Partial characteristic decomposition for multi-species Euler equations

Abstract

High-order finite difference schemes employing characteristic decomposition are widely used for the simulation of compressible gas flows with multiple species. A challenge for the computational efficiency of such schemes is the quadratically increasing dimensionality of the convective flux eigensystem as the number of species increases. Considering the sparsity of the multi-species eigensystem, a remedy is proposed to split the eigensystem into two parts. One is the gas mixture part, which is subjected to the established characteristic decomposition schemes for single-fluid Euler equations. The other part corresponds to the species partial mass equations, which can be solved directly in physical space as the decoupled sub-eigensystem for the species part is composed of two diagonal identity matrices. This property relies on the fact that species are advected with the same convective velocity. In this way, only the gas mixture part requires a characteristic decomposition, resulting in a much higher efficiency for the convective-flux calculation. To cure the inconsistency due to splitting, a consistent update of species mass fractions is proposed. Non-reactive and reactive test cases demonstrate that the proposed scheme reduces the computational cost without deteriorating high-order accuracy.