A Two-Stage Fourth-Order Gas-Kinetic Scheme for Compressible Multicomponent Flows (Communications in Computational Physics, 2017)
With the use of temporal derivative of flux function, a two-stage temporaldiscretization has been recently proposed in the design of fourth-order schemes basedon the generalized Riemann problem (GRP) [21] and gas-kinetic scheme (GKS) [28].In this paper, the fourth-order gas-kinetic scheme will be extended to solve the compressiblemulticomponent flow equations, where the two-stage temporal discretizationand fifth-order WENO reconstruction will be used in the construction of the scheme.Based on the simplified two-species BGK model [41], the coupled Euler equations forindividual species will be solved. Each component has its individual gas distributionfunction and the equilibrium states for each component are coupled by the physicalrequirements of total momentum and energy conservation in particle collisions. Thesecond-order flux function is used to achieve the fourth-order temporal accuracy, andthe robustness is as good as the second-order schemes. At the same time, the sourceterms, such as the gravitational force and the chemical reaction, will be explicitly includedin the two-stage temporal discretization through their temporal derivatives.Many numerical tests from the shock-bubble interaction to ZND detonative waves arepresented to validate the current approach.