A Gas-Kinetic Riemann Solver for Stiffened Gas Interface and Its Application in Multimaterial Flows (Communications in Computational Physics, 2018)
A new kinetic model is proposed to solve the Riemann problem for stiffenedgas interface from piecewise linear discontinuous initial distributions. In the modelgas particles on each side of the fluid interface are reflected back from the interface,respectively, which is moving with a velocity to achieve the force balance betweenboth sides. Compared with the existing Riemann solver, the present model can keepsecond order accuracy in both space and time. It is also capable of eliminating thenumerical mixing at the fluid interface which is different from existing kinetic models.The new model is applied to the numerical flux calculation at a cell interface andwith the help of homogeneous equilibrium mixture assumption within a cell, a newgas-kinetic scheme is developed for multimaterial flow with stiffened equation of state.The scheme is tested with several typical high-speed multifluid flows, including thewater-gas shock tube flows and the shock-water cylinder interaction. The computedresults are in good agreement with other numerical and experimental studies. Fluidinterfaces as well as shock waves are sharply captured, free of numerical oscillationnear the interface, even for density ratio up to about one thousand, which validate itshigh accuracy, strong robustness and good parallel performance.
Keywords: Non-mixing interface model; stiffened equation of state; gas kinetic scheme; homogeneous equilibrium mixture model; stratified model.