Combined monotone bicompact scheme of higher order accuracy in domains of influence of nonstationary shock waves. (English. Russian original) Zbl 07424598
Dokl. Math. 101, No. 3, 239-243 (2020); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 492, 79-84 (2020).
Summary: A new method is proposed for constructing a combined shock-capturing scheme that monotonically localizes shock wave fronts and, at the same time, has increased accuracy in smoothness regions of calculated generalized solutions. In this method, the solution of the combined scheme is constructed using monotonic solutions of a bicompact scheme of the first order of approximation in time and the fourth order of approximation in space obtained for different time steps in the entire computational domain. This construction method is much simpler than a previously proposed method. Test calculations are presented that demonstrate the advantages of the new scheme compared to the WENO5 scheme of the fifth order of approximation in space and the third order of approximation in time.
References:
| [1] | Ostapenko, V. V., Comput. Math. Math. Phys., 40, 1784-1800 (2000) · Zbl 1001.76069 |
| [2] | Ladonkina, M. E.; Neklyudova, O. A.; Ostapenko, V. V.; Tishkin, V. F., Comput. Math. Math. Phys., 58, 1344-1353 (2018) · Zbl 1412.76056 · doi:10.1134/S0965542518080122 |
| [3] | Kovyrkina, O. A.; Ostapenko, V. V., Dokl. Math., 97, 77-81 (2018) · Zbl 1393.65014 · doi:10.1134/S1064562418010246 |
| [4] | Ladonkina, M. E.; Nekliudova, O. A.; Ostapenko, V. V.; Tishkin, V. F., Dokl. Math., 100, 519-524 (2019) · Zbl 1444.76085 · doi:10.1134/S106456241906005X |
| [5] | Ostapenko, V. V.; Khandeeva, N. A., Dokl. Math., 64, 197-201 (2019) |
| [6] | Rogov, B. V., Dokl. Math., 86, 582-586 (2012) · Zbl 1255.65161 · doi:10.1134/S1064562412040448 |
| [7] | Rogov, B. V.; Bragin, M. D., Dokl. Math., 96, 339-343 (2017) · Zbl 1376.65123 · doi:10.1134/S1064562417040081 |
| [8] | Mikhailovskaya, M. N.; Rogov, B. V., Comput. Math. Math. Phys., 52, 578-600 (2012) · Zbl 1274.35235 · doi:10.1134/S0965542512040124 |
| [9] | Rusanov, V. V., Dokl. Akad. Nauk SSSR, 180, 1303-1305 (1968) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
