A hybrid OpenMP and MPI implementation of a conservative spectral method for the Boltzmann equation

Abstract

We demonstrate the implementation of a hybrid OpenMP and MPI parallelization of a conservative spectral method for the Boltzmann equation originally developed by Gamba and Tharkabhushaman. We perform a scaling analysis to demonstrate that the problem is well suited to parallelization, and find that the computational time scales linearly with the number of compute nodes on high performance computing resources. The original method has also been improved to higher order in space and time and is implemented on non-uniform grids in physical space. We test this scheme for an example problem in which a kinetic boundary layer generates a shock wave for large space and long times. This is the first time that the fully nonlinear Boltzmann collision operator has been used to compute this problem.