Geodesic
Large time step HLL and HLLC schemes
Prebeg, Marin1  ; Flåtten, Tore2 ; Müller, Bernhard1
1 Department of Energy and Process Engineering, Norwegian University of Science and Technology, Kolbjørn Hejes vei 2, NO-7491 Trondheim, Norway
2 SINTEF Materials and Chemistry, P.O. Box 4760 Sluppen, NO-7465 Trondheim, Norway
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 4, pp. 1239-1260

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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.

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2017051
Classification : 65M08, 35L65, 65Y20
Keywords: Large Time Step, HLL, HLLC, euler equations, riemann solver

Prebeg, Marin 1 ; Flåtten, Tore 2 ; Müller, Bernhard 1

1 Department of Energy and Process Engineering, Norwegian University of Science and Technology, Kolbjørn Hejes vei 2, NO-7491 Trondheim, Norway
2 SINTEF Materials and Chemistry, P.O. Box 4760 Sluppen, NO-7465 Trondheim, Norway 
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     title = {Large time step {HLL} and {HLLC} schemes},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1239--1260},
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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

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