Robust Numerical Schemes for Hyperbolic Balance Laws

Abstract: In this talk, we consider the Ten-Moment Gaussian closure hyperbolic system (and related plasma flow models), which is used to model rarified gas flows. In contrast to Euler equations, the derivation of these equations does not assume local thermodynamic equilibrium, which allows anisotropic effects in the flow. We will present positivity preserving MUSCL scheme for the two dimensional flow system. This is then generalized to design positivity preserving Discontinuous Galerkin (DG) methods. We will also discuss well-balancing issues related to the model and present a well-balanced scheme. In the second part of the talk, we will discuss two plasma flow models, namely, TenMoment Two-fluid equations and Two fluid extended MHD model equations. We will discuss a robust MUSCL based scheme for the first model and a positivity preserving DG scheme for the second model.