Matter flow method for alleviating checkerboard oscillations in triangular mesh SGH Lagrangian simulation

When the SGH Lagrangian based on triangle mesh is used to simulate compressible hydrodynamics, because of the stiffness of triangular mesh, the problem of physical quantity cell-to-cell spatial oscillation (also called "checkerboard oscillation") is easy to occur. A matter flow method is proposed to alleviate the oscillation of physical quantities caused by triangular stiffness. The basic idea of this method is to attribute the stiffness of triangle to the fact that the edges of triangle mesh can not do bending motion, and to compensate the effect of triangle edge bending motion by means of matter flow. Three effects are considered in our matter flow method: (1) transport of the mass, momentum and energy carried by the moving matter; (2) the work done on the element, since the flow of matter changes the specific volume of the grid element; (3) the effect of matter flow on the strain rate in the element. Numerical experiments show that the proposed matter flow method can effectively alleviate the spatial oscillation of physical quantities.