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 Utility of GPU Accelerated High-Order Methods for Unsteady Flow Simulations: A Comparison with Industry-Standard Tools. B. C. Vermeire, F. D. Witherden, P. E. Vincent. Journal of Computational Physics, Volume 334, Pages 497-521, 2017.
Abstract: First- and second-order accurate numerical methods, implemented for CPUs, underpin the majority of industrial CFD solvers. Whilst this technology has proven very successful at solving steady-state problems via a Reynolds Averaged Navier-Stokes approach, its utility for undertaking scale-resolving simulations of unsteady flows is less clear. High-order methods for unstructured grids and GPU accelerators have been proposed as an enabling technology for unsteady scale-resolving simulations of flow over complex geometries. In this study we systematically compare accuracy and cost of the high-order Flux Reconstruction solver PyFR running on GPUs and the industry-standard solver STAR-CCM+ running on CPUs when applied to a range of unsteady flow problems. Specifically, we perform comparisons of accuracy and cost for isentropic vortex advection (EV), decay of the Taylor-Green vortex (TGV), turbulent flow over a circular cylinder, and turbulent flow over an SD7003 aerofoil. We consider two configurations of STAR-CCM+: a second-order configuration, and a third-order configuration, where the latter was recommended by CD-Adapco for more effective computation of unsteady flow problems. Results from both PyFR and Star-CCM+ demonstrate that third-order schemes can be more accurate than second-order schemes for a given cost e.g. going from second- to third-order, the PyFR simulations of the EV and TGV achieve 75x and 3x error reduction respectively for the same or reduced cost, and STAR-CCM+ simulations of the cylinder recovered wake statistics significantly more accurately for only twice the cost. Moreover, advancing to higher-order schemes on GPUs with PyFR was found to offer even further accuracy vs. cost benefits relative to industry-standard tools.

On the Behaviour of Fully-Discrete Flux Reconstruction Schemes. B. C. Vermeire, P. E. Vincent. Computer Methods in Applied Mechanics and Engineering, Volume 315, Pages 1053-1079, 2017.
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.



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.