite volume formulation of the governing equations is rederived in a dimension-independent manner, where the negative Spalart-Allmaras turbulence model is employed. This one-equation model is reasonably accurate for many flow conditions, and its simplicity makes it a good starting point for the development of numerical algorithms. Then, the three-dimensional mesh preprocessing steps for a finite volume simulation are presented, including higher-order accurate numerical quadrature, and capturing the boundary curvature in highly anisotropic meshes. Also, the issues of k-exact reconstruction in handling highly anisotropic meshes are reviewed and addressed. Since three-dimensional problems can require much more memory than their two-dimensional counter-parts, solution methods that work in two dimensions might not be feasible in three dimensions anymore. As an attempt to overcome this issue, a practical and parallel scalable method for the solution of the discretized system of nonlinear equations is presented. Finally, the solution of four three-dimensional test problems are studied: Poisson’s equation in a cubic domain, inviscid flow over a sphere, turbulent flow over a flat plate, and turbulent flow over an extruded NACA 0012 airfoil. The solution is verified, and the resource consumption of the flow solver is measured. The results demonstrate the benefit and practicality of using higher-order methods for obtaining a certain level of accuracy.

View record

Mesh adaptation for wakes via surface insertion (2019)

In this thesis, we present a new procedure for mesh adaptation for wakes. The approachstarts by tracking the wake centerline with an initial isotropic unstructured mesh. A vertex-centered finite volume method is used, and the velocity field is obtained from solution reconstruction. The velocity data is integrated numerically using an adaptive fourth-orderRunge-Kutta method. We insert the wake centerline into the existing unstructured meshas an internal boundary and use a metric-based anisotropic mesh adaptation to generateanisotropic cells in regions with large second derivatives of flow variables. In the secondstep, the problem is solved on adapted mesh and a new wake centerline is tracked. Wethen move the previous wake centerline (which is now a part of adapted mesh) to matchthe centerline obtained from the adapted mesh. To move the wake centerline, a solid mechanics analogy is used and the linear elasticity equation is solved on the adapted mesh.As a result, the displacement is propagated throughout the mesh and the already adaptedregions along the wake centerline are preserved. The process is then followed for subsequentcycles of anisotropic mesh adaptation to obtain a more accurate approximation of the wakecenterline. As an alternate strategy for obtaining an anisotropic mesh in the wake, we take the first geometry, together with the captured wake centerline from an unstructured triangular mesh,as an initial geometry to produce a quad dominant mesh, using an advancing layer method. The correctness of the streamline tracking algorithm is verified using an analytical velocity field. The mesh morphing approach is tested using the method of manufactured solutions,demonstrating that the linear finite element solution is second-order accurate. The resultsof laminar flow test cases for the attached and separated flow are presented and compared with some well-established numerical results in the literature. Our results show that the advancing layer mesh is more efficient in resolving the wake. In the end, one case for turbulentsubsonic flow is considered. For turbulent flow, a cell-centered finite volume method is usedand we only track the wake centerline at different angles of attack.

View record

A higher-order unstructured finite volume solver for three-dimensional compressible flows (2017)

High-order accurate numerical discretization methods are attractive for their potential to significantly reduce the computational costs compared to the traditional second-order methods. Among the various unstructured higher-order discretization schemes, the k-exact reconstruction finite volume method is of interest for its straightforward mathematical formulation, and its compatibility with the current lower-order industrial solvers. However, current three-dimensional finite volume solvers are limited to the solution of inviscid and laminar viscous flow problems. Since three-dimensional turbulent flows appear in many industrial applications, the current thesis takes the first step towards the development of a three-dimensional higher-order finite volume solver for the solution of both inviscid and viscous turbulent steady-state flow problems. The k-exact finite volume formulation of the governing equations is rederived in a dimension-independent manner, where the negative Spalart-Allmaras turbulence model is employed. This one-equation model is reasonably accurate for many flow conditions, and its simplicity makes it a good starting point for the development of numerical algorithms. Then, the three-dimensional mesh preprocessing steps for a finite volume simulation are presented, including higher-order accurate numerical quadrature, and capturing the boundary curvature in highly anisotropic meshes. Also, the issues of k-exact reconstruction in handling highly anisotropic meshes are reviewed and addressed. Since three-dimensional problems can require much more memory than their two-dimensional counter-parts, solution methods that work in two dimensions might not be feasible in three dimensions anymore. As an attempt to overcome this issue, a practical and parallel scalable method for the solution of the discretized system of nonlinear equations is presented. Finally, the solution of four three-dimensional test problems are studied: Poisson’s equation in a cubic domain, inviscid flow over a sphere, turbulent flow over a flat plate, and turbulent flow over an extruded NACA 0012 airfoil. The solution is verified, and the resource consumption of the flow solver is measured. The results demonstrate the benefit and practicality of using higher-order methods for obtaining a certain level of accuracy.

View record

The impact of mesh regularity on errors (2017)

Mesh quality plays an important role in improving the accuracy of the numerical simulation. There are different quality metrics for specific numerical cases. A regular mesh consisting of the equilateral triangles is one of them and is expected to improve the error performance. In this study, Engwirda’s frontal-Delaunay scheme and Marcum’s advancing front local reconnection scheme are described along with the conventional Delaunay triangulation. They are shown to improve the mesh regularity effectively. Even though several numerical test cases show that more regular meshes barely improve the error performance, the time cost in the solver of regular meshes is smaller than the Delaunay mesh. The time cost decrease in the solver pays off the additional cost in the mesh generation stage. For simple test cases, more regular meshes obtain lower errors than conventional Delaunay meshes with similar time costs. For more complicated cases, the improvement in errors is small but regular meshes can save time, especially for a high order solver. Generally speaking, a regular mesh does not improve the error performance as much as we expect, but it is worth generating.

View record

Adaptive Creation of Orthogonal Anisotropic Triangular Meshes Using Target Matrices (2016)

We present a new procedure to adaptively produce anisotropic metric-orthogonal meshes in this thesis. The approach is based on mesh optimization techniques: point insertion designed to improve mesh alignment as well as conforming to a metric, swapping in the metric space, point movement defined by target elements from a metric, and point deletion based on quality and metric length. These techniques are intended to produce quasi-structured meshes which have the advantages of flexibility for complex geometries of unstructured meshes and the directional accuracy of structured meshes. The result is reliable alignment for anisotropic meshes reducing our previous work's reliance on smoothing for good alignment. The methodology is implemented in 2D and extended to 3D. Examples of analytical metrics and error estimation metrics on a numerical simulation of a flow are shown.

View record

Improving Finite-Volume Diffusive Fluxes Through Better Reconstruction (2016)

The overarching goal of CFD is to compute solutions with low numerical error. For finite-volume schemes, this error originates as error in the flux integral. For diffusion problems on unstructured meshes, the diffusive flux (computed from reconstructed gradients) is one order less accurate than the reconstructed solution. Worse, the gradient errors are not smooth, and so no error cancellation accompanies the flux integration, reducing the flux integral to zero order for second-order schemes. Our aim is to compute the gradient and flux more accurately at the cell boundaries and hence obtain a better flux integral for a slight increase in computational cost. We propose a novel reconstruction method and flux discretization to improve diffusive flux accuracy on cell-centred, isotropic unstructured meshes. Our approach uses a modified least-squares system to reconstruct the solution to second-order accuracy in the H₁ norm instead of the prevalent L₂ norm, thus ensuring second-order accurate gradients. Either circumcentres or containment centres are chosen as the control-volume reference points based on a criteria to facilitate calculation of second-order gradients at flux quadrature points using a linear interpolation scheme along with a high-accuracy jump term to enhance stability of the system. Numerical results show a significant improvement in the order of accuracy of the computed diffusive flux as well as the flux integral. When applied to a channel flow advection-diffusion problem, the scheme resulted in an increased order of accuracy for the flux integral along with gains in solution accuracy by a factor of two. The characteristics of the new scheme were studied through stability, truncation error and cost analysis. The increase in computational costs were modest and affordable. The behaviour of the scheme was also tested by implementing a variation of it within the ANSYS Fluent discretization framework.

View record

Stability Analysis and Stabilization of Unstructured Finite Volume Method (2016)

In this thesis, we develop a stability analysis model for the unstructured finite volume method. This model employs the matrix method to implement stability analysis. For the full discretization, where the temporal discretization employs backward Euler time-stepping, a linearization is used to construct the model. Both for the full discretization and semi-discretization, the stability condition is expressed in terms of eigenvalues. The validity of the stability analysis model is verified for linear cases and nonlinear cases. The analysis in this thesis also explains the phenomena that the defined energy can locally increase in the energy stability analysis method. This model can be applied to both linear problems and nonlinear problems; in this thesis, we focus on the 2D Euler equations. We also develop a stabilization methodology. This methodology is aimed at optimizing the eigenvalues of the Jacobian matrix by changing the coordinates of interior vertices of a mesh. Specifically, for an unstable spatial discretization, we can shift the unstable eigenvalues into stability region by changing the mesh. The stabilization methodology is verified by numerical cases as well. The success of this stabilization relies on a developed method to change the eigenvalues of a matrix in a quantitative and controllable way. This method is a general approach to optimize the eigenvalues of a matrix, which means it can be applied to other systems as well.

View record

Thread-Parallel Mesh Generation and Improvement Using Face-Edge Swapping and Vertex Insertion (2015)

The purpose of this thesis is three-fold. First, we devise a memory model for unstructured mesh data for efficient use of memory on parallel shared memory architectures with the purpose of lowering the synchronization overhead between threads and also excluding the probability of occurring race conditions. Second, we present a new thread-parallel edge and face swapping algorithm for two and three dimensional meshes using OpenMP for shared memory architectures. We show how removing the conflicts from the reconfiguration procedure by applying a vertex locking strategy can result in a near linear speed-up with parallel efficiency of close to one on two threads and 70% with sixteen threads on shared-memory processors. Finally, we derive a parallel mesh generation and refinement module for shared memory architectures based on pre-existing serial modules — GRUMMP — by implementing Chernikov and Chrisochoides’ parallel insertion algorithm along with the two above tools. Experiments show a worst case parallel efficiency of 60% for parallel refinement with 16 threads.

View record

Truncation Error Analysis for Diffusion Schemes in Boundary Regions of Unstructured Meshes (2015)

Accuracy of numerical solution is of paramount importance for any CFD simulation. The error in satisfying the continuous partial differential equations by their discrete form results in truncation error and it has a direct influence on discretization errors. Discretization error, which is the difference in the numerical solution and the exact solution to a CFD problem, is generally the largest source of numerical errors. Understanding the relationship between the discretization and truncation error is crucial for reducing numerical errors. Studies have been carried out to understand the truncation-discretization error relationship in the interior regions of a computational domain but fewer for the boundary regions. The effect of different solution reconstruction methods, face gradient averaging schemes and boundary condition implementation methods on boundary truncation error in specific and overall truncation and solution error are the subject of research for this thesis. To achieve the goals laid out, the error has to be quantified first and then tests performed to compare the schemes. The Poisson's equation is chosen as the model diffusion equation. The truncation error coefficients, analogous to the analytical coefficients of the spatial derivatives in Taylor series expansion of truncation error, are quantified using error metrics. The solution error calculation is made possible by a careful selection of exact solutions and their appropriate source terms for Poisson's equation. Analytic tests are performed on a family of topologically regular meshes to test and verify the theoretical implementation of different schemes and to eliminate schemes performing poorly from consideration for numerical tests. The numerical tests are performed on unstructured triangular, mixed and pure quad meshes to extend the accuracy assessment for general meshes. The results obtained from both the tests are utilized to arrive at schemes where the overall truncation error and discretization error can be minimized simultaneously.

View record

Anisotropic Mesh Adaptation: Recovering Quasi-Structured Meshes (2013)

An adaptive method for producing anisotropic quasi-structured meshes is presented in this thesis. Current anisotropic adaptation schemes produce meshes without any regular structure which can hurt accuracy and efficiency of the solution. By modifying the anisotropic adaptation schemes, producing aligned, quasi-structured meshes is possible which means that the accuracy and efficiency of the flow solution are improved. By using quasi-structured meshes, we can get the advantages of flexibility of unstructured meshes for complex geometries and accuracy of the high directional qualities of the structured meshes at the same time. The construction of the quasi-structured meshes from initial isotropic unstructured meshes is accomplished by assigning metrics to vertices based on the error estimation methods. The metrics are used to communicate the desired anisotropy to the meshing program. After assigning a metric to each vertex, the mesh is refined anisotropically using four mesh quality improvements operations to produce high quality anisotropic quasi-structured meshes: swapping to choose the diagonal of the quadrilateral formed by two neighboring triangles which results the maximum quality, inserting vertices for large triangles, vertex removal to eliminate small edges and vertex movements to optimize the location of the vertices so that quasi-structured meshes are created. The idea in the optimization process is to smooth a vertex location by seeking so that the final mesh contains target elements dictated by the metrics assigned in the three vertices of that triangle. The final, high quality mesh is produced by using these operations iteratively based on the metrics assigned to each vertex in an adaptive, solution-based process.

View record

Truncation Error Analysis of Unstructured Finite Volume Discretization Schemes (2012)

Numerical experiments have proved that numerical errors are at least as large as other sources of error in numerical simulation of fluid flows. Approximating the continuous partial differential equations that govern the behavior of a fluid with discrete relations results in truncation error which is the initial source of numerical errors. Reducing numerical error requires the ability to quantify and reduce the truncation error. Although the truncation error can be easily found for structured mesh discretizations, there is no generic methodology for the truncation error analysis of unstructured finite volume discretizations. In this research, we present novel techniques for the analysis and quantification of the truncation error produced by finite volume discretization on unstructured meshes. These techniques are applied to compare the truncation error produced by different discretization schemes commonly used in cell-centered finite volume solvers. This comparison is carried out forfundamental scalar equations that model the fluid dynamic equations. These equations model both the diffusive and convective fluxes which appear in the finite volume formulation of the fluid flow equations. Two classes of tests are considered for accuracy assessment. Analytical tests on topologically perfect meshes are done to find the general form of the truncation error. Moreover, these tests allow us to eliminate from consideration thoseschemes that do not perform well even for slightly perturbed meshes. Given the results of the analytic tests, we define a truncation error metric based on the coefficients associated with the spatial derivatives in the series expansion of the truncation error. More complexnumerical tests are conducted on the remaining schemes to extend the accuracy assessment to general unstructured meshes consisting of both isotropic and anisotropic triangles. These results will guide us in the choice of appropriate discretization schemes for diffusive andconvective fluxes arising from discretization of real governing equations.

View record

Effects of cold wall quenching on unburned hydrocarbon emissions from a natural gas HPDI engine (2011)

The quenching of hydrocarbon flames on cold surfaces is considered to be a potential source of unburned hydrocarbon (UHC) emissions from internal combustion engines, but its contribution to emissions has been difficult to determine due to the strong coupling between physics, chemistry and flame/wall geometry. This is particularly problematic for high pressure direct injection (HPDI) engines where high pressures, inhomogeneous mixtures and complex piston geometry are present.In this work, a computational model is implemented to determine the distance at which hydrocarbon flames quench on cold walls during numerical simulation. This model accounts for variable pressure, temperature, gas mixture and the geometry conditions. The model presented in this work is an extension of the experimental work done by Boust et. al. with stoichiometric premixed flames at low pressures. The validation of this model for high pressure and diffusion flames is presented and shows that the correct trends in heat flux and order of magnitude of quench distance are observed. This model is further refined for engine simulation and enhanced by a two-zone mass diffusion model to account for post-quench oxidation of boundary fuel.A selection of engine cases are simulated for a variety of different conditions to determine the spatial distribution and temporal evolution of unburned fuel cold surfaces. It was found that wall quenching on the piston contributes up to 50% of the total UHC during the combustion cycle, the majority of which is oxidized during the expansion stroke; the final contribution is at most 10% but frequently near or less than 1%. As the injection pressure was increased, quenching on the piston surface became more extensive, through the quenching thickness itself decreased. UHC from wall quenching occurs more readily for higher load conditions due to the richer mixtures and incomplete mixing. Altered engine timing introduced coupled effects of changed flame/wall interaction and combustion characteristics. The data obtained from the model can be used to evaluate attempts to reduce UHC by changing combustion chamber geometry.

View record


Current Students & Alumni

This is a small sample of students and/or alumni that have been supervised by this researcher. It is not meant as a comprehensive list.

If this is your researcher profile you can log in to the Faculty & Staff portal to update your details and provide recruitment preferences.


Get key application advice, hear about the latest research opportunities and keep up with the latest news from UBC's graduate programs.