Reminiscences about Difference Schemes

Journal of Computational Physics

Volumn 153, Issue 1, 1999, Pages 6-25

  Godunov, Sergei Konstantinovich ^a  

^a SOBOLEV INSTITUTE OF MATHEMATICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENCE SCHEMES;

EID: 0013109025     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1999.6271     Document Type: Article

References (45)

1. G. B. Alalikin, S. K. Godunov, I. L. Kireeva, and L. A. Pliner, Solution of One-Dimensional Gasdynamic Problems Using Moving Grids (Nauka, Moscow, 1970). [In Russian]
2. K. A. Bagrinovskii and S. K. Godunov, Difference schemes for one-dimensional problems, Dokl. Akad. Nauk SSSR 115(3), 431 (1957). [In Russian]
3. V. F. Diachenko, On Cauchy problem for quasilinear equations, Dokl. Akad. Nauk SSSR 136(1), 16 (1961). [In Russian]
4. K. O. Friedrichs, Conservation equations and the laws of motion in classical physics, Comm. Pure Appl. Math. 31, 123 (1978).
5. K. O. Friedrichs and P. D. Lax, Systems of conservation equations with a convex extension, Proc. Math. Acad. Sci. U.S.A. 68(8), 1696 (1971).
6. I. M. Gelfand, Lectures on quasilinear equations, Uspekhi Mat. Nauk 14(2), 87 (1959). [In Russian]
7. J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math. 18, 697 (1965).
8. S. K. Godunov, A difference scheme for numerical computation of discontinuous solution of hydrodynamic equations, Math. Sb. 47, 271 (1959) [In Russian]; translation, U.S. Joint Publ. Res. Service, JPRS 7226 (1969).
9. S. K. Godunov, Thermodynamics of gases and differential equations, Uspekhi Mat. Nauk 14(5), 97 (1959). [In Russian]
10. S. K. Godunov, On the concept of generalized solution, Dokl. Akad. Nauk SSSR 134(6), 1279 (1960). [In Russian]
11. S. K. Godunov, On non unique "smearing" of discontinuities of the solutions of quasi-linear systems, Dokl. Akad. Nauk SSSR 136(2), 272 (1960). [In Russian]
12. S. K. Godunov, Residues estimations for the approximate solutions of the simplest equations of gasdynamics, J. Comput. Math. Math. Phys. 1(4), 622 (1961). [In Russian]
13. S. K. Godunov, Sur la construction des réseaux dan les domaines compliques d'une dacon automatique pour les equations aux differences finies, Act. Congress Int. Math. 3, 99 (1970).
14. S. K. Godunov, Elements of Mechanics of Continuous Media (Nauka, Moscow, 1978). [In Russian]
15. Numerical Solution of Multidimensional Gas Dynamics Problems, edited by S. K. Godunov (Nauka, Moscow, 1976) [In Russian]; Resolution numerique des problémes multibimensionnels de la dynamiqe des gas, edited by S. Godunov (Mir, Moscow, 1979). [In French]
16. Numerical Solution of Multidimensional Gas Dynamics Problems, edited by S. K. Godunov (Nauka, Moscow, 1976) [In Russian]; Resolution numerique des problémes multibimensionnels de la dynamiqe des gas, edited by S. Godunov (Mir, Moscow, 1979). [In French]
17. S. K. Godunov, The problem of guaranteed precision of numerical methods of linear algebra, in Proc. Int. Congr. Math., Berkeley, CA, 1986, Vol. 2, p. 1353.
18. S. K. Godunov, Lois de conservation et integrales d'énergie des équations hyperboliques, in Nonlinear Hyperbolic Problems, Proc. of Workshop, St.-Etienne, France, Jan. 13-19, 1988, Lecture Notes in Mathematics (Springer-Verlag, New York, 1988), Vol. 1270, p. 135.
19. S. K. Godunov, Modern Aspects of Linear Algebra (Nauchnaja Kniga, Novosibirsk, 1997) [In Russian]; English translation, Modern Aspects of Linear Algebra, Translations of Mathematical Monographs (Amer. Math. Soc., Providence, 1998), Vol. 175.
20. S. K. Godunov, Modern Aspects of Linear Algebra (Nauchnaja Kniga, Novosibirsk, 1997) [In Russian]; English translation, Modern Aspects of Linear Algebra, Translations of Mathematical Monographs (Amer. Math. Soc., Providence, 1998), Vol. 175.
21. S. K. Godunov and G. P. Prokopov, On the computations of conformal mappings and grid generation, J. Comput. Math. Math. Phys. 7(5), 1031 (1967). [In Russian]
22. S. K. Godunov and G. P. Prokopov, On the solution of a discrete Laplace's equation, J. Comput. Math. Math. Phys. 9(2), 462 (1969). [In Russian]
23. S. K. Godunov and G. P. Prokopov, Application of the method of minimal iterations for the evaluation of the eigenvalues of elliptic problems, J. Comput. Math. Math. Phys. 10(5), 1180 (1970). [In Russian]
24. S. K. Godunov and G. P. Prokopov, On the utilization of moving grids in gasdynamics computations, J. Comput. Math. Math. Phys. 12(2), 429 (1972). [In Russian]
25. S. K. Godunov and E. I. Romensky, Thermodynamical foundations for special evolution differential equations of continuous media, in Trends in Applications of Mathematics to Mechanics (Longman, Harlow/New York, 1995).
26. S. K. Godunov and E. I. Romenskii, Thermodynamic, conservation laws and symmetric forms of differential equations in mechanics of continuous media, in Computational Fluid Dynamics Review, 1995, edited by M. Hafez and K. Oshima (Wiley, New York, 1995), p. 19.
27. K. S. Godunov and E. I. Romensky, Symmetric forms of thermodynamically compatible systems of conservation laws in continuum mechanics, in Numerical Methods in Engineering, Proc. Second ECCOMAS Conf., Paris, France, 1996 (Wiley, Sons. New York, 1996).
28. S. K. Godunov and K. A. Semendjaev, Difference methods for numerical solution of gasdynamic problems, J. Comput. Math. Math. Phys. 2(1), 3 (1962). [In Russian]
29. S. K. Godunov and A. V. Zabrodin, On multidimensional difference schemes of second order accuracy, J. Comput. Math. Math. Phys. 2(4), 706 (1962). [In Russian]
30. S. K. Godunov, V. M. Gordienko, and G. A. Chumakov, Variational principle for 2-D regular quasi-isometric grid generation. Int. J. Comp. Fluid Dynamics 1995, V5, N1-2, pp. 99-118.
31. S. K. Godunov, T. Y. Mikhailova, and E. I. Romenskii, Systems of thermodynamically coordinated laws of conservation invariant under rotations, Siberian Math. J. 37(4), 690 (1996). [In Russian]
32. S. K. Godunov, V. V. Ogneva, and G. P. Prokopov, On the convergence of the steepest descend method for the eigenvalue problems, in Partial Differential Equations, Proceedings of the Symposium on 60th Anniversary of Academician S. L. Sobolev (Nauka, Moscow, 1970). [In Russian]
33. S. K. Godunov, A. V. Zabrodin, and G. P. Prokopov, A difference scheme for two-dimensional unsteady aerodynamics and an example of calculations with a separated shock wave, J. Comput. Math. Math. Phys. 2(6), 1020 (1961). [In Russian]
34. S. K. Godunov, A. G. Antonov, O. P. Kiriluk, and V. I. Kostin, Guaranteed Accuracy in Numerical Linear Algebra (Kluwer Academic, Dordrecht, 1993); Russian edition published in 1992.
35. S. K. Godunov, A. A. Deribas, A. V. Zabrodin, and N. S. Kozin, Hydrodynamics effects in colliding solids, J. Comput. Phys. 5, 517 (1970).
36. A. Harten, A high resolution schemes for hyperbolic conservation laws, J. Comput. Phys. 49, 357 (1983).
37. A. Harten and P. D. Lax, A random choice finite difference scheme for hyperbolic conservation laws, J. Numer. Anal. 18(2), 289 (1981).
38. M. J. Ivanov and A. N. Kraiko, Calculation of a transient (sub-super) nozzle flows, in Transactions of the Section for Numerical Methods in Gasdynamics of the Second International Meeting on the Gasdynamics of Explosion and Reacting Flows, Novosibirsk, Moscow, 1969 (Computational Center of AN SSSR, 1971), p. 3. [In Russian]
39. P. D. Lax, Weak solutions of nonlinear hyperbolic equations and their numerical computation, Comm. Pure Appl. Math. 7(1), 159 (1954).
40. G. P. Prokopov, On numerical implementation of the Vladimirov's variational principle, J. Comput. Math. Math. Phys. 8(1), 228 (1968). [In Russian]
41. G. P. Prokopov and M. V. Stepanova, The calculation of the axisymmetric interaction of the interaction of a shock wave with a blunt body at supersonic speeds, preprint, IPM AN SSSR, No. 72, 1974. [In Russian]
42. M. Sever, Estimate of the time rate of entropy dissipation for systems of conservation laws, J. Differential Equations 130, 127.
43. T. D. Taylor and B. S. Mason, Application of the unsteady numerical method of Godunov to computation of supersonic flows past bell shaped bodies, J. Comput. Phys. 5(3), 443 (1970).
44. B. Van Leer, Towards the ultimate conservative difference scheme. V. A second order sequel to Godunov's methods, J. Comput. Phys. 32, 101 (1979).
45. P. R. Woodward and P. Colella, The piecewise parabolic method (PPM) for gas dynamical calculations, J. Comput. Phys. 54, 174 (1984).