Numerical Solver for the Boltzmann Equation With Self-Adaptive Collision Operators

We solve the Boltzmann equation whose collision term is modeled by the hybridization of the binary collision and the BGK approximation. The parameter controlling the ratio of these two collision mechanisms is selected adaptively on every grid cell at every time step. This self-adaptation is based on a heuristic error indicator describing the difference between the model collision term and the original binary collision term. The indicator is derived by controlling the quadratic terms in the modeling error with linear operators. Our numerical experiments show that such error indicator is effective and computationally affordable.