Simplified hyperbolic moment equations

Hyperbolicity is a necessary property of model equations for the solution of the BGK equation to achieve stable and physical solutions. However, the standard approach for velocity space discretization developed by Grad only yields locally hyperbolic equations. The method has recently been improved and several new globally hyperbolic model systems have been derived such as the Hyperbolic Moment Equations (HME) and the Quadrature-Based Moment Equations (QBME). We will describe the derivation and properties of a new model system called Simplified Hyperbolic Moment Equations (SHME) which inherits hyperbolicity from the other models but is simpler to implement and to solve. First simulation results show a good accuracy of the new SHME model in comparison to the existing models.