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Spectral deferred corrections with fast-wave slow-wave splitting
Publikationstyp
Journal Article
Date Issued
2016-08-16
Sprache
English
Author(s)
Volume
38
Issue
4
Start Page
A2535
End Page
A2557
Citation
SIAM Journal on Scientific Computing 38 (4): A2535-A2557 (2016-08-16)
Publisher DOI
Scopus ID
ArXiv ID
Peer Reviewed
true
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 i λfₐst, i λslₒw, having Δ t (| λfₐst | + | λslₒw | ) < 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.
Subjects
Acoustic advection
Euler equations
Fast-wave slow-wave splitting
Spectral deferred corrections
Mathematics - Numerical Analysis
Mathematics - Numerical Analysis
Computer Science - Numerical Analysis
65M70, 65M20, 65L05, 65L04