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

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.


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


Zbl 1045.76029
Full Text: DOI


[1] Adams, N.A.; Shariff, K., A high-resolution hybrid compact-ENO scheme for shock-turbulence interaction problems, J. comput. phys., 127, 27, (1996) · Zbl 0859.76041
[2] Balsara, D.; Shu, C.-W., Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy, J. comput. phys., 160, 405, (2000) · Zbl 0961.65078
[3] Chatterjee, A., Shock wave deformation in shock – vortex interactions, Shock waves, 9, 95, (1999) · Zbl 0934.76036
[4] Cockburn, B.; Shu, C.-W., Nonlinearly stable compact schemes for shock calculation, SIAM J. numer. anal., 31, 607, (1994) · Zbl 0805.65085
[5] Deng, X.; Maekawa, H., Compact high-order accurate nonlinear schemes, J. comput. phys., 130, 77, (1997) · Zbl 0870.65075
[6] Deng, X.; Zhang, H., Developing high-order weighted compact nonlinear schemes, J. comput. phys., 165, 22, (2000) · Zbl 0988.76060
[7] Garnier, E.; Sagaut, P.; Deville, M., A class of explicit ENO filters with application to unsteady flows, J. comput. phys., 170, 184, (2001) · Zbl 1011.76056
[8] Harten, A.; Engquist, B.; Osher, S.; Chakravarthy, S., Uniformly high order essentially non oscillatory schemes, III, J. comput. phys., 71, 213, (1987)
[9] Jiang, G.S.; Shu, C.-W., Efficient implementation of weighted ENO schemes, J. comput. phys., 126, 202, (1996) · Zbl 0877.65065
[10] Pirozzoli, S., J. comput. phys., 178, 81, (2002)
[11] Sanders, R.; Morano, E.; Druguet, M., Multidimensional dissipation for upwind schemes: stability and applications to gas dynamics, J. comput. phys., 145, 511, (1998) · Zbl 0924.76076
[12] Shu, C.-W., High order ENO and WENO schemes for computational fluid dynamics, (), 439-582 · Zbl 0937.76044
[13] Shu, C.-W.; Osher, S., Efficient implementation of essentially non-oscillatory shock-capturing schemes II, J. comput. phys., 83, 32, (1989) · Zbl 0674.65061
[14] Wang, Z.; Huang, G.P., An essentially nonoscillatory high-order Padé-type (ENO-Padé) scheme, J. comput. phys., 177, 37, (2002) · Zbl 1063.76070
[15] Woodward, P.; Colella, P., Numerical simulations of two-dimensional fluid flow with strong shocks, J. comput. phys., 54, 115, (1984) · Zbl 0573.76057
[16] Yee, H.C.; Sandham, N.D.; Djomehri, M.J., Low-dissipative high-order shock-capturing methods using characteristic-based filters, J. comput. phys., 150, 199, (1999) · Zbl 0936.76060
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