A fourth-order auxiliary variable projection method for zero-Mach number gas dynamics

Authors:
Samet Y. Kadioglu;Rupert Klein;Michael L. Minion
Affiliations:
Advanced Nuclear Energy Systems Department, Idaho National Laboratory, P.O. Box 1625, MS 3840, Idaho Falls, ID 83415, United States;FB Mathematik and Informatik, Freie Universität Berlin, Konrad Zuse Zentrum Für Informationstechnik, Takustr. 7, 14195 Berlin,Germany;Department of Mathematics, Phillips Hall, CB 3250, University of North Carolina, Chapel Hill, NC 27599, United States
Venue:
Journal of Computational Physics
Year:
2008

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Abstract

A fourth-order numerical method for the zero-Mach-number limit of the equations for compressible flow is presented. The method is formed by discretizing a new auxiliary variable formulation of the conservation equations, which is a variable density analog to the impulse or gauge formulation of the incompressible Euler equations. An auxiliary variable projection method is applied to this formulation, and accuracy is achieved by combining a fourth-order finite-volume spatial discretization with a fourth-order temporal scheme based on spectral deferred corrections. Numerical results are included which demonstrate fourth-order spatial and temporal accuracy for non-trivial flows in simple geometries.