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.


'Turbulent Channel Flow' - Checkout our latest paper on identifying eigenmodes of averaged small-amplitude perturbations to turbulent channel flow

'Step Inside a Jet Engine' - Results from our latest PyFR simulations of flow over low pressure turbine blades on show at the Imperial Fringe

'Implant may Offer Kidney Patients Easier Dialysis' - Our latest work on suppressing unsteady flow in arterio-venous fistulae featured in the Times

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


Recent Papers

A Simulated Single Ventilator / Dual Patient Ventilation Strategy for Acute Respiratory Distress Syndrome During the COVID-19 Pandemic. J. A. Solis-Lemus, E. Costar, D. Doorly, E. C. Kerrigan, C. H. Kennedy, F. Tait, S. A. Niederer, P. E. Vincent, S. E. Williams. Royal Society Open Science, Volume 7, Issues 8, 7200585, 2020.
Abstract: The potential for acute shortages of ventilators at the peak of the COVID-19 pandemic has raised the possibility of needing to support two patients from a single ventilator. To provide a system for understanding and prototyping designs we have developed a mathematical model of two patients supported by a mechanical ventilator. We propose a standard setup where we simulate the introduction of T-splitters to supply air to two patients and a modified setup where we introduce a variable resistance in each inhalation pathway and one-way valves in each exhalation pathway. Using the standard setup, we demonstrate that ventilating two patients with mismatched lung compliances from a single ventilator will lead to clinically-significant reductions in tidal volume in the patient with the lowest respiratory compliance. Using the modified setup, we demonstrate that it could be possible to achieve the same tidal volumes in two patients with mismatched lung compliances, and we show that the tidal volume of one patient can be manipulated independently of the other. The results indicate that, with appropriate modifications, two patients could be supported from a single ventilator with independent control of tidal volumes.

On Nodal Point Sets for Flux Reconstruction. F. D. Witherden, P. E. Vincent. Journal of Computational and Applied Mathematics, Volume 381, 113014, 2021.
Abstract: Nodal point sets, and associated collocation projections, play an important role in a range of high-order methods, including Flux Reconstruction (FR) schemes. Historically, efforts have focused on identifying nodal point sets that aim to minimise the L error of an associated interpolating polynomial. The present work combines a comprehensive review of known approximation theory results, with new results, and numerical experiments, to motivate that in fact point sets for FR should aim to minimise the L2 error of an associated interpolating polynomial. New results include identification of a nodal point set that minimises the L2 norm of an interpolating polynomial, and a proof of the equivalence between such an interpolating polynomial and an L2 approximating polynomial with coefficients obtained using a Gauss-Legendre quadrature rule. Numerical experiments confirm that FR errors can be reduced by an order-of-magnitude by switching from popular point sets such as Chebyshev, Chebyshev-Lobatto and Legendre-Lobatto to Legendre point sets.



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

Towards Green Aviation with Python at Petascale. P. E. Vincent. Tokyo University of Science, Tokyo, Japan. December 2017.
Next Generation CFD: High-Order Accurate Simulations using Many-Core Platforms. P. E. Vincent. Swiss National Supercomputing Center, Lugano, Switzerland. August 2016.