Geodesic
Monotonization of a family of implicit schemes
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 5, pp. 672-679 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An algorithm is proposed for monotonizing the correction of implicit schemes with high order of approximation of the space derivatives. The transport equation with one space variable is used as an example to prove that the corrected schemes are indeed monotone, provided that the time-step is restricted. 
@article{ZVMMF_1990_30_5_a3,
     author = {V. I. Pinchukov},
     title = {Monotonization of a~family of implicit schemes},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {672--679},
     year = {1990},
     volume = {30},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_5_a3/}
}
TY  - JOUR
AU  - V. I. Pinchukov
TI  - Monotonization of a family of implicit schemes
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 1990
SP  - 672
EP  - 679
VL  - 30
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_5_a3/
LA  - ru
ID  - ZVMMF_1990_30_5_a3
ER  - 
%0 Journal Article
%A V. I. Pinchukov
%T Monotonization of a family of implicit schemes
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 1990
%P 672-679
%V 30
%N 5
%U http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_5_a3/
%G ru
%F ZVMMF_1990_30_5_a3
V. I. Pinchukov. Monotonization of a family of implicit schemes. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 5, pp. 672-679. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_5_a3/

[1] Kolgan V. P., “Primenenie printsipa minimalnykh znachenii proizvodnoi k postroeniyu konechnoraznostnykh skhem dlya rascheta razryvnykh reshenii gazovoi dinamiki”, Uch. zap. TsAGI, 3:6 (1972), 68–77

[2] Boris J. P., Book D. L., “Flux-corrected transport. 1: Shasta, a fluid transport algorithm that works”, J. Comput. Phys., 11:1 (1973), 38–69 | DOI | Zbl

[3] Zalesak S. T., “Fully multydimensional flux-corrected transport algorithms for fluids”, J. Comput. Phys., 31:3 (1979), 335–362 | DOI | MR | Zbl

[4] Harten A., “A high resolution scheme for the computation of weak solutions of hiperbolic conservation laws”, J. Comput. Phys., 49 (1983), 357–393 | DOI | MR | Zbl

[5] Chakravarty S. R., The versatility and reliability of Euler solver based on high-accuracy TVD formulations, AIAA Paper No. 243, 1986

[6] Yee H. C., “Linearized form of implicit TVD schemes for multidimensional Euler and Navier-Stokes equations”, Internat. J. Comput. Math. Applic., 12A:4/5 (1986), 413–432 | DOI | MR | Zbl

[7] Sankin V. M., Levi B. I., Zaidel Ya. M., “Ispolzovanie raznostnykh skhem s peremennym shablonom dlya povysheniya tochnosti chislennogo resheniya uravnenii filtratsii”, Chisl. metody mekhan. sploshnoi sredy, 14, no. 3, ITPM SO AN SSSR, Novosibirsk, 1983, 156–170

[8] Zelinskii N. N., Sapozhnikov V. A., “Metod korrektirovki dlya postroeniya raznostnykh skhem zadach gazovoi dinamiki”, Chisl. metody mekhan. sploshnoi sredy, ITPM SO AN SSSR, Novosibirsk, 1983, 76–87 | MR

[9] Pinchukov V. I., Kvazimonotonnye skhemy povyshennoi tochnosti dlya resheniya zadach aerodinamiki, Preprint No 19-88, ITPM SO AN SSSR, Novosibirsk, 1988