A positive and stable L2-minimization based moment method for the Boltzmann equation of gas dynamics

We consider the method-of-moments approach to solve Boltzmann equation of rarefied gas dynamics, which results in following moment-closure problem. Given a set moments, find underlying probability density function. The problem has infinitely many solutions and requires an additional optimality criterion single-out unique solution. Motivated from discontinuous Galerkin velocity discretization, we based upon L2-minimization. To ensure positive solution problem, enforce positivity constraints on This quadratic optimization with moments constraints. show that (Courant-Friedrichs-Lewy) CFL-type condition ensures both feasibility L2-stability moment approximation. Numerical experiments showcase accuracy our method.