Ruprecht, D orcid.org/0000-0003-1904-2473 and Speck, R (2016) Spectral deferred corrections with fast-wave slow-wave splitting. SIAM Journal on Scientific Computing, 38 (4). A2535-A2557. ISSN 1064-8275
Abstract
The paper investigates a variant of semi-implicit spectral deferred corrections (SISDC) in which the stiff, fast dynamics correspond to fast propagating waves ("fast-wave slow-wave problem"). We show that for a scalar test problem with two imaginary eigenvalues iλ_fast, iλ_slow, having Δt(|λ_fast|+|λ_slow|)<1 is sufficient for the fast-wave slow-wave SDC (FWSW-SDC) iteration to converge and that in the limit of infinitely fast waves the convergence rate of the non-split version is retained. Stability function and discrete dispersion relation are derived and show that the method is stable for essentially arbitrary fast-wave CFL numbers as long as the slow dynamics are resolved. The method causes little numerical diffusion and its semi-discrete phase speed is accurate also for large wave number modes. Performance is studied for an acoustic-advection problem and for the linearised Boussinesq equations, describing compressible, stratified flow. FWSW-SDC is compared to a diagonally implicit Runge-Kutta (DIRK) and IMEX Runge-Kutta (IMEX) method and found to be competitive in terms of both accuracy and cost.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016, Society for Industrial and Applied Mathematics. This is a published version of a paper published in SIAM Journal on Scientific Computing. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | spectral deferred corrections, fast-wave slow-wave splitting, Euler equations, acoustic-advection |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mechanical Engineering (Leeds) > Institute of Engineering Thermofluids, Surfaces & Interfaces (iETSI) (Leeds) The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 21 Jun 2016 10:01 |
Last Modified: | 30 Jun 2020 14:48 |
Published Version: | http://dx.doi.org/10.1137/16M1060078 |
Status: | Published |
Publisher: | Society for Industrial and Applied Mathematics |
Identification Number: | 10.1137/16M1060078 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:101093 |