Application of Gridless Method to Simulation of Compressible Multi-Material Flows

The least-square gridless method was extended to simulate the compressible multi-material flows. The algorithm was accomplished to solve the Arbitrary Lagrange-Euler( ALE) formulation. The local least-square curve fits was adopted to approximate the spatial derivatives of a point on the base of the points in its circular support domain,and the basis function was linear. The HLLC( Harten-Lax-van Leer-Contact) scheme was used to calculate the inviscid flux. On the material interfaces,the gridless points were endued with a dual definition corresponding to different materials. The moving velocity of the interface points was updated by solving the Riemann problem. The interface boundary condition was built by using the Ghost Fluid Method( GFM).Computations were performed for several one and two dimensional typical examples. The numerical results show that the interface and the shock wave are well captured,which proves the effectiveness of gridless method in dealing with multi-material flow problems.