Improving the staggered grid Lagrangian hydrodynamics for modeling multi-material flows

In this work, we make two improvements on the staggered grid hydrodynamics (SGH) Lagrangian scheme for modeling 2-dimensional compressible multi-material flows on triangular mesh. The first improvement is the construction of a dynamic local remeshing scheme for preventing mesh distortion. The remeshing scheme is similar to many published algorithms except that it introduces some special operations for treating grids around multi-material interfaces. This makes the simulation of extremely deforming and topology-variable multi-material processes possible, such as the complete process of a heavy fluid dipping into a light fluid. The second improvement is the construction of an Euler-like flow on each edge of the mesh to count for the "edge-bending" effect, so as to mitigate the "checkerboard" oscillation that commonly exists in Lagrangian simulations, especially the triangular mesh based simulations. Several typical hydrodynamic problems are simulated by the improved staggered grid Lagrangian hydrodynamic method to test its performance.