A characteristic-wise hybrid compact-WENO scheme for solving hyperbolic conservation laws. (English) Zbl 1037.65090

Ren, Yuxin; Liu, Miao’er; Zhang, Hanxin

J. Comput. Phys. 192, No. 2, 365-386 (2003).

Summary: This paper presents a fifth-order conservative hybrid compact weighted essentially non-oscillatory (WENO) scheme scheme for shock-capturing calculation. The hybrid scheme is considered as the weighted average of two sub-schemes: the conservative compact scheme proposed by S. Pirozzoli [ibid. 178, 81–117 (2002; Zbl 1045.76029)] and the WENO scheme. The weight function is designed so that the abrupt transition from one sub-scheme to another is avoided and the resulting hybrid scheme is essentially oscillation free near the flow discontinuities. A Roe type, characteristic-wise finite difference scheme is proposed which generalizes the hybrid scheme for the scalar equation to the system of conservation laws. Several test cases are presented to validate the proposed scheme.

MSC:

65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65	Hyperbolic conservation laws
76N15	Gas dynamics (general theory)

Keywords:

Compact scheme; WENO scheme; Hybrid scheme; Shock-capturing; High-order scheme; Conservation laws; numerical examples finite difference scheme; essentially non-oscillatory scheme

Citations:

Zbl 1045.76029

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