Rescaling of the Roe Scheme in Low Mach-Number Flow Regions II: Artificial Speed of Sound and Low Mach Number Fix
Résumé
We look at two simple modifications of the Roe scheme in the incompressible limit, based on different ideas: the Rossow's artificial speed of sound and the Rieper's low Mach number fix. Both schemes modify the eigenspaces of the dissipation matrix. The analysis emphasizes the properties of the dissipation matrix for the Von Neumann stability, the asymptotic behaviour and the solution accuracy in the incompressible limit. Numerical results in the very low-speed limit are discussed for robustness, consistency and accuracy issues of the numerical procedure. Possible occurrence of checkerboard pressure modes, when using a collocated arrangement for velocity components and pressure in the finite-volume scheme, and spurious acoustic modes, is also illustrated for both schemes.
Mots clés
- Incompressible time-scale
- Characteristic time-step
- Implicit scheme
- Stability
- Checkerboard pressure-velocity decoupling
- Wave equation
- Acoustic time-scale
- Euler equations
- Low Mach number fix
- Artificial speed of sound
- Roe scheme
- Finite-volume method
- Difference scheme
- Potential flow
- Compressible flow
- Low Mach number
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