An efficient γ-model BGK scheme for multicomponent flows on unstructured meshes

Based on the gamma-model, the BGK scheme and the time-dependent gas distribution function, we present an efficient second-order gas-kinetic BGK scheme for compressible multicomponent flows on unstructured meshes. The second-order accuracy of the scheme is achieved by including slopes in the reconstruction step and the efficiency lies in the fact that the slopes in a cell are constructed by using the information in the cell only. Using the explicitly constructed time-dependent gas distribution function, we can obtain in addition the values of the flow variables at cell edges of the cell, which together with the cell averaged values make it possible to construct the slopes of the flow variables in the cell, avoiding the use of the values from neighboring cells in the usual process. Thus, with the stencil of a first-order scheme, we construct a second-order gas-kinetic scheme. Numerical examples illustrate the accuracy and efficiency of the scheme.