Abstract: A multi-material arbitrary Lagrangian-Eulerian method is developed.Fluid equations are discretized by a compatible finite element method.A two-dimensional closure model for multi-material cells is presented.It is based on approximate Riemann solver HLLC and isentropic assumption.Interface in mixed cells is constructed by MOF methods.An accurate,conservative integration remapping method is used as mesh is rezoned.Example calculations are presented to show accuracy and robustness of the method.

Key words: multi-material arbitrary Lagranyian-Eulorian method, compatible finite element method, moment-of-fluid method