Abstract
A fourth-order numerical method for the zero-Mach-number limit of the equations for compressible flow is presented. The method is formed by discretizing a new auxiliary variable formulation of the conservation equations, which is a variable density analog to the impulse or gauge formulation of the incompressible Euler equations. An auxiliary variable projection method is applied to this formulation, and accuracy is achieved by combining a fourth-order finite-volume spatial discretization with a fourth-order temporal scheme based on spectral deferred corrections. Numerical results are included which demonstrate fourth-order spatial and temporal accuracy for non-trivial flows in simple geometries.
| Original language | English |
|---|---|
| Pages (from-to) | 2012-2043 |
| Number of pages | 32 |
| Journal | Journal of Computational Physics |
| Volume | 227 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 10 Jan 2008 |
| Externally published | Yes |
Funding
M.M. acknowledges the support of the Alexander-von-Humboldt Stiftung through a research stipend, and funding of part of the present work by the US Department of Energy. S.K. was funded by the US Department of Energy through the Scientific Discovery Through Advanced Computing program. R.K. appreciates partial funding of the present work by Deutsche Forschungsgemeinschaft, grants KL 611/6, KL 611/14. The authors thank Matthias Münch for helping out with the second-order calculations in Section 4.3.2 .
| Funders | Funder number |
|---|---|
| Alexander-von-Humboldt Stiftung | |
| U.S. Department of Energy | |
| Deutsche Forschungsgemeinschaft | KL 611/6, KL 611/14 |
Keywords
- Auxiliary variable methods
- Deferred corrections
- Gas dynamics
- Gauge methods
- Impulse methods
- Projection methods