Simulation of dynamic processes in spherical and cylindrical shells
DOI:
https://doi.org/10.7242/1999-6691/2010.3.4.36Keywords:
mathematical modeling, difference scheme, entropy generation, von Neumann-Richtmyer viscosity, Kuropatenko method, converging and diverging shells, perfect plasticityAbstract
Differences between the results obtained in the numerical simulation of dynamic processes that occur in continua and the results obtained in physical experiments come from an error of three types: an error in the physical model (∆Ph), an error in the mathematical model (∆M), and a measurement error (∆m). The paper focuses on the comparison of ∆Mand ∆Phсonsidering a medium placed in a spherically symmetric shell as an example. It is shown that within a certain velocity range the energy dissipation defined by an error in a finite-difference approximation may exceed the energy dissipation generated by a perfect plasticity model.
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Kuropatenko V.F. O tocnosti vycislenia entropii v raznostnyh shemah dla uravnenij gazovoj dinamiki. // Cislennye metody mehaniki splosnoj sredy: sb. nauc. tr. - Novosibirsk, 1978. - T. 9, No 7. - S. 49-59.
Kuropatenko V.F. Svaz’ divergentnosti s konservativnost’u raznostnyh shem dla uravnenij gazovoj dinamiki: Prepr. No 192 / AN SSSR. In-t prikladnoj matematiki. - M., 1982. - 26 s.
Kuropatenko V.F. Lokal’naa konservativnost’ raznostnyh shem dla uravnenij gazovoj dinamiki // Z. vycisl. matematiki i matem. fiziki.- 1985. - T. 25, No 8. - S. 1176-1188.
Kuropatenko V.F. Mezomehanika odnokomponentnyh i mnogokomponentnyh materialov // Fizic. mezomehanika.- 2001. - T. 4, No 3. - S. 49-55.
Kuropatenko V.F. Ob odnoj modeli uprugoplastceskogo deformirovania // Cislennye metody mehaniki splosnoj sredy: sb. nauc. tr. - Novosibirsk, 1973. - T. 4, No 5. - S. 189-194.
Glusak B.L., Kuropatenko V.F., Novikov S.A. Issledovanie procnosti materialov pri dinamiceskih nagruzkah. - Novosibirsk: Nauka, 1992. - 393 s.
Neumann J., Richtmyer R. A method for the numerical calculation of hydrodynamical shocks // J. Appl. Phys. - 1950. - V. 21, N. 3. - P. 232-237. DOI
Rihtmaejr R., Morton K.. Raznostnye metody resenia kraevyh zadac. - M.: Mir, 1972. - 418 s.
Rihtmajer R. Raznostnye metody resenia kraevyh zadac. - M.: Mir, 1960. - 262 s.
Kuropatenko V.F. Metod rasceta udarnyh voln // DAN SSSR. - 1960. - T. 133, No 4. - S. 771-772.
Alekseeva T.N., Kuropatenko V.F. Adaptivnyj bezuslovno ustojcivyj raznostnyj metod rasceta melkih neodnorodnostej gidrodinamiceskogo potoka // Cislennye metody mehaniki splosnoj sredy: sb. nauc. tr. - Novosibirsk, 1981. - T. 12, No 4. - S. 3-14.
Kuropatenko V.F., Kovalenko G.V., Kuznecova V.I., Mihajlova G.I., Sapoznikova G.N. Kompleks programm <> i neodnorodnyj raznostnyj metod dla rasceta neustanovivsihsa dvizenij szimaemyh splosnyh sred. Cast’ 1. Neodnorodnyj raznostnyj metod // Voprosy atomnoj nauki i tehniki. Ser. Matematiceskoe modelirovanie fiziceskih processov. - 1989. - Vyp. 2. - S. 9-17.
Uilkins M.L. Rascet uprugo-plasticeskih tecenij // Vycislitel’nye metody v gidrodinamike / Pod red. B. Oldera, S. Fernbaha, M. Rotenberga. - M.: Mir, 1967. - S. 212-263.
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