On the accuracy of finite-difference schemes in smooth parts of calculated weak solutions

On the accuracy of finite-difference schemes in smooth parts of calculated weak solutions Full article

Conference

INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2019, ICNAAM 2019
23-28 Sep 2019 , Rhodes

Source

AIP CONFERENCE PROCEEDINGS
Compilation, American Institute of Physics – AIP. America.2020.

Output data

Year: 2020, Volume: 2293, Article number : 370002, Pages count : 4 DOI: 10.1063/5.0026831

Authors

Kovyrkina Olyana ¹ , Ostapenko Vladimir ^1,2

Affiliations

1	Lavrentyev Institute of Hydrodynamics of SB RAS, Lavrentyev avenue, 15, Novosibirsk, 630090, Russia
2	Novosibirsk State University, Pirogova street, 2, Novosibirsk, 630090, Russia

Funding (1)

Российский научный фонд

16-11-10033-Продление

We consider explicit two-layer in time finite-difference schemes intended for the shock capturing calculation of weak solutions of quasilinear hyperbolic systems of conservation laws. The accuracy of these schemes in the areas of smoothness of the calculated weak solution is studied. It is shown that in these regions the errors of the difference solution approximately satisfy the hyperbolic system of differential equations, which have characteristics fields that are the same as the approximated system of conservation laws. This implies that in the shock influence region the convergence rate of the difference solution essentially depends on the accuracy with which the scheme approximates the Hugoniot conditions at the shock front. This explains the decrease in the convergence order of NFC (Nonlinear Flux Correction) schemes in the shock influence regions.

Kovyrkina O. , Ostapenko V.
On the accuracy of finite-difference schemes in smooth parts of calculated weak solutions
In compilation AIP CONFERENCE PROCEEDINGS. – American Institute of Physics – AIP., 2020. DOI: 10.1063/5.0026831 Scopus РИНЦ OpenAlex

Scopus:	2-s2.0-85098004267
Elibrary:	45059596
OpenAlex:	W3107726839

Пока нет цитирований