A Node-Centered Artificial Viscosity Method for Two-Dimensional Lagrangian Hydrodynamics Calculations on a Staggered Grid (Communications in Computational Physics, 2010)
This work deals with the simulation of two-dimensional Lagrangian hydrodynamicsproblems. Our objective is the development of an artificial viscosity that is tobe used in conjunction with a staggered placement of variables: thermodynamics variablesare centered within cells and position and fluid velocity at vertices. In [J. Comput.Phys., 228 (2009), 2391-2425], Maire develops a high-order cell-centered schemefor solving the gas dynamics equations. The numerical results show the accuracy andthe robustness of the method, and the fact that very few Hourglass-type deformationsare present. Our objective is to establish the link between the scheme of Maire and theintroduction of artificial viscosity in a Lagrangian code based on a staggered grid. Ouridea is to add an extra degree of freedom to the numerical scheme, which is an approximationof the fluid velocity within cells. Doing that, we can locally come down toa cell-centered approximation and define the Riemann problem associated to discretevariable discontinuities in a very natural way. This results in a node-centered artificialviscosity formulation. Numerical experiments show the robustness and the accuracyof the method, which is very easy to implement.