Numerical schemes for low Mach wave breaking

Abstract

In this work, we describe a finite volume scheme for the computation of incompressible air–water flows. We use an artificial compressibility approach that permits us to use a completely explicit scheme. We describe successively the low Mach preconditioning of the scheme, the Riemann solver and then the non-conservative approach that is used to suppress velocity-pressure oscillations, the second order extensions and the parallel implementation. Then this is applied to the simulation of the breaking of a wave on a 15% slope.

Keywords:

• Wave breaking
• Isothermal model
• Air–water
• Riemann solver

Keywords:

• 76M12
• 65M12

Notes

^¶ [email protected]

^§ MUSCL stands for monotonic upwind scheme for conservation laws.

^∥ WLSQR stands for weighted least SQUare.

^# WENO stands for weighted essentially non oscillatory.

Additional information

Notes on contributors

Philippe Helluy

1 ¶ [email protected]