Polynomial Least-Squares reconstruction for semi-Lagrangian Cell-Centered Hydrodynamic Schemes

Gilles Carré¹ ; Stéphane Del Pino¹ ; Kirill Pichon Gostaf² ; Emmanuel Labourasse¹ ; Alexander V. Shapeev³

¹ CEA, DAM, DIF, F-91297 Arpajon, France.
² Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 175 rue du Chevaleret, 75013 Paris.
³ Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543.

ESAIM. Proceedings, Tome 28 (2009), pp. 100-116.

Résumé

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.

Détail

DOI : 10.1051/proc/2009041