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A compatible finite element multi‐material ALE hydrodynamics algorithm
Author(s) -
Barlow A. J.
Publication year - 2007
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1593
Subject(s) - finite element method , lagrangian , finite volume method , mathematics , scheme (mathematics) , eulerian path , robustness (evolution) , lagrangian relaxation , mixed finite element method , computer science , mathematical optimization , algorithm , mathematical analysis , engineering , physics , mechanics , structural engineering , biochemistry , chemistry , gene
The main ideas of compatible Lagrangian hydrodynamics were originally developed in the form of a finite volume scheme by Caramana et al . at LANL. A new compatible finite element Lagrangian hydrodynamics method has been developed and implemented in a 2D arbitrary Lagrangian Eulerian (ALE) code CORVUS. The new finite element method was developed in preference to the published finite volume schemes in order to see if the fundamental principles of compatible hydro could be translated across to other numerical methods in use in hydrocodes and to facilitate a more direct comparison of the performance of the compatible hydro scheme with the existing finite element scheme in CORVUS. The new finite element scheme provides total energy conservation to round off for the Lagrangian step. The edge artificial viscosities and sub‐zonal pressures that have been introduced through the framework of the compatible hydro scheme provide further improvements in terms of accuracy and robustness for Lagrangian calculations. The details of the compatible finite element Lagrangian scheme and the extensions required to the scheme to allow it to be applied as the Lagrangian step of a multi‐material ALE code are discussed. Test problems will be presented to demonstrate some of the benefits and the performance of the new method for hydrocode applications. © British Crown Copyright 2007/MOD. Reproduced with permission. Published by John Wiley & Sons, Ltd.