According to advection upstream splitting method,a flux splitting method called K-CUSP is proposed.The greatest difference between K-CUSP and two traditional CUSP schemes,namely H-CUSP and E-CUSP,is splitting of total energy:All kinematic quantities and thermodynamic quantities should be separately split into convective term and pressure term by K-CUSP scheme.Numerical tests indicate that:① K-CUSP scheme inherits the simplicity and robustness of FVS scheme.It is less prone to pressure overshoot after shock and no oscillations in expansion area,which is better than AUSM and WPS schemes.② K-CUSP scheme also inherits resolution of FDS scheme.Shock resolution is almost the same with H-CUSP and E-CUSP schemes.Contact discontinuity resolution is better than FVS schemes,a little worse than Roe,AUSM and WPS schemes.However,velocity of contact discontinuity in AUSM and WPS schemes exist large oscillation,while our scheme does not.

Droplets in liquid-liquid two-phese flow are simulated by a perturbation finite volume (PFV) method and Level Set technique. Numerical results show that the PFV scheme has advantages in fewer nodes, high accuracy and efficiency, h facilitates programming. PFV scheme successfully simulates liquid-liquid two-phase flows.

Space-time conservation element and solution element(CE/SE) method with second order accuracy is modified on hexahedral grids. High-order accuracy in space and time is obtained by expanding variables in SEs with high order.CE/SE method is used to capture shock waves in chemical reaction flows,elastic-plastic flows and unsteady multi-phase incompressible flows.Numerical results are compared with experimental and theoretical results of classical examples.It is indicated that the method is easy to implement, accurate and efficient.Application of high order CE/SE method is extended.

We extend the CE/SE scheme and present a complete Eulerian approach for two-dimensional(plane strain and axisymmetry) elastic-plastic flows with solid features.Eulerian governing equations are adopted and solved on a fixed Cartesian grid.Johnson-Cook constituted equations and Mie-Grüneisen equation of state are used to describe materials.A hybrid particle level set method is used to trace interfaces of materials.Two types of boundary condition are presented in tracking interface.The penetration of a steel target by a WHA long rod is simulated and the computational results are carefully compared with those in other literatures.