Applying Richardson’s Extrapolation to Improve the Accuracy of Shock Capturing Combined Schemes

Applying Richardson’s Extrapolation to Improve the Accuracy of Shock Capturing Combined Schemes Full article

Journal

Mathematical Models and Computer Simulations
ISSN: 2070-0482

Output data

Year: 2026, Volume: 18, Number: 4, Pages: 538-546 Pages count : 9 DOI: 10.1134/s2070048226700249

Tags

high accurate schemes, shallow water equations, Richardson’s extrapolation, combined schemes

Authors

Kovyrkina O.A. ¹ , Kolotilov V.A. ¹ , Ostapenko V.V. ¹ , Khandeeva N.A. ¹

Affiliations

1	Lavrentiev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia

A numerical algorithm that employs Richardson’s extrapolation to improve the accuracy of combined schemes including the solution of Cauchy problems with discontinuous initial data for systems of hyperbolic differential equations is proposed. Richardson’s extrapolation is applied for a numerical solution obtained by the basic scheme included in the combined scheme in the regions where there are no noticeable nonphysical oscillations. Constraints on the absolute value of the numerical solution errors obtained by Richardson’s formula is used as a criterion for identifying the areas where the internal NFC (Nonlinear Flux Correction) scheme should be applied for smoothing out the oscillations arising in calculations by the basic QL (Quasi-Linear) scheme. The new numerical algorithm was tested on two Cauchy problems with discontinuous initial data for one-dimensional shallow water equations.

Kovyrkina O.A. , Kolotilov V.A. , Ostapenko V.V. , Khandeeva N.A.
Applying Richardson’s Extrapolation to Improve the Accuracy of Shock Capturing Combined Schemes
Mathematical Models and Computer Simulations. 2026. V.18. N4. P.538-546. DOI: 10.1134/s2070048226700249 Scopus OpenAlex

Submitted:	Oct 7, 2025
Accepted:	Dec 15, 2025
Published print:	Aug 21, 2026

≡ Scopus:	2-s2.0-105047862346
≡ OpenAlex:	W7203862134