×
Gabutti, Bruno

On two upwind finite-difference schemes for hyperbolic equations in non- conservative form. (English) Zbl 0529.65057

Comput. Fluids 11, 207-230 (1983).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0529.65057

Cited in 10 Documents

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L15 Initial value problems for second-order hyperbolic equations
35L70 Second-order nonlinear hyperbolic equations

Keywords:

upwind finite-difference schemes; non-conservative form; consistency; stability; convergence; dissipativity; phase error; splitting methods
Cite Review PDF
Full Text: DOI

References:

[1] Ansorge, R., Die Adams-Verfahren als Charakteristikenverfahren höherer Ordnung zur Lösung von hyperbolischen Systemen halblinearer Differentialgleichungen, Num. Math., 5, 443-462 (1963) · Zbl 0118.12203
[2] Anucina, N. N., Some difference schemas for hyperbolic systems, Tr. MIAN SSSR, 74, 5, 1-13 (1966)
[3] Courant, R.; Friedrichs, K. O., Supersonic Flow and Shock Waves, ((1948), Interscience: Interscience New York) · Zbl 0365.76001
[4] Courant, R.; Isaacson, E.; Rees, M., On the solution of nonlinear hyperbolic differential equations by finite differences, Comm. Pure Appl. Math., 5, 243-255 (1952) · Zbl 0047.11704
[5] B. Gabutti and L. Zannutti, Mixed and boundary value problems: Upwind schemes and their applications. Eighth Int. Conf. Numer. Meth. Fluid Dynamics; B. Gabutti and L. Zannutti, Mixed and boundary value problems: Upwind schemes and their applications. Eighth Int. Conf. Numer. Meth. Fluid Dynamics
[6] Gottlieb, D.; Turkel, E., Phase error and stability of second order methods for hyperbolic problems II, J. Comp. Phys., 15, 251-256 (1974) · Zbl 0284.65078
[7] Hirt, C. W., Heuristic stability theory for finite difference equations, J. Comp. Phys., 2, 339-355 (1968) · Zbl 0187.12101
[8] Karlsen, L. K., Computation of steady shocks by second-order finite-difference schemes, Math. Comp., 34, 391-400 (1980) · Zbl 0422.65051
[9] Kreiss, H. G., On difference approximations of the dissipative type for hyperbolic differential equations, Comm. Pure Appl. Math., 17, 335-353 (1964) · Zbl 0279.35059
[10] Lax, P. D., Hyperbolic systems of conservation law and the mathematical theory of shock waves, (SIAM Reg. Conf. Series, Appl. Math., 11 (1973)) · Zbl 0108.28203
[11] Lax, P. D.; Wendroff, B., System of conservation laws, Comm. Pure Appl. Math., 23, 217-237 (1960) · Zbl 0152.44802
[12] Lerat, A.; Peyret, R., Sur l’origine des oscillations apparaissant dan les profiles de choc calculés par des methodes aux difference, C.R. Acad. Sci. Paris, Ser. A, 276, 759-762 (1973) · Zbl 0255.76081
[13] Lerat, A.; Peyret, R., Proprietés dispersives et dissipatives d’une classe de schéma aux differences pour les systémes hyperboliques non lineaires, La Recherche Aerospatiale, 2, 61-79 (1975) · Zbl 0313.76024
[14] MacCormack, R. W., The effect of viscosity in hypervelocity impact cratering, AIAA Paper, 69-354 (1969)
[15] MacCormack, R. W.; Paullay, A. T., Computational efficiency achieved by time splitting of finite difference operators, AIAA Paper N, 72-154 (1972)
[16] Majda, A.; Osher, S., A systematic approach for correcting nonlinear instability, Numer. Math., 30, 429-452 (1978) · Zbl 0368.65048
[17] Moretti, G., The lambda scheme, Computers and Fluids, 7, 191 (1979) · Zbl 0419.76034
[18] Moretti, G., Numerical analysis of compressible flow: an introspective survey, AIAA Paper N., 79-1510 (1979)
[19] Moretti, G.; Pandolfi, M., Critical study of calculation of subsonic flows in duct, AIAA J., 19, 449-457 (1981)
[20] Pandolfi, M.; Zannetti, L., Some tests on finite difference algorithms for computing boundaries in hyperbolic flows, Notes on Num. Fluid Mech., 1 (1978) · Zbl 0422.76016
[21] Richtmeyer, R. D.; Morton, K. W., Difference Methods for Initial Value Problems (1967), Interscience: Interscience New York · Zbl 0155.47502
[22] Strang, G., On the construction and comparison of difference schemes, SIAM J. Numer. Anal., 5, 506-517 (1968) · Zbl 0184.38503
[23] Turkel, E., Phase error and stability of second order methods for hyperbolic problems—I, J. Comput. Phys., 15, 226-250 (1974) · Zbl 0285.65057
[24] Warming, R. F.; Beam, R. M., Upwind second-order difference schemes and applications in aerodynamic flows, AIAA J., 14, 1241-1249 (1976) · Zbl 0364.76047
[25] Warming, R. F.; Hyett, B. J., The modified equation approach to the stability and accuracy analysis of finite difference methods, J. Comput. Phys., 14, 159-179 (1974) · Zbl 0291.65023
[26] Yanenko, N. N., The Method of Fractional Steps (1971), Springer-Verlag: Springer-Verlag Berlin · Zbl 0209.47103
[27] Yanenko, N. N.; Shokin, Y. I., First differential approximation method and approximate viscosity of difference schemes, (Int. Symp. on High Speed Comput. in Fluid Dyn.. Int. Symp. on High Speed Comput. in Fluid Dyn., Monterey 1968. Int. Symp. on High Speed Comput. in Fluid Dyn.. Int. Symp. on High Speed Comput. in Fluid Dyn., Monterey 1968, Phys. Fluids, 12 (1969)), II.28-II.33 · Zbl 0206.39502
[28] Zannetti, L.; Colasurdo, G., A finite difference method based on bicharacteristic for solving multidimensional hyperbolic flow, Ist. Macchine e Motori per Aeromobili, Politecnico di Torino, Publ., 217 (1979)
[29] Zannetti, L.; Moretti, G., Numerical experiments on the leading edge flow field, AIAA Paper N, 81-1011 (1981)
[30] Zhu Youlan, Y.; Chen, B.; Zhan, Z.; Zhong, X.; Qin, B.; Zhang, G., Difference schemes for initial-boundary value problems of hyperbolic systems and examples of application, Scientia Sinica, 2, 261-280 (1979), Special Issue
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.