Multiple Pressure Variable (MPV) Approach for Low Mach Number Flows Based on Asymptotic Analysis
An asymptotic analysis of the compressible Euler equations in the limit of vanishing Mach numbers is used as a guideline for the development of a low Mach number extension of an explicit higher order shock capturing scheme. For moderate and large Mach numbers the underlying explicit compressible flow solver is active without modification. For low Mach numbers, the scheme employs an operator splitting technique motivated by the asymptotic analysis. Advection of mass and momentum as well as long wave acoustics are discretized explicitly, while in solving the sonic terms, the scheme uses an implicit pressure correction formulation to guarantee both divergence-free flow in the zero Mach number limit and appropriate representation of weakly nonlinear acoustic effects for small but finite Mach numbers. This asymptotics based approach is also used to show how to modify incompressible flow solvers to capture weakly compressible flows.
KeywordsMach Number Euler Equation Incompressible Flow Compressible Flow Divergence Constraint
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- Weimer M., Meinke M., Krause E., ”Numerical Simulation of Incompressible Flows with the Method of Artifical Compressibility”, In this publication.Google Scholar
- Klein R., Munz C.D., ”The Multiple Pressure Variable (MPV) Approach for the Numerical Approximation of Weakly Compressible Fluid Flow”, Proc. of the Int. Conf. on Num. Meth. in Cont. Mech., Prague, June 1994.Google Scholar
- Klein R., Lange K., Willems W., Munz C.D., ”Semi-Implicit High Resolution Schemes for Low Mach Number Flows”, Proc. of Fifth Int. Conf. on Hyperbolic Problems, Theory, Numerics, and Applications, Stony Brook, 1994.Google Scholar
- Klein R., Munz C.D., ”The Extension of Incompressible Flow Solvers to the Weakly Compressible Regime”, submitted to Theoretical and Numerical Fluid Mechanics, Sept. 1995.Google Scholar
- LINSOL, Solver for Large and Sparce Linear Systems, Rechenzentrum der Universität Karlsruhe, http://www.rz.uni-karlsruhe.de/Uni/RZ/Forschung/Numerik/linsol/index.htmp.Google Scholar
- Gresho P.M., Chan S.T., ”On the Theory of Semi-Implicit Projection Methods for Viscous Incompressible Flow and its Implementation via a Finite Element Method That Also Introduces a Nearly Consistent Mass Matrix. Part2: Implementation”, Int. J. for Num. Meth. in Fluids, 11 (1990), pp. 621–659.MathSciNetzbMATHCrossRefGoogle Scholar