Accelerating the Convergence of the Moment Method for the Boltzmann Equation Using Filters

The moment method is a successful way to approximate the solution of the Boltzmann equation in reasonable runtime with relatively few unknowns while allowing for non-equilibrium effects of the gas. However, the convergence of the moment method with respect to an increasing number of moments is typically slow. This paper aims to improve the convergence of the moment method by introducing filtered hyperbolic moment equations that result in virtually no additional computational overhead while significantly reducing the error. The filter approach is based on a careful study of averaging solutions of two adjacent moment systems and the reformulation of the averaging using an artificial collision method that naturally gives rise to the filter. We study the properties of the filter and show numerical test cases of one-dimensional problems that demonstrate the superior quality of the new filtered moment method.