This work deals with the simulation of two-dimensional Lagrangian hydrodynamics problems.Our objective is the development of an artificial viscosity that is to be used in conjunction with a staggered placement of vari...This work deals with the simulation of two-dimensional Lagrangian hydrodynamics problems.Our objective is the development of an artificial viscosity that is to be used in conjunction with a staggered placement of variables:thermodynamics variables are 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 scheme for solving the gas dynamics equations.The numerical results show the accuracy and the robustness of the method,and the fact that very few Hourglass-type deformations are present.Our objective is to establish the link between the scheme of Maire and the introduction of artificial viscosity in a Lagrangian code based on a staggered grid.Our idea is to add an extra degree of freedom to the numerical scheme,which is an approximation of the fluid velocity within cells.Doing that,we can locally come down to a cell-centered approximation and define the Riemann problem associated to discrete variable discontinuities in a very natural way.This results in a node-centered artificial viscosity formulation.Numerical experiments show the robustness and the accuracy of the method,which is very easy to implement.展开更多
文摘This work deals with the simulation of two-dimensional Lagrangian hydrodynamics problems.Our objective is the development of an artificial viscosity that is to be used in conjunction with a staggered placement of variables:thermodynamics variables are 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 scheme for solving the gas dynamics equations.The numerical results show the accuracy and the robustness of the method,and the fact that very few Hourglass-type deformations are present.Our objective is to establish the link between the scheme of Maire and the introduction of artificial viscosity in a Lagrangian code based on a staggered grid.Our idea is to add an extra degree of freedom to the numerical scheme,which is an approximation of the fluid velocity within cells.Doing that,we can locally come down to a cell-centered approximation and define the Riemann problem associated to discrete variable discontinuities in a very natural way.This results in a node-centered artificial viscosity formulation.Numerical experiments show the robustness and the accuracy of the method,which is very easy to implement.
