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We introduce a fast Fourier spectral method for the multi-species Boltzmanncollision operator. The method retains the riveting properties of thesingle-species fast spectral method (Gamba et al. SIAM J. Sci. Comput., 39 pp.B658--B674 2017) including: (a) spectral accuracy, (b) reduced computationalcomplexity compared to direct spectral method, (c) reduced memory requirementin the precomputation, and (d) applicability to general collision kernels. Thefast collision algorithm is then coupled with discontinuous Galerkindiscretization in the physical space (Jaiswal et al. J. Comp. Phys., 378 pp.178--208 2019) to result in a highly accurate deterministic method (DGFS) forthe full Boltzmann equation of gas mixtures. A series of numerical tests isperformed to illustrate the efficiency and accuracy of the proposed method.Various benchmarks highlighting different collision kernels, different massratios, momentum transfer, heat transfer, and in particular the diffusivetransport have been studied. The results are directly compared with the directsimulation Monte Carlo (DSMC) method.

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