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Title: An AMR capable finite element diffusion solver for ALE hydrocodes [An AMR capable diffusion solver for ALE-AMR]

Journal Article · · Plasma Science and Technology
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  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
+ Show Author Affiliations

Here, we present a novel method for the solution of the diffusion equation on a composite AMR mesh. This approach is suitable for including diffusion based physics modules to hydrocodes that support ALE and AMR capabilities. To illustrate, we proffer our implementations of diffusion based radiation transport and heat conduction in a hydrocode called ALE-AMR. Numerical experiments conducted with the diffusion solver and associated physics packages yield 2nd order convergence in the L2 norm.

Research Organization:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE
DOE Contract Number:
AC52-07NA27344
OSTI ID:
1226207
Report Number(s):
LLNL-JRNL-558861
Journal Information:
Plasma Science and Technology, Vol. 17, Issue 2; ISSN 1009-0630
Country of Publication:
United States
Language:
English

References (17)

Three-dimensional HYDRA simulations of National Ignition Facility targets journal May 2001
Debris and shrapnel mitigation procedure for NIF experiments journal May 2008
Multi-Material ALE with AMR for Modeling Hot Plasmas and Cold Fragmenting Materials journal February 2015
An arbitrary Lagrangian–Eulerian method with adaptive mesh refinement for the solution of the Euler equations journal September 2004
A cell by cell anisotropic adaptive mesh ALE scheme for the numerical solution of the Euler equations journal September 2007
ALE-AMR: A new 3D multi-physics code for modeling laser/target effects journal August 2010
Multiple levels of cell by cell Adaptive Mesh Refinement in the Lagrangian step of the ALE code CORVUS journal July 2011
Solution of Equilibrium Radiation Diffusion Problems Using Implicit Adaptive Mesh Refinement journal January 2006
A cell-centered diffusion scheme on two-dimensional unstructured meshes journal June 2007
Radiation diffusion for multi-fluid Eulerian hydrodynamics with adaptive mesh refinement journal January 2003
Mimetic finite difference methods for diffusion equations on non-orthogonal non-conformal meshes journal September 2004
Modeling heat conduction and radiation transport with the diffusion equation in NIF ALE-AMR journal August 2010
A finite element for transition from a fine to a coarse grid journal January 1978
Combining Cell- and Point-Centered Methods in 3D, Unstructured-Grid Radiation–Hydrodynamic Codes journal June 2001
Benchmark results for the non-equilibrium Marshak diffusion problem journal September 1996
A Scalable Parallel Algorithm for Incomplete Factor Preconditioning journal January 2001
Solution of the diffusion equation by finite elements in Lagrangian hydrodynamic Codes journal June 1988

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Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
42 ENGINEERING
97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
hydrodynamic simulation
heat conduction
thermal radiation
adaptive mesh refinement
finite element method