Numerical solution of hyperbolic moment models for the Boltzmann equation

The Boltzmann equation can be used to model rarefied gas flows in the transition or kinetic regime, i.e. for moderate to large Knudsen numbers. However, standard moment methods like Grad’s approach lack hyperbolicity of the equations. This can lead to instabilities and nonphysical solutions. Based on recent developments in this field we have recently derived a quadrature-based moment method leading to globally hyperbolic and rotationally invariant moment equations. We present a 1D five moment case of the equations and use numerical simulations to compare the new model with standard approaches. The tests are done with dedicated numerical methods to solve the new non-conservative moment equations. These first results using the new method show the accuracy of the new method and its benefits compared with Grad’s method or other existing models like discrete velocity.