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.


'New Flux Reconstruction Correction Functions' - Checkout our latest paper on stable-symmetric-conservative Flux Reconstruction correction functions

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


Recent Papers

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.

An Analysis of Solution Point Coordinates for Flux Reconstruction Schemes on Tetrahedral Elements. F. D. Witherden, J. S. Park, P. E. Vincent. Accepted for publication in Journal of Scientific Computing.
Abstract: The Flux Reconstruction (FR) approach offers an efficient route to high-order accuracy on unstructured grids. In this work we study the effect of solution point placement on the stability and accuracy of FR schemes on tetrahedral grids. To accomplish this we generate a large number of solution point candidates that satisfy various criteria at polynomial orders P = 3,4,5. We then proceed to assess their properties by using them to solve the non-linear Euler equations on both structured and unstructured meshes. The results demonstrate that the location of the solution points is important in terms of both the stability and accuracy. Across a range of cases it is possible to outperform the solution points of Shunn and Ham for specific problems. However, there appears to be a degree of problem-dependence with regards to the optimal point set, and hence overall it is concluded that the Shunn and Ham points offer a good compromise in terms of practical utility.



PhD Position - The Impact of Boundary Representation and Mesh Quality on the Performance of High-Order Accurate Flow Solvers for Complex Aerodynamic Flows
Summary: A fully funded PhD position is currently available. The project, undertaken in collaboration with Airbus, will involve using the high-order flow solver PyFR to solve challenging flow problems in the vicinity of complex geometries. Candidates should hold, or expect to obtain, a 1st Class undergraduate degree in a numerate discipline from a world-leading university.


Recent Seminars

Next-Generation Computational Fluid Dynamics: High-Order Methods and Many-Core Hardware. P. E. Vincent. The School of Mechanical Aerospace & Civil Engineering, The University of Manchester, Manchester, UK. March 2015.
PyFR: Next-Generation High-Order Computational Fluid Dynamics on Modern Hardware Platforms. P. E. Vincent. NASA Langley, Hampton, VA, USA. October 2014.