An Arbitrary Lagrangian-Eulerian method with local structured adaptive mesh refinement for modeling shock hydrodynamics

Abstract

Approved for public release; further dissemination unlimited DISCLAIMER This document was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor the University of California nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or the University of California, and shall not be used for advertising or product endorsement purposes. This is a preprint of a paper intended for publication in a journal or proceedings. Since changes may be made before publication, this preprint is made available with the understanding that it will not be cited or reproduced without the permission of the author. This report has been reproduced directly from the best available copy.

Mimetic finite difference methods for diffusion equations on non-orthogonal non-conformal meshes

“…While the vast majority of existing AMR schemes use orthogonal meshes, it is clear that non-orthogonal mesh schemes are more versatile. Non-orthogonal AMR meshes have been used in adaptive arbitrary Lagrangian-Eulerian hydrodynamics algorithms [1]. Our scheme would be suitable for coupled radiation diffusion/hydrodynamics calculations on such meshes.…”

Enhancing scalability of parallel structured AMR calculations

“…SAMR was originally developed to achieve higher resolution shock calculations [5,6]. Subsequent developments have expanded the SAMR algorithm space and the range of problems to which SAMR is applied, including incompressible flow [1,21]; ALE hydrodynamics [2]; particle-continuum hybrids [17,27]; flow in porous media [20]; solid mechanics [16,26]; magnetohydrodynamics [4,12,15]; laser-plasma instabilities [13]; and astrophysics [8,9].…”

A finite volume scheme for solving anisotropic diffusion on ALE‐AMR grids

“…AMR grids are usually based on quadrangular cells in 2D and hexahedral cells in 3D, but they will present hanging‐node between two level of refinement when two cells share a face with one cell. While classical AMR schemes deal with orthogonal meshes , we will use non‐orthogonal grids as we want to couple our diffusion scheme with a Lagrangian or ALE hydrodynamics code in which the grid is moving and is thus deformed .…”