×

Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods. (English) Zbl 0468.76066


MSC:

76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
65N06 Finite difference methods for boundary value problems involving PDEs
35L60 First-order nonlinear hyperbolic equations
65Z05 Applications to the sciences

Software:

MACSYMA
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Warming, R. F.; Beam, R. M., AIAA J., 14, 1241 (1976) · Zbl 0364.76047
[2] Warming, R. F.; Beam, R. M., On the construction and application of implicit factored schemes for conservation laws, (Symposium on Computational Fluid Dynamics. Symposium on Computational Fluid Dynamics, New York, April 16-17, 1977. Symposium on Computational Fluid Dynamics. Symposium on Computational Fluid Dynamics, New York, April 16-17, 1977, SIAM-AMS Proc., 11 (1978)), 85 · Zbl 0392.65038
[3] Courant, R.; Isaacson, E.; Rees, M., Comm. Pure Appl. Math., 5, 243 (1952) · Zbl 0047.11704
[4] Godunov, S. K., Mat. Sb., 47, 271 (1959), also Cornell Aeronautical Lab. Translation.
[5] Richtmyer, R. D.; Morton, K. W., Difference Methods for Initial-Value Problems (1967), Interscience: Interscience New York · Zbl 0155.47502
[6] Anucina, N. N., Soviet Math., 5, 60 (1964)
[7] Gordon, P., The diagonal form of quasi-linear hyperbolic systems as a basis for difference equations, (Sect. II-D of General Electric Company Document No. 69SD7056 (Final Report-Theoretical Investigation of Nuclear Burst Phenomena, Naval Ordnance Laboratory, Contract No. N 60921-7164) (1969))
[8] Yanenko, N. N., The Method of Fractional Steps (1971), Springer-Verlag: Springer-Verlag New York · Zbl 0209.47103
[9] Fromm, J. E., J. Comput. Phys., 3, 176 (1968) · Zbl 0172.20202
[10] Van Leer, B., J. Comput. Phys., 23, 263 (1977) · Zbl 0339.76039
[11] Steger, J. L., Comput. Methods Appl. Mech. Eng., 13, 175 (1978) · Zbl 0382.76061
[12] Moretti, G., Comput. Fluids, 7, 191 (1979) · Zbl 0419.76034
[13] Chakravarthy, S. R.; Anderson, D. A.; Salas, M. D., The Split Coefficient Matrix Method for Hyperbolic Systems of gas-Dynamic Equations, (AIAA Paper 80-0268 (1980)), Pasadena, Calif.
[14] Sells, C. C.L., Numerical solutions of the Euler equations for steady transonic flow past a lifting aerofoil, (Proceedings, GAMM Workshop. Proceedings, GAMM Workshop, Stockholm, Sweden (1979)) · Zbl 0202.26001
[15] Courant, R., (Differential and Integral Calculus, Vol. II (1936), Interscience: Interscience New York)
[16] Warming, R. F.; Beam, R. M.; Hyett, B. J., Math. Comp., 29, 1037 (1975) · Zbl 0313.65084
[17] Turkel, E., Math. Comp., 27, 729 (1973) · Zbl 0298.65064
[18] Schiff, L. B.; Steger, J. L., Numerical Simulation of Steady Supersonic Viscous flow, (AIAA Paper 79-0130 (1979)), New Orleans, La. · Zbl 0462.76058
[20] (“MACSYMA Reference Manual,” Version 9, Mathlab Group (1977), Laboratory for Computer Science, MIT)
[21] Maccormack, R. W., The effect of Viscosity in Hypervelocity Impact Cratering, (AIAA Paper 69-354 (1969)), Cincinnati Ohio · Zbl 1047.76550
[22] Fromm, J. E., A numerical study of byoyancy driven flows in room enclosures, (Lecture Notes in Physics, Vol. 8 (1971), Springer-Verlag: Springer-Verlag Berlin), 120-126 · Zbl 0222.76034
[23] Beam, R. M.; Warming, R. F., An Implicit Factored scheme for the Compressible Navier-Stokes Equations. II. The Numerical ODE Connection, AIAA Paper 79-1446 (1979), Williamsburg, Va.
[24] Liepmann, H. W.; Roshko, A., Elements of Gasdynamics (1957), Wiley: Wiley New York · Zbl 0078.39901
[25] Maccormack, R. W.; Baldwin, B. S., A numerical Method for Solving the Navier-Stokes Equations with Application to shock-boundary layer interactions, AIAA Paper 75-1 (1975), Pasadena, Calif. · Zbl 0325.76070
[26] Beam, R. M.; Warming, R. F., AIAA J., 16, 393 (1978) · Zbl 0374.76025
[27] Steger, J. L., AIAA J., 16, 679 (1978) · Zbl 0383.76013
[28] Beam, R. M.; Warming, R. F., J. CompmPhys., 22, 87 (1976) · Zbl 0336.76021
[29] Jameson, A.; Turkel, E., Implicit Schemes and Lu Decompositions, ICASE Report No. 79-24 (1979) · Zbl 0533.65060
[30] Viviand, H., Formes conservatives des équations de la dynamique uvxuaz, La Recherche Aerosp. No. 1974-1, 65-66 (1974) · Zbl 0277.76062
[31] Strang, G., Linear Algebra and its applications (1976), Academic Press: Academic Press New York · Zbl 0338.15001
[32] Gantmacher, F. R., (The Theory of Matrices, Vol. I (1959), Chelsea: Chelsea New York) · Zbl 0085.01001
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.