NUMERICAL SIMULATION OF FLOWS WITH SHOCKS
DOI:
https://doi.org/10.7242/1999-6691/2008.1.1.5Keywords:
Abstract
Using the non-monotone Lax-Wendroff scheme, it is shown that the reduction in the accuracy (to the order not higher than the first) of TVD schemes in unsteady shock calculations is mainly due to decreasing smoothness of the difference flux operators, which is related to the use of minimax procedures. It is shown theoretically and numerically that the Lax-Wendroff scheme, in contrast to its TVD modifications, approximates with the second order the Hugoniot conditions on the fronts of unsteady shocks. At the same time, the Lax-Wendroff scheme reduces the order of convergence to the first in the vicinity of the point of gradient catastrophe, where the shock is forming. Such reduction in the order of convergence is related to the fact that this scheme, in contrast to the compact schemes with high-order divergent artificial viscosity, has only the first order of weak approximation for discontinuous solutions.
Downloads
References
Stoker Dz. Dz. Volny na vode. - M.: IL, 1959. - 618 c.
Rozdestvenskij B.L., Anenko N.N. Sistemy kvazilinejnyh uravnenij i ih prilozenia k gazovoj dinamike. - M.: Nauka, 1978. - 688 c.
Kulikovskij A.G., Pogorelov N.V., Semenov A.U. Matematiceskie voprosy cislennogo resenia giperboliceskih sistem uravnenij. - M.: Fizmatlit, 2001. - 608 c.
Harten A. High resolution schemes for hyperbolic conservation laws // J. Comp. Phys. - 1983. - V. 49. -P. 357-393. DOI
Lax P., Wendroff B. Systems of conservation laws // Commun. Pure Appl. Math. - 1960. - V. 13. - P. 217-237. DOI
Ostapenko V.V. O shodimosti raznostnyh shem za frontom nestacionarnoj udarnoj volny // Z. vycisl. matem. i matem. fiz. - 1997. - T. 37, No 10. - S. 1201-1212.
Ostapenko V.V. O konecno-raznostnoj approksimacii uslovij Gugonio na fronte udarnoj volny, rasprostranausejsa s peremennoj skorost’u // Z. vycisl. matem. i matem. fiz. - 1998. - T. 38, No 8. - S. 1355-1367.
Ostapenko V.V. O slaboj shodimosti na razryvnyh reseniah TVD shemy Hartena vtorogo poradka approksimacii. // Vycislitel’nye tehnologii. - Novosibirsk, 1997. - T. 2, No 5. - S. 57-65.
Ostapenko V.V. O postroenii raznostnyh shem povysennoj tocnosti dla skvoznogo rasceta nestacionarnyh udarnyh voln // Z. vycisl. matem. i matem. fiz. - 2000. - T. 40, No 12. - S. 1857-1874.
Downloads
Published
Issue
Section
License
Copyright (c) 2008 Computational Continuum Mechanics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.