Imperial College London

Professor Peter Vincent

Faculty of EngineeringDepartment of Aeronautics

Professor of Computational Fluid Dynamics



+44 (0)20 7594 1975p.vincent




211City and Guilds BuildingSouth Kensington Campus






BibTex format

author = {Vermeire, B and Loppi, N and Vincent, P},
doi = {10.1016/},
journal = {Journal of Computational Physics},
pages = {55--71},
title = {Optimal Runge-Kutta schemes for pseudo time-stepping with high-order unstructured methods},
url = {},
volume = {383},
year = {2019}

RIS format (EndNote, RefMan)

AB - In this study we generate optimal Runge-Kutta (RK) schemes forconverging the Artificial Compressibility Method (ACM) using dualtime-stepping with high-order unstructured spatial discretizations. Wepresent optimal RK schemes with between s = 2 and s = 7 stages forSpectral Difference (SD) and Discontinuous Galerkin (DG) discretizations obtained using the Flux Reconstruction (FR) approach withsolution polynomial degrees of k = 1 to k = 8. These schemes are optimal in the context of linear advection with predicted speedup factors inexcess of 1.80× relative to a classical RK4,4 scheme. Speedup factors ofbetween 1.89× and 2.11× are then observed for incompressible ImplicitLarge Eddy Simulation (ILES) of turbulent flow over an SD7003 airfoil.Finally, we demonstrate the utility of the schemes for incompressibleILES of a turbulent jet, achieving good agreement with experimental data. The results demonstrate that the optimized RK schemesare suitable for simulating turbulent flows and can achieve significantspeedup factors when converging the ACM using dual time-steppingwith high-order unstructured spatial discretizations.
AU - Vermeire,B
AU - Loppi,N
AU - Vincent,P
DO - 10.1016/
EP - 71
PY - 2019///
SN - 0021-9991
SP - 55
TI - Optimal Runge-Kutta schemes for pseudo time-stepping with high-order unstructured methods
T2 - Journal of Computational Physics
UR -
UR -
VL - 383
ER -