We extend the traditional kinetic scheme for ideal gases to the Euler equations with the equation of state for a multi-component stiffened gas. Based on a careful analysis of the oscillation mechanism of the tradition...We extend the traditional kinetic scheme for ideal gases to the Euler equations with the equation of state for a multi-component stiffened gas. Based on a careful analysis of the oscillation mechanism of the traditional kinetic scheme across contact discontinuities, we propose a new non-oscillatory kinetic （NOK） scheme for multi-component stiffened gases. The basic idea in the construction is to use a flux splitting technique to construct numerical fluxes which do not depend on the concrete form of the equilibrium state. The new scheme can not only can avoid spurious oscillations of the pressure and velocity near a material interface which are observed in the traditional kinetic schemes such as the kinetic flux vector splitting （KFVS） and BGK schemes, but also can deal with the stiffened gas equation of state. Moreover, we also carry out a careful analysis on the consistency condition, truncation error and positivity of the NOK scheme. A number of 1D and 2D numerical tests are presented which demonstrate the accuracy and robustness of the new scheme in the simulation of problems with smooth, weak and strong shock wave regions.展开更多
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 reconstr...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 frame-work 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 watergas 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.展开更多
文摘We extend the traditional kinetic scheme for ideal gases to the Euler equations with the equation of state for a multi-component stiffened gas. Based on a careful analysis of the oscillation mechanism of the traditional kinetic scheme across contact discontinuities, we propose a new non-oscillatory kinetic （NOK） scheme for multi-component stiffened gases. The basic idea in the construction is to use a flux splitting technique to construct numerical fluxes which do not depend on the concrete form of the equilibrium state. The new scheme can not only can avoid spurious oscillations of the pressure and velocity near a material interface which are observed in the traditional kinetic schemes such as the kinetic flux vector splitting （KFVS） and BGK schemes, but also can deal with the stiffened gas equation of state. Moreover, we also carry out a careful analysis on the consistency condition, truncation error and positivity of the NOK scheme. A number of 1D and 2D numerical tests are presented which demonstrate the accuracy and robustness of the new scheme in the simulation of problems with smooth, weak and strong shock wave regions.
基金supported by Science Challenge Project(TZ2016001)National Natural Science Foundation of China(U1430235)Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund(the second phase).
文摘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 frame-work 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 watergas 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.
