Aufsatz in einer Fachzeitschrift
Stability of preconditioned finite volume schemes at low Mach numbers
Details zur Publikation
Autor(inn)en: | Birken, P.; Meister, A. |
Publikationsjahr: | 2005 |
Zeitschrift: | BIT Numerical Mathematics |
Seitenbereich: | 463-480 |
Jahrgang/Band : | 45 |
Heftnummer: | 2 |
Erste Seite: | 463 |
Letzte Seite: | 480 |
ISSN: | 0006-3835 |
DOI-Link der Erstveröffentlichung: |
Zusammenfassung, Abstract
A finite volume method for inviscid unsteady flows at low Mach numbers is studied. The method uses a preconditioning of the dissipation term within the numerical flux function only. It can be observed by numerical experiments that the preconditioned scheme combined with an explicit time integrator is unstable if the time step Delta t does not satisfy the requirement to be O(M-2) as the Mach number M tends to zero, whereas the corresponding standard method remains stable up to Delta t = O(M), M --> 0, though producing unphysical results. A comprehensive mathematical substantiation of this numerical phenomenon by means of a von Neumann stability analysis is presented, which reveals that in contrast to the standard approach, the dissipation matrix of the preconditioned numerical flux function possesses an eigenvalue growing like M-2 as M tends to zero, thus causing the diminishment of the stability region of the explicit scheme. The theoretical results are afterwards confirmed by numerical experiments.
A finite volume method for inviscid unsteady flows at low Mach numbers is studied. The method uses a preconditioning of the dissipation term within the numerical flux function only. It can be observed by numerical experiments that the preconditioned scheme combined with an explicit time integrator is unstable if the time step Delta t does not satisfy the requirement to be O(M-2) as the Mach number M tends to zero, whereas the corresponding standard method remains stable up to Delta t = O(M), M --> 0, though producing unphysical results. A comprehensive mathematical substantiation of this numerical phenomenon by means of a von Neumann stability analysis is presented, which reveals that in contrast to the standard approach, the dissipation matrix of the preconditioned numerical flux function possesses an eigenvalue growing like M-2 as M tends to zero, thus causing the diminishment of the stability region of the explicit scheme. The theoretical results are afterwards confirmed by numerical experiments.
