We present Large Time Step (LTS) extensions of the Harten-Lax-van Leer (HLL) and Harten-Lax-van Leer-Contact (HLLC) schemes. Herein, LTS denotes a class of explicit methods stable for Courant numbers greater than one. The original LTS method (R.J. LeVeque, SIAM J. Numer. Anal. 22 (1985) 1051–1073) was constructed as an extension of the Godunov scheme, and successive versions have been developed in the framework of Roe's approximate Riemann solver. In this paper, we formulate the LTS extension of the HLL and HLLC schemes in conservation form. We provide explicit expressions for the flux-difference splitting coefficients and the numerical viscosity coefficients of the LTS-HLL scheme. We apply the new schemes to the one-dimensional Euler equations and compare them to their non-LTS counterparts. As test cases, we consider the classical Sod shock tube problem and the Woodward-Colella blast-wave problem. We numerically demonstrate that for the right choice of wave velocity estimates both schemes calculate entropy satisfying solutions.
Accepté le :
DOI : 10.1051/m2an/2017051
Mots clés : Large Time Step, HLL, HLLC, euler equations, riemann solver
@article{M2AN_2018__52_4_1239_0,
author = {Prebeg, Marin and Fl\r{a}tten, Tore and M\"uller, Bernhard},
title = {Large time step {HLL} and {HLLC} schemes},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1239--1260},
publisher = {EDP-Sciences},
volume = {52},
number = {4},
year = {2018},
doi = {10.1051/m2an/2017051},
mrnumber = {3875285},
zbl = {1417.65160},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2017051/}
}
TY - JOUR AU - Prebeg, Marin AU - Flåtten, Tore AU - Müller, Bernhard TI - Large time step HLL and HLLC schemes JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2018 SP - 1239 EP - 1260 VL - 52 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2017051/ DO - 10.1051/m2an/2017051 LA - en ID - M2AN_2018__52_4_1239_0 ER -
%0 Journal Article %A Prebeg, Marin %A Flåtten, Tore %A Müller, Bernhard %T Large time step HLL and HLLC schemes %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2018 %P 1239-1260 %V 52 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2017051/ %R 10.1051/m2an/2017051 %G en %F M2AN_2018__52_4_1239_0
Prebeg, Marin; Flåtten, Tore; Müller, Bernhard. Large time step HLL and HLLC schemes. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 4, pp. 1239-1260. doi : 10.1051/m2an/2017051. http://www.numdam.org/articles/10.1051/m2an/2017051/
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