On implementation of monotonicity preserving reconstruction of variables in EBR schemes

M. V. Abakumov^a, I. V. Abalakin^b, V. A. Isakov^a, T. K. Kozubskaya<sup>b

a</sup> Lomonosov Moscow State University
^b Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow

Abstract: The paper considers a vertex-centered scheme built using monotonicity-preseving edge-based reconstruction of variables for solving the Euler equations on unstructured meshes. In contrast to a similar scheme based on quasi-one-dimensional WENO-reconstructions, the new method provides less dissipation and as a result higher accuract of numerical solution. This property is demonstrated by solving two-dimensional model problems on uniform, quasi-uniform and stretching triangular meshes.

Keywords: Euler equations, monotonicity preserving scheme, EBR scheme, edge oriented reconstruction, WENO-reconstruction, unstructured mesh.

Received: 28.04.2025
Revised: 25.06.2025
Accepted: 30.06.2025

DOI: 10.20948/mm-2026-01-03