Imperial College London


Faculty of EngineeringDepartment of Aeronautics

Reader in Aeronautics



+44 (0)20 7594 1975p.vincent




211City and Guilds BuildingSouth Kensington Campus






BibTex format

author = {Loppi, NA and Witherden, FD and Jameson, A and Vincent, PE},
doi = {10.1016/},
journal = {Journal of Computational Physics},
title = {Locally adaptive pseudo-time stepping for high-order Flux Reconstruction},
url = {},
volume = {399},
year = {2019}

RIS format (EndNote, RefMan)

AB - This paper proposes a novel locally adaptive pseudo-time stepping convergence acceleration technique for dual time stepping which is a common integration method for solving unsteady low-Mach preconditioned/incompressibleNavier-Stokes formulations. In contrast to standard local pseudo-time stepping techniques that are based on computing the local pseudo-time stepsdirectly from estimates of the local Courant-Friedrichs-Lewy limit, the proposed technique controls the local pseudo-time steps using local truncationerrors which are computed with embedded pair RK schemes. The approachhas three advantages. First, it does not require an expression for the characteristic element size, which are difficult to obtain reliably for curved mixedelement meshes. Second, it allows a finer level of locality for high-ordernodal discretisations, such as FR, since the local time-steps can vary between solution points and field variables. Third, it is well-suited to beingcombined with P-multigrid convergence acceleration. Results are presentedfor a laminar 2D cylinder test case at Re = 100. A speed-up factor of 4.16is achieved compared to global pseudo-time stepping with an RK4 scheme,while maintaining accuracy. When combined with P-multigrid convergenceacceleration a speed-up factor of over 15 is achieved. Detailed analysis ofthe results reveals that pseudo-time steps adapt to element size/shape, solution state, and solution point location within each element. Finally, resultsare presented for a turbulent 3D SD7003 airfoil test case at Re = 60, 000.Speed-ups of similar magnitude are observed, and the flow physics is foundto be in good agreement with previous studies.
AU - Loppi,NA
AU - Witherden,FD
AU - Jameson,A
AU - Vincent,PE
DO - 10.1016/
PY - 2019///
SN - 0021-9991
TI - Locally adaptive pseudo-time stepping for high-order Flux Reconstruction
T2 - Journal of Computational Physics
UR -
UR -
UR -
VL - 399
ER -