Abstract: 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.

Key words: CE/SE method, shock wave capture, chemical reaction flow, elastic-plastic flow, multi-phase incompressible flow