A cell-centered Lagrangian-mesh diffusion differencing scheme

A new cell-centered diffusion differencing scheme for the quadrilateral meshes associated with Lagrangian hydrodynamics codes is described. Computational comparisons of this scheme and existing schemes are given. It is shown that the new scheme is much more accurate than existing schemes when the mesh is significantly skewed. The new scheme is also more costly because there are special cell-edge unknowns in addition to the standard cell-center unknowns, and the associated diffusion matrix is asymmetric. The disadvantages of an asymmetric diffusion matrix are mitigated by a multigrid solution technique that is quite effective.