Finite-difference method for computation of 3-D gas dynamics equations with artificial viscosity

A new numerical method for the solution of gas dynamics problems for three-dimensional (3D) systems in Eulerian variables is presented in the paper. The proposed method uses the approximation O (τ 2 + h x 2 + h y 2 + h z 2 ) in the areas of the solution’s smoothness and beyond the compression waves;...

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Bibliographic Details
Published in:Mathematical models and computer simulations 2011-10, Vol.3 (5), p.587-595
Main Authors: Popov, I. V., Fryazinov, I. V.
Format: Article
Language:English
Subjects:
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Simulation and Modeling
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Summary:A new numerical method for the solution of gas dynamics problems for three-dimensional (3D) systems in Eulerian variables is presented in the paper. The proposed method uses the approximation O (τ 2 + h x 2 + h y 2 + h z 2 ) in the areas of the solution’s smoothness and beyond the compression waves; τ is the time step; and h x , h y , and h z are space variable steps. In the proposed difference scheme, in addition to Lax-Wendroff corrections, artificial viscosity μ that monotonizes the scheme is introduced. The viscosity is obtained from the conditions of the maximum principle. The results of the computation of the 3D test problem for the Euler equation are presented.
ISSN:2070-0482
2070-0490
DOI:10.1134/S2070048211050103