Uniformly high order accurate essentially non-oscillatory schemes. III. (English) Zbl 0652.65067

Harten, Ami; Engquist, Bjorn; Osher, Stanley; Chakravarthy, Sukumar

J. Comput. Phys. 71, 231-303 (1987).

[For part I cf. the first and the third author, SIAM J. Numer. Anal. 24, 279-309 (1987; Zbl 0627.65102).]
The authors continue the studying of essentially nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws. New schemes which generalize Godunov’s scheme and its second-order extension are constructed. Algorithms for numerical solution of the Euler equations of gas dynamics are described and some numerical experiments are discussed.

Reviewer: P.I.Ialamov

MSC:

65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65	Hyperbolic conservation laws

Keywords:

numerical examples; nonoscillatory shock capturing methods; hyperbolic conservation laws; Godunov’s scheme; Algorithms; Euler equations; gas dynamics

References:

[1]	\scM. Ben-Artzi and J. Falcowitz, SIAM J. Sci. Comput., in press.
[2]	Chakravarthy, S.R.; Harten, A.; Osher, S., Essentially non-oscillatory shock-capturing schemes of arbitrarily high accuracy, Aiaa 86-0339, (1986), Reno, NA
[3]	Chorin, A.J., J. comput. phys., 22, 517, (1976)
[4]	Colella, P.; Woodward, P.R., J. comput. phys., 54, 174, (1984)
[5]	Godunov, S.K., Mat. sb., 47, 271, (1959)
[6]	Harabetian, E., A convergent series expansion for hyperbolic systems of conservation laws, NASA contractor report 172557, ICASE report no. 85-13, (1985), (unpublished)
[7]	Harten, A., Math. comp., 32, 363, (1978)
[8]	Harten, A., J. comput. phys., 49, 151, (1983)
[9]	Harten, A., J. comput. phys., 49, 357, (1983)
[10]	Harten, A., Sinum, 21, 1, (1984)
[11]	Harten, A., On high-order accurate interpolation for non-oscillatory shock capturing schemes, (), (unpublished) · Zbl 0606.76084
[12]	Harten, A., Preliminary results on the extension of ENO schemes to two-dimensional problems, (), (in preparation) · Zbl 0626.65082
[13]	Harten, A.; Hyman, J.M., J. comput. phys., 50, 235, (1983)
[14]	Harten, A.; Lax, P.D.; van Leer, B., SIAM rev., 25, 35, (1983)
[15]	SINUM, in press.
[16]	\scA. Harten, B. Engquist S. Osher, and S. R. Chakravarthy, Uniformly high-order accurate non-oscillatory schemes, II, in preparation. · Zbl 0866.65058
[17]	Harten, A.; Osher, S.; Engquist, B.; Chakravarthy, S.R., J. appl. num. math., 2, 347, (1986)
[18]	Lax, P.D., Comm. pure appl. math., 7, 159, (1954)
[19]	Lax, P.D., Hyperbolic systems of conservation laws and the mathematical theory of shock waves, () · Zbl 0108.28203
[20]	Lax, P.D.; Wendroff, B., Commun. pure appl. math., 13, 217, (1960)
[21]	Lax, P.D.; Wendroff, B., Commun. pure appl. math., 17, 381, (1964)
[22]	van Leer, B., J. comput. phys., 32, 101, (1979)
[23]	Osher, S., Sinum, 21, 217, (1984)
[24]	\scS. Osher and E. Tadmor, Math. Comp., in press.
[25]	Roe, P.L., J. comput. phys., 43, 357, (1981)
[26]	Roe, P.L., Some contributions to the modeling of discontinuous flows, () · Zbl 0741.65077
[27]	Sever Mock, M., Order of dissipation near rarefaction centers, (), 395
[28]	Sod, G.A., J. comput. phys., 27, 1, (1978)
[29]	Strang, G., Sinum, 5, 506, (1968)
[30]	Sweby, P.K., Sinum, 21, 995, (1984)
[31]	Woodward, P.; Collella, P., J. comput. phys., 54, 115, (1984)
[32]	Wu, Xiong-Hau; Zhu, You-Lan, A scheme of the singularity-separating method for the nonconvex problem, (), (unpublished) · Zbl 0584.76111