views: 1485
Readers community rating: votes 0
1. Godunov S.K., Zabrodin A.V., Ivanov M.Ya., Krajko A.N., Prokopov G.P. Chislennoe reshenie mnogomernykh zadach gazovoj dinamiki. M.: Nauka, 1976. S. 100–110.
2. Godunov S.K. Raznostnyj metod chislennogo rascheta razryvnykh reshenij uravnenij gidrodinamiki // Matem. sbornik. 1959. № 47. Vyp. 3. S. 271–306.
3. Neumann J., Richtmyer R. A method for the numerical calculation of hydrodynamic shocks // J. Appl. Phys. 1950. 21. № 3. P. 232–237.
4. Kulikovskij A.G., Pogorelov N.V., Semenov A.Yu. Matematicheskie voprosy chislennogo resheniya giperbolicheskikh sistem uravnenij. M.: Fizmatlit, 2001.
5. Safronov A.V. Kineticheskie interpretatsii chislennykh skhem dlya uravnenij gazodinamiki. Fiziko-khimicheskaya kinetika v gazovoj dinamike. 2009. № 8. S. 7.
6. Friedrichs K.O. Symmetric hyperbolic linear differential equations// Comm. Pure Appl. Math. 1954. 7. R. 345.
7. Lax P.D. Weak solutions of nonlinear hyperbolic equations and their numerical computation// Comm. Pure Appl. Math. 1954. 7. R. 159.
8. Rusanov V.V. Raschet vzaimodejstviya nestatsionarnykh udarnykh voln s prepyatstviyami// Zh. vychisl. matem. i matem. fiz. 1961. T. 1. № 2. S. 267–279.
9. Harten A., Lax P.D., Van Leer B. On upstream differencing and Godunov-type schemes for hyperbolic conservation laws // SIAM Review. 1981. 25. № 1. R. 35–61.
10. Roe P.L. Approximate Riemann solvers, parameter vectors, and difference schemes // J. Comput. Phis. 1981. 43. № 2. R. 357–372.
11. Kholodov A.S. O postroenii raznostnykh skhem s polozhitel'noj approksimatsiej dlya uravnenij giperbolicheskogo tipa // Zh. vychisl. matem. i matem. fiz. 1978. T. 18. № 6. S. 1476–1492.
12. Enguist B., Osher S. One-sided difference approximation for nonlinear conservation laws//Math. Comp. 1981. 36. R. 321–351.
13. Osher S. Riemann solvers, the entropy condition, and difference approximations//SIAM J. Numer. Analys. 1984. 21(2). R. 217–235.
14. Toro E.F., Spruce M., Speares S. Restoration of the Contact Surface in the HLL Riemann Solver // Shock Saves. 1994. № 4. R. 25–34.
15. Kolgan V.P. Primenenie printsipa minimal'nykh proizvodnykh k postroeniyu konechno- raznostnykh skhem dlya rascheta razryvnykh reshenij gazovoj dinamiki // Uchenye zapiski TsAGI. 1972. 3. № 6. R. 68–77.
16. Toro E. F. Riemann solvers and numerical methods for fluid dynamics. Berlin: Springer second Ed. June, 1999.
17. LeVeque R.J. Finite volume methods for hyperbolic problems. cambridge texts in applied mathematics. 2004.
18. Stein E., de Borst R., Hughes T. Encyclopedia of computational mechanics. London: John Wiley & Sons., 2004.
19. Bram van Leer. REVIEW ARTICLE. Upwind and high-resolution methods for compressible flow: From Donor Cell to Residual-Distribution Schemes// Commun. Comput. Phys. April 2006. V. 1. № 2. P. 192–206.
20. Berger M., Aftosmis M.J. Analysis of slope limiters on irregular grids. AIAA Paper 2005–0490. 2005.