On New Method and 3D Codes for Shock Wave Simulation in Fluids and Solids in Euler Variables based on a Modified Godunov Scheme

Abstract

A three-dimensional technique for modeling shock-wave processes both in fluids and solids and for modeling fluid-structure interaction problems is proposed. The technique is based on a modified Godunov's scheme of increased accuracy, which is the same for both fluids and solids, and uses Eulerian-Lagrangian multimesh algorithms. Improving the accuracy of the scheme is achieved only by changing the "predictor" step of the original Godunov scheme. A three-dimensional and time-dependent solution of Riemann's problem is used, which provides a second-order approximation in time and space in the domain of smooth solutions. Monotonicity in the domain of discontinuous solutions is ensured by the transition to the "predictor" step of the first-order scheme. A similar solution of the Riemann problem is used at the contact "fluids - solids”. For each body, three types of computational grids are used with an explicit Lagrangian choice of movable free and contact surfaces. The first type of mesh used is a Lagrangian surface mesh in the form of a continuous set of triangles (STL file), which is used both to set the initial geometry of an object and to accompany it in the calculation process, and two types of volumetric three-dimensional meshes. These are the basic Cartesian fixed grid for each object, and auxiliary movable local Euler-Lagrangian grids associated with each triangle of the surface Lagrangian grid. The results of numerical simulation of the processes of the impact of ice fragments on a titanium plate, acceleration by detonation products of deformable elastoplastic bodies of various shapes, and steel strikers piercing an aluminum plate are presented.