A discontinuous Galerkin fast spectral method for the multi-species Boltzmann equation

Abstract

We introduce a fast Fourier spectral method for the multi-species Boltzmann collision operator. The method retains the advantages of the single-species fast spectral method Gamba et al. (2017) including: (a) spectral accuracy, (b) reduced computational complexity compared to direct spectral method, (c) reduced memory requirement in the precomputation, and (d) applicability to general collision kernels. The fast collision algorithm is then coupled with discontinuous Galerkin discretization in the physical space Jaiswal et al. (2019) to result in a highly accurate deterministic method (DGFS) for the full Boltzmann equation of gas mixtures. A series of numerical tests is performed to illustrate the efficiency and accuracy of the proposed method. Various benchmarks highlighting different collision kernels, different mass ratios, momentum transfer, heat transfer, and in particular the diffusive transport have been studied. The results are directly compared with the direct simulation Monte Carlo (DSMC) method.