An Eulerian particle level set method for compressible deforming solids with arbitrary EOS

Abstract

SUMMARYIn this study, an Eulerian, finite-volume method is developed for the numerical simulation of elasticplastic response of compressible solid materials with arbitrary equation of state (EOS) under impact loading. The governing equations of mass, momentum, and energy along with evolution equations for deviatoric stresses are solved in Eulerian conservation law form. Since the position of material boundaries is determined implicitly by Eulerian schemes, the solution procedure is split into two separate subproblems, which are solved sequentially at each time step. First, the conserved variables are evolved in time with appropriate boundary conditions at the material interfaces. In the present work a fourth-order central weighted essentially non-oscillatory shock-capturing method that was developed for gas dynamics has been extended to high strain rate solids problems. In this method fluxes are determined on a staggered grid at places where solution is smooth. As a result, the method does not rely on the solution of Riemann problems but enjoys the flexibility of using any type of EOS. Boundary conditions at material interfaces are also treated by a special ghost cell approach. Then in the second subproblem, the position of material interfaces is advanced to the new time using a particle level set method. A fifth-order Godunov-type central scheme is used to solve the Hamilton-Jacobi equation of level sets in two space dimensions. The capabilities of the proposed method are evaluated at the end by comparing numerical results with the experimental results and the reported benchmark solutions for the Taylor rod impact, spherical groove jetting, and void collapse problems.

A Robust Riemann Solver for Multiple Hydro-Elastoplastic Solid Mediums

“…In the Lagrangian framework, the equations for mass, momentum and energy conservations are solved using a computational mesh that conforms to the material boundaries and moves with particles [2,3], which benefits from its simplicity and natural description of deformation, but suffers from mesh distortion when dealing with large deformation problems. In Eulerian framework the mesh is fixed in space, which makes these methods very suitable for flows with large deformations, such as Udaykumar et al [4][5][6][7][8][9], Liu et al [10][11][12][13][14][15], Mehmandoust et al [16], Sijoy et al [17], and so on. A typical procedure of multi-medium interaction in Eulerian grids mainly consists of two steps.…”

A Robust Riemann Solver for Multiple Hydro-Elastoplastic Solid Mediums

“…In the Lagrangian framework, the equations for mass, momentum and energy conservations are solved using a computational mesh that conforms to the material boundaries and moves with particles [2,3], which benefits from its simplicity and natural description of deformation, but suffers from mesh distortion when dealing with large deformation problems. In Eulerian framework the mesh is fixed in space, which makes these methods very suitable for flows with large deformations, such as Udaykumar et al [4,5,6,7,8,9], Liu et al [10,11,12,13,14,15], Mehmandoust et al [16], Sijoy et al [17], and so on. A typical procedure of multi-medium interaction in Eulerian grids mainly consists of two steps.…”

Two‐fluid model with interface sharpening

“…On the other side, various multi-dimensional interface tracking models-more accurate than two-fluid models-were developed to simulate stratified flows: Lagrangian grid methods (Hirt [10] and Hyman [11]), volume of fluid method-VOF (Hirt [12],Černe [13]), level set method (Osher [14], Sussman [15], Mehmandoust [16], Andreykiv [17]) and front tracking method (Harlow [18], Tryggvason [19]). These methods are able to accurately capture the physics of the stratified flows.…”