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An artificial compression method for ENO schemes: The slope modification method. (English) Zbl 0705.65062
The author introduces a simple and efficient method of artificial compression to improve the performance of an essentially non-oscillatory (ENO) scheme at the contact discontinuities. The method combines the ENO scheme with an artificial compression method. The method is applied to the system of Euler equations for gas dynamics. A number of standard problems are treated as examples.
Reviewer: K.T.S.R.Iyengar

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
76N15 Gas dynamics (general theory)
Full Text: DOI
[1] Harten, A., Math. comput., 32, 363, (1978)
[2] Harten, A.; Osher, S., SIAM J. numer. anal., 24, 279, (1987)
[3] Harten, A.; Osher, S.; Engquist, B.; Chakravarthy, S., J. appl. numer. math., 2, 347, (1986)
[4] Harten, A.; Engquist, B.; Osher, S.; Chakravarthy, S., J. comput. phys., 71, 231, (1987)
[5] Osher, S.; Sweby, P.K., Recent developments in the numerical solution of non-linear conservation laws, (), 681 · Zbl 0615.65094
[6] Shu, C.-W.; Osher, S.; Shu, C.-W.; Osher, S., ICASE report no. 87-33, J. comput. phys., 83, 32, (1989)
[7] Shu, C.-W.; Osher, S., J. comput. phys., 83, 32, (1989)
[8] Katzer, E.; Osher, S., UCLA CAM report no. 88-14, (1988), (unpublished)
[9] Harten, A., ICASE report 87-56 UCLA, (August 1987), (unpublished)
[10] Harten, A., Preliminary results on the extension of the ENO schemes to two dimensional problems, () · Zbl 0626.65082
[11] Mao, D.K., A treatment of discontinuities in shock capturing finite difference methods I. single conservation law, (1988), (unpublished)
[12] McKenzie, J.F.; Westphal, K.O., Phys. fluids, 11, 2350, (1968)
[13] Lax, P.D.; Wendroff, B., Commun. pure appl. math., 13, 217, (1960)
[14] Woodward, P.; Colella, P., J. comput. phys., 54, 115, (1984)
[15] Zalesak, S., A preliminary comparison of modern shock-capturing schemes: linear advection, ()
[16] {\scH. Yang}, Ph. D. thesis, in preparation.
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