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An Isaac Newton Institute Workshop

Effective Computational Methods for Highly Oscillatory Problems: The Interplay between Mathematical Theory and Applications

A Mach-uniform algorithm based on regularized fluid equations

Author: Sebastian Reich (University of Potsdam)

Abstract

A Mach-uniform algorithm is an algorithm suitable for simulations at any level of the Mach number. Semi-implicit time discretization methods and pressure correction algorithms are among the popular choices to obtain Mach-uniform algorithms with applications to meteorology and combustion simulations. Here we suggest an alternative (although related) approach based on a regularized pressure formulation of the Euler equations. The equations are integrated in time by a staggered time-stepping method which avoids artificial numerical damping of large scale accoustic waves. The regularization is motivated by a simple spatial multi-scale analysis.

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