On the Behavior of Upwind Schemes in the Low Mach Number Limit - Archive ouverte HAL Access content directly
Reports Year : 1997

## On the Behavior of Upwind Schemes in the Low Mach Number Limit

Hervé Guillard
Cécile Viozat
• Function : Author

#### Abstract

This paper presents an asymptotic analysis in power of the Mach number of the flux difference splitting approximation of the compressible Euler equations in the low Mach number limit. We prove that the solutions of the discrete system contain pressure fluctuations of order $Ma$ while the continuous pressure scales with the square of the Mach number. This explains in a rigorous manner why this approximation of the compressible equations fails to compute very subsonic flow. We then show that a preconditioning of the numerical dissipation tensor allows to recover a correct scaling of the pressure. These theoretical results are totally confirmed by numerical experiments.

#### Domains

Computer Science [cs] Other [cs.OH]

### Dates and versions

inria-00073529 , version 1 (24-05-2006)

### Identifiers

• HAL Id : inria-00073529 , version 1

### Cite

Hervé Guillard, Cécile Viozat. On the Behavior of Upwind Schemes in the Low Mach Number Limit. RR-3160, INRIA. 1997. ⟨inria-00073529⟩

### Export

BibTeX TEI Dublin Core DC Terms EndNote Datacite

108 View