Numerical schemes for a multi-species BGK model with velocity-dependent collision frequency

We consider a kinetic description of multi-species gas mixture modeled with Bhatnagar-Gross-Krook (BGK) collision operators, in which the frequency varies not only time and space but also microscopic velocity. In this model, Maxwellians typically used standard BGK operators are replaced by generalization such target functions, defined variational procedure [20]. paper we present numerical method for simulating uses an Implicit-Explicit (IMEX) scheme to minimize certain potential function, mimicking Lagrange functional that appears theoretical derivation. show properties as conservation mass, total momentum energy well positivity distribution functions preserved method, illustrate its usefulness effectiveness examples.