We develop novel numerical methods and apply them to solve challenging fluid flow problems in various areas of science, engineering, and medicine. We are particularly interested in theoretical aspects of high-order numerical methods for unstructured grids, as well as their implementation for a range of modern hardware platforms.


'Towards Green Aviation with Python at Petascale' - Our simulations with PyFR on Piz Daint and Titan shortlisted for 2016 Gordon Bell Prize

'New Symmetric Quadrature Rules' - Checkout our latest paper on identification of symmetric quadrature rules for finite element methods

'Analysis of Tetrahedral Solution Points' - Checkout our latest paper on solution point placement for Flux Reconstrustion schemes on tetrahedra

'Lifelines' - Our image of blood flow patterns in an arterio-venous fistulae wins prestigious BHF Reflections of Research award


Recent Papers

On the Properties of Energy Stable Flux Reconstruction Schemes for Implicit Large Eddy Simulation. B. C. Vermeire, P. E. Vincent. Accepted for publication in Journal of Computational Physics.
Abstract: We begin by investigating the stability, order of accuracy, and dispersion and dissipation characteristics of the extended range of energy stable flux reconstruction (E-ESFR) schemes in the context of implicit large eddy simulation (ILES). We proceed to demonstrate that subsets of the E-ESFR schemes are more stable than collocation nodal discontinuous Galerkin methods recovered with the flux reconstruction approach (FRDG) for marginally-resolved ILES simulations of the Taylor-Green vortex. These schemes are shown to have reduced dissipation and dispersion errors relative to FRDG schemes of the same polynomial degree and, simultaneously, have increased Courant-Friedrichs-Lewy (CFL) limits. Finally, we simulate turbulent flow over an SD7003 aerofoil using two of the most stable E-ESFR schemes identified by the aforementioned Taylor-Green vortex experiments. Results demonstrate that subsets of E-ESFR schemes appear more stable than the commonly used FRDG method, have increased CFL limits, and are suitable for ILES of complex turbulent flows on unstructured grids.

On the Connections Between Discontinuous Galerkin and Flux Reconstruction Schemes: Extension to Curvilinear Meshes. G. Mengaldo, D. De Grazia, P. E. Vincent, S. J. Sherwin. Journal of Scientific Computing, Volume 67, Issue 3, Pages 1272-1292, 2016.
Abstract: This paper investigates the connections between many popular variants of the well-established discontinuous Galerkin method and the recently developed high-order flux reconstruction approach on irregular tensor-product grids. We explore these connections by analysing three nodal versions of tensor-product discontinuous Galerkin spectral element approximations and three types of flux reconstruction schemes for solving systems of conservation laws on irregular tensor-product meshes. We demonstrate that the existing connections established on regular grids are also valid on deformed and curved meshes for both linear and nonlinear problems, provided that the metric terms are accounted for appropriately. We also find that the aliasing issues arising from nonlinearities either due to a deformed/curved elements or due to the nonlinearity of the equations are equi- valent and can be addressed using the same strategies both in the discontinuous Galerkin method and in the flux reconstruction approach. In particular, we show that the discontinuous Galerkin and the flux reconstruction approach are equivalent also when using higher-order quadrature rules that are commonly employed in the context of over- or consistent-integration-based dealiasing methods. The connections found in this work help to complete the picture regarding the relations between these two numerical approaches and show the possibility of using over- or consistent-integration in an equivalent manner for both the approaches.



Postdoctoral Position - GPU Accelerated High-Order Computational Fluid Dynamics
Summary: A fully funded Postdoctoral position is currently available. The project, will involve development of PyFR, an open-source high-order massively-parallel cross-platform CFD solver, as well as its application to solve a range of challenging unsteady flow problems. Candidates should hold, or expect to obtain, a PhD in a numerate discipline from a world-leading university.


Recent Seminars

Next Generation CFD: High-Order Accurate Simulations using Many-Core Platforms. P. E. Vincent. Swiss National Supercomputing Center, Lugano, Switzerland. August 2016.
PyFR: High-Order Accurate Cross-Platform Petascale Computational Fluid Dynamics with Python. F. D. Witherden, P. E. Vincent. NASA Ames, Moffett Field, CA, USA. May 2016.