Work

Stability of the DuFort–Frankel Scheme on Unstructured Grids

Year: 2025

Type: article

Abstract: The DuFort–Frankel scheme was introduced in the 1950s to solve parabolic equations, and has been widely used ever since due to its stability and explicit nature. However, for over seven decades, its application has been limited to Cartesian grids. In this work, we propose a generalization of the DuFort–Frankel scheme that could be applied to arbitrary unstructured grids. Specifically, we focus on Voronoi grids in both 2D and 3D, and use the finite volume method for spatial discretization. Additionally, we present a proof of its stability based on the analysis of the spectrum of the amplification matrix, along with numerical examples.

Source: Computation

DOI: 10.3390/computation13100246

Authors: Nikolay Yavich, Evgeny Burnaev, Vladimir Vanovskiy

Institutions: Skolkovo Institute of Science and Technology, AIRI - Artificial Intelligence Research Institute

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,172

Funder: Russian Science Foundation