An Improved Gas-Kinetic Scheme for Multimaterial Flows

The efficiency of recently developed gas-kinetic scheme for multimaterial flows is increased through the adoption of a new iteration method in the kinetic non-mixing Riemann solver and an interface sharpening reconstruction method at a cell interface. The iteration method is used to determine the velocity of fluid interface, based on the force balance between both sides due to the incidence and bounce back of particles at the interface. An improved Aitken method is proposed with a simple hybrid of the modified Aitken method (Aitken-Chen) and the Steffensen method. Numerical tests validate its efficiency with significantly less calls to the function not only for the average number but also for the maximum. The new reconstruction is based on the tangent of hyperbola for interface capturing (THINC) but applied only to the volume fraction, which is very simple to be implemented under the stratified framework and capable of resolving fluid interface in mixture. Furthermore, the directional splitting is adopted rather than the previous quasi-one-dimensional method. Typical numerical tests, including several water-gas shock tube flows, and the shock-water cylinder interaction flow show that the improved gas-kinetic scheme can capture fluid interfaces much sharper, while preserving the advantages of the original one.