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arXiv · 1108.2876

An Asymptotic-Preserving all-speed scheme for the Euler and Navier-Stokes equations

Floraine Cordier·Pierre Degond·Anela Kumbaro
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Abstract

We present an Asymptotic-Preserving 'all-speed' scheme for the simulation of compressible flows valid at all Mach-numbers ranging from very small to order unity. The scheme is based on a semi-implicit discretization which treats the acoustic part implicitly and the convective and diffusive parts explicitly. This discretization, which is the key to the Asymptotic-Preserving property, provides a consistent approximation of both the hyperbolic compressible regime and the elliptic incompressible regime. The divergence-free condition on the velocity in the incompressible regime is respected, and an the pressure is computed via an elliptic equation resulting from a suitable combination of the momentum and energy equations. The implicit treatment of the acoustic part allows the time-step to be independent of the Mach number. The scheme is conservative and applies to steady or unsteady flows and to general equations of state. One and Two-dimensional numerical results provide a validation of the Asymptotic-Preserving 'all-speed' properties.

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Floraine Cordier, Pierre Degond, Anela Kumbaro. 2011-08-14. An Asymptotic-Preserving all-speed scheme for the Euler and Navier-Stokes equations. https://doi.org/10.1016/j.jcp.2012.04.025

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