Abstract: We perform a comparative analysis of the accuracy of second-order TVD (Total Variation Diminishing), third-order RBM (Rusanov–Burstein–Mirin), and fifth-order in space and third-order in time A-WENO (Alternative Weighted Essentially Non-Oscillatory) difference schemes for solving a special Cauchy problem for shallow water equations with discontinuous initial data. The exact solution of this problem contains a centered rarefaction wave, but does not contain a shock wave. It is shown that in the centered rarefaction wave and its influence area, the solutions of these three schemes converge with different orders to different invariants of the exact solution. This leads to a decrease in the accuracy of these schemes when they used to calculate the vector of base variables of the considered Cauchy problem. The P-form of the first differential approximation of the difference schemes is used for theoretical justification of these numerical results.

Cite: Ostapenko V.V. , Polunina E.I. , Khandeeva N.A.
On the accuracy of calculating invariants in centered rarefaction waves and in their influence area
Doklady Mathematics. 2024. V.110. N349-356. P.8. DOI: 10.1134/S1064562424702211 WOS Scopus РИНЦ OpenAlex

Original: Остапенко В.В. , Полунина Е.И. , Хандеева Н.А.
О точности вычисления инвариантов внутри центрированных волн разрежения и в областях их влияния
ДОКЛАДЫ РОССИЙСКОЙ АКАДЕМИИ НАУК. МАТЕМАТИКА, ИНФОРМАТИКА, ПРОЦЕССЫ УПРАВЛЕНИЯ. 2024. Т.518. №1. С.65-74. DOI: 10.31857/s2686954324040109 РИНЦ OpenAlex

Dates:

Submitted:	Mar 27, 2024
Accepted:	Jul 23, 2024
Published print:	Oct 20, 2024

Identifiers:

Web of science:	WOS:001336761400006
Scopus:	2-s2.0-85207038575
Elibrary:	74958549
OpenAlex:	W4403572622

Citing: Пока нет цитирований

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