Positivity-preserving high-order discontinuous Galerkin schemes for Ten-Moment Gaussian closure equations

Euler equations for compressible flows treats pressure as a scalar quantity. However, for several applications this description of pressure is not suitable. Many extended model based on the higher moments of Boltzmann equations are considered to overcome this issue. One such model is Ten-Moment Gaussian closure equations, which treats pressure as symmetric tensor. In this work, we develop a higher-order, positivity preserving Discontinuous Galerkin (DG) scheme for Ten-Moment Gaussian closure equations. The key challenge is to preserve positivity of density and symmetric pressure tensor. This is achieved by constructing a positivity limiter. In addition to preserve positivity, the scheme also ensures the accuracy of the approximation for smooth solutions. The theoretical results are then verified using several numerical experiments.