Carl Ollivier-Gooch

Professor

B.A. Russian, B.S.M.E. (Rice); M.S., Ph.D. (Stanford); Member ASME, Senior Member AIAA, Member Canadian CFD Society

Research Interests

Algorithm development for computational aerodynamics.

Current Projects

Developing high-order accurate methods for compressible, turbulent flows, with applications in aerodynamics and aerodynamic optimization. Anisotropic unstructured mesh adaptation and generation in parallel. Developing methods to assess and control numerical error in CFD simulations.

Current Research Work

• Computational Aerodynamics: Dr. Ollivier-Gooch’s research group specializes in developing techniques for numerical solution of problems in aerodynamic. In particular, we are working to take advantage of both the geometric flexibility of unstructured mesh methods and the accuracy benefits of high-order methods. Recent work has exploited Newton-GMRES techniques to develop extremely efficient, high-order accurate methods for inviscid compressible aerodynamics problems, including showing that high-order methods can achieve solutions of engineering accuracy more quickly than second-order methods. Current work is focused on extending these results to turbulent viscous flows and on developing high-order accurate optimization techniques.
• Unstructured Mesh Generation: Hand-in-hand with research in unstructured mesh flow solvers, Dr. Ollivier-Goochs group also studies unstructured mesh generation, which is the process of decomposing a domain into triangular or tetrahedral cells. Past work has included development of highly successful techniques for unstructured mesh improvement; and extension of meshing techniques with known mesh quality guarantees to allow better control of cell size in both two and three dimensions and to work with curved boundary data in two and three dimensions. Ongoing work includes generation and refinement of anisotropic meshes (especially for high Reynolds number viscous flows). Dr. Ollivier-Gooch and his group have written and maintain a software library for unstructured mesh generation. This software has been freely available for non-profit use on the WWW since January 1998, and is now in its tenth version. The software has been downloaded by over 6000 users in 62 countries. Applications vary from fluid and solid mechanics to cancer research and microbiology to simulation of star and planet formation.
• Error Assessment and Control for Unstructured Mesh Methods: The ultimate goal of CFD simulations is to provide an answer that is not just acurate, but which has known error bounds.  Assessment of error in output quantities like lift and drag is well established for finite element methods, but these methods are less commonly used for finite volume methods, perhaps because of the poor behavior of some measures of error.  Dr. Ollivier-Gooch’s group is working to improve understanding of error for unstructured mesh finite volume methods and to exploit that understanding to provide good error bounds on output quantities. At the same time, we are working to identify mesh features that are particularly harmful for accuracy and use that knowledge to generate better meshes.
• Stability and Convergence for Unstructured-Mesh Finite-Volume Methods: Fairly often, an aerodynamics simulation doesn’t converge properly to steady-state, even though the physical flow should be steady. Sometimes, this takes the form of the solution “blowing up” — growing without bounds in ways that are clearly unphysical.  Other times, the solution does eventually reach steady state, but does this very slowly. Dr. Ollivier-Gooch’s research group is working to address both of these problems, using a combination of modal analysis, machine learning, and mesh improvement techniques.

Selected Publications

• M. Zandsalimy and C. Ollivier-Gooch. A Novel Approach to Mesh Optimization to Stabilize Unstructured Finite Volume Simulations. Journal of Computational Physics, v 453, March, 2022. doi:10.1016/j.jcp.2022.110959
• Z. Xiao, C. Ollivier-Gooch and J. D. Zuniga-Vazquez. Anisotropic tetrahedral mesh adaptation with improved metric alignment and orthogonality. Computer Aided Design, v 143, February, 2022. doi:10.1016/j.cad.2021.103136
• Z. Xiao and C. Ollivier-Gooch. Smooth Gradation of Anisotropic Meshes Using Log-Euclidean Metrics. AIAA Journal, v 59 (10), October, 2021. doi:10.2514/1.J059864
• S. Hoshyari, E. Mirzaee, and C. Ollivier-Gooch. Efficient Steady-State Convergence for a Higher-Order Unstructured Finite Volume Solver for Compressible Flows. AIAA Journal, v 58 (4), pp 1490-1505, April, 2020. doi:10.2514/1.J058537
• R. Zangeneh and C. Ollivier-Gooch. Boundary Condition Optimization to Improve the Stability of Finite-Volume Methods on Unstructured Meshes. Computers and Fluids, v 199, March, 2020. doi:10.1016/j.compfluid.2019.104418
• W. Tyson, G. Yan, C. Roy, and C. Ollivier-Gooch. Relinearization of the Error Transport Equations for Arbitrarily High-Order Error Estimates. Journal of Computational Physics, v 397, November, 2019. doi:10.1016/j.jcp.2019.108867
• R. Zangeneh and C. Ollivier-Gooch. Stability Analysis and Improvement of the Solution Reconstruction for Cell-Centered Finite Volume Methods on Unstructured Meshes. Journal of Computational Physics, v 393(15), pp 375-405, September, 2019. doi:10.1016/j.jcp.2019.05.002
• G. Yan and C. Ollivier-Gooch. Applications of the Unsteady Error Transport Equation on Unstructured Meshes. American Institute for Aeronautics and Astronautics Journal, v 56(11), pp 4463-4473, November, 2018. doi:10.2514/1.J057024
• M. Sharbatdar and C. Ollivier-Gooch. Adjoint-Based Functional Correction for Unstructured Mesh Finite Volume Methods. Journal of Scientific Computing, v 76(1), pp 1-23, July, 2018. doi:10.1007/s10915-017-0611-8
• M. Sharbatdar and C. Ollivier-Gooch. Mesh Adaptation using C^{1} Interpolation of the Solution in an Unstructured Finite Volume Solver. International Journal for Numerical Methods in Fluids, v 86(10), pp 637-654, April, 2018. doi:10.1002/fld.4471
• R. Zangeneh and C. Ollivier-Gooch. Thread-Parallel Mesh Improvement using Face and Edge Swapping and Vertex Insertion. Computational Geometry: Theory and Applications, v 70, pp 31-48, February, 2018. doi:10.1016/j.comgeo.2018.01.006
• A. Jalali and C. Ollivier-Gooch. An hp-Adaptive Unstructured Finite Volume Solver for Compressible Flows. International Journal for Numerical Methods in Fluids, v 85(10), pp 563-582, December 2017. doi:10.1002/fld.4396
• G. Yan and C. Ollivier-Gooch. On Efficiently Obtaining Higher-Order Discretization Error Estimates for Unstructured Finite-Volume Methods using the Error Transport Equation. ASME Journal of Verification, Validation and Uncertainty Quantification, v 2(4), December, 2017. doi:10.1115/1.4039188
• R. Zangeneh and C. Ollivier-Gooch. Mesh Optimization to Improve the Stability of Finite-Volume Methods on Unstructured Meshes. Computers and Fluids, v 156, pp 590-601, October, 2017. doi:10.1016/j.compfluid.2017.04.020
• G. Yan and C. Ollivier-Gooch. Towards Higher Order Discretization Error Estimation by Error Transport using Unstructured Finite-Volume Methods for Unsteady Problems. Computers and Fluids, v 154, pp 245-255, September, 2017. doi:10.1016/j.compfluid.2017.06.012
• A. Jalali and C. Ollivier-Gooch. Higher-order Unstructured Finite Volume RANS Solution of Turbulent Compressible Flows. Computers and Fluids, v 143, pp 32-47, January, 2017. doi:10.1016/j.compfluid.2016.11.004

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