MATHEMATICS

On a grid-characteristic second order scheme for systems of hyperbolic equations with piecewise constant coefficients on non-fitted meshes

K. E. Shilnikov^ab, N. I. Khokhlov^bcd, I. B. Petrov<sup>b

a</sup> National Engineering Physics Institute "MEPhI", Moscow
^b Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region
^c National Research Centre "Kurchatov Institute", Moscow
^d Innopolis University, Kazan, Moscow, Russia

Abstract: In this paper, a novel approach to increasing the accuracy of the grid-characteristic method in the area of a coefficient jump for cases of an non-fitted computational grid is presented.

Keywords: grid-characteristic method, immersed interface, non-fitted meshes.

UDC: 519.633

Received: 23.07.2025
Revised: 11.09.2025
Accepted: 12.09.2025

DOI: 10.7868/S3034504925050123

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