Abstract
We present a stochastic Galerkin formulation of the Euler equations based on the variables introduced by P. L. Roe in 1981 for the well-known and widely used Roe solver. For numerical discretization, a Roe average matrix for the standard MUSCL-Roe scheme with Roe variables is derived. The Roe variable formulation is robust for supersonic problems where failure occurs for the standard implementation based on the conservative variable formulation. The robustness properties can be significantly improved with a stochastic basis that admits an eigenvalue decomposition with constant eigenvectors of the inner triple product matrix that occur frequently in the evaluation of pseudospectral operations. When this is the case, the Roe variables and conservative variables are similar in performance using the same time-step.
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