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 Behaviour of Fully-Discrete Flux Reconstruction Schemes. B. C. Vermeire, P. E. Vincent. Accepted for publication in Computer Methods in Applied Mechanics and Engineering.
Abstract: In this study we employ von Neumann analyses to investigate the dispersion, dissipation, group velocity, and error properties of several fully discrete flux reconstruction (FR) schemes. We consider three FR schemes paired with two explicit Runge-Kutta (ERK) schemes and two singly diagonally implicit RK (SDIRK) schemes. Key insights include the dependence of high-wavenumber numerical dissipation, relied upon for implicit large eddy simulation (ILES), on the choice of temporal scheme and time-step size. Also, the wavespeed characteristics of fully-discrete schemes and the relative dominance of temporal and spatial errors as a function of wavenumber and time-step size are investigated. Salient properties from the aforementioned theoretical analysis are then demonstrated in practice using a linear advection test cases. Finally, a Burgers turbulence test case is used to demonstrate the importance of the temporal discretisation when using FR schemes for ILES.

On the Properties of Energy Stable Flux Reconstruction Schemes for Implicit Large Eddy Simulation. B. C. Vermeire, P. E. Vincent. Journal of Computational Physics, Volume 327, Pages 368-388, 2016.
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.



PhD Studentship - Development of In-situ Visualisation and Analysis Technology for High-Fidelity Computational Fluid Dynamics
Summary: A PhD Studentship is currently available. The project, will involve addition of 'in-situ' visualisation, processing, and analysis technology to PyFR, an open-source high-order massively-parallel CFD platform, as well as its application to solve a range of challenging unsteady flow problems. Candidates should hold, or expect to obtain, an undergraduate degree in a numerate discipline. Previous programming experience is important (ideally Python, C++ and CUDA).


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.