Polynomial Least-Squares reconstruction for semi-Lagrangian Cell-Centered Hydrodynamic Schemes
ESAIM. Proceedings, Tome 28 (2009), pp. 100-116
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In Inertial Confinement Fusion (ICF) simulation, use of Lagrangian hydrodynamic numerical schemes is a cornerstone. It avoids mixing of materials and allows for symmetry preservation in dimension two. Recently, [6] and then [8] proposed an interesting alternative to the historical VNR scheme [14]. These two first order schemes are multidimensional generalizations of the Godunov acoustic solver. Alternatively, a WENO Lagrangian scheme was proposed in [5]. This scheme suffers from non-preservation of symmetries and its velocity computation can be discussed.
The aim of this work is to evaluate the later scheme on ICF representative test cases and to derive a polynomial reconstruction that preserves symmetries for the three cell-centered scheme. This reconstruction is inspired by [11]. Since this paper focuses on the approximation of Euler equations, considered test cases are purely hydrodynamic and do not illustrate all difficulties encountered in ICF.
We first briefly recall different schemes used for this study. We then explain the Least-Squares ENO reconstruction that we chose for symmetry preservation and describe the limiting strategy. We finally illustrates the presented results by some representative numerical experiments.
Affiliations des auteurs :
Gilles Carré 1 ; Stéphane Del Pino 1 ; Kirill Pichon Gostaf 2 ; Emmanuel Labourasse 1 ; Alexander V. Shapeev 3
@article{EP_2009_28_a6,
author = {Gilles Carr\'e and St\'ephane Del Pino and Kirill Pichon Gostaf and Emmanuel Labourasse and Alexander V. Shapeev},
title = {Polynomial {Least-Squares} reconstruction for {semi-Lagrangian} {Cell-Centered} {Hydrodynamic} {Schemes}},
journal = {ESAIM. Proceedings},
pages = {100--116},
year = {2009},
volume = {28},
doi = {10.1051/proc/2009041},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/2009041/}
}
TY - JOUR AU - Gilles Carré AU - Stéphane Del Pino AU - Kirill Pichon Gostaf AU - Emmanuel Labourasse AU - Alexander V. Shapeev TI - Polynomial Least-Squares reconstruction for semi-Lagrangian Cell-Centered Hydrodynamic Schemes JO - ESAIM. Proceedings PY - 2009 SP - 100 EP - 116 VL - 28 UR - http://geodesic.mathdoc.fr/articles/10.1051/proc/2009041/ DO - 10.1051/proc/2009041 LA - en ID - EP_2009_28_a6 ER -
%0 Journal Article %A Gilles Carré %A Stéphane Del Pino %A Kirill Pichon Gostaf %A Emmanuel Labourasse %A Alexander V. Shapeev %T Polynomial Least-Squares reconstruction for semi-Lagrangian Cell-Centered Hydrodynamic Schemes %J ESAIM. Proceedings %D 2009 %P 100-116 %V 28 %U http://geodesic.mathdoc.fr/articles/10.1051/proc/2009041/ %R 10.1051/proc/2009041 %G en %F EP_2009_28_a6
Gilles Carré; Stéphane Del Pino; Kirill Pichon Gostaf; Emmanuel Labourasse; Alexander V. Shapeev. Polynomial Least-Squares reconstruction for semi-Lagrangian Cell-Centered Hydrodynamic Schemes. ESAIM. Proceedings, Tome 28 (2009), pp. 100-116. doi: 10.1051/proc/2009041
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