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Finite-volume WENO schemes for three-dimensional conservation laws. (English) Zbl 1059.65078
Summary: We firstly carry out an extension of the finite-volume weighted essentially non-oscillatory (WENO) schemes to three space dimensions and higher orders of accuracy. Secondly, we propose to use more accurate fluxes as the building block. These are the HLLC and MUSTA fluxes of E. F. Toro [Multi-stage predictor-corrector fluxes for hyperbolic equations. Preprint (2003)] and of E. F. Toro, M. Spruce, and W. Speares [Restoration of the contact surface in the HLL Riemann solver, Report CoA 9204, June 1992; J. Shock Waves 4, No. 1, 25–34 (1994; Zbl 0811.76053)]. The numerical results suggest that the new WENO-HLLC and WENO-MUSTA schemes compare satisfactorily with the state-of-the-art finite-volume scheme of J. Shi, C. Hu, and C.-W. Shu [J. Comput. Phys. 175, No. 1, 108–127 (2002; Zbl 0992.65094)].

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
Software:
HE-E1GODF
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References:
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