Exploration of a superposition and reconciliation based approach to cell-centered Lagrangian hydrodynamic methods

Abstract

Applications and experiments involving the hypervelocity deformation of solids are difficult to devise, implement, and occur on microsecond time scales. As a result, simulations play a large role in the study of hypervelocity deformation. This study explored a superposition and reconciliation based approach using cell-centered Lagrangian hydro methods. The reconciliation forces that are not explicitly calculated for mesh movement were analyzed on an existing hydrocode by Pierre-Henri Maire (PHM) and a truncated form of the Runnels-Gilman method (implemented without using the reconciliation forces as additional forces to form a new hydro method called the Runnels-Gilman method). Results from both the 1D Piston and Saltzman test problems illustrate that the unaccounted reconciliation forces are acting on the mesh both at the shock front and behind the shock wave in PHM's method, while in the truncated Runnels- Gilman method, reconciliation forces are acting only on the vertices at the shock front. In test problems using PHM's method, reconciliation forces may be capturing the additional forces that account for more stable density and internal energy solution during shock wave propagation as compared to the truncated Runnels-Gilman method.