Work

Numerical solution of the mixed boundary value problem for the heat equation in two-dimensional domains of complex shape

Year: 2024

Type: article

Abstract: A finite-difference computational algorithm is proposed for solving a mixed boundary value problem for heat equation given in a two-dimensional domains of complex shape. To solve the problem, generalized curvilinear coordinates are used. The physical domain is mapped to the computational domain (unit square) in the space of generalized coordinates. The original problem is written in curvilinear coordinates and approximated on a uniform grid in the computational domain. The obtained results are mapped on a non-uniform boundary-fitted difference grid in the physical domain. The second-order approximations of mixed Neumann – Dirichlet boundary conditions are constructed. The results of computational experiments are presented. The second order of accuracy of the presented computational algorithm is confirmed.

Source: Proceedings of the National Academy of Sciences of Belarus Physics and Mathematics Series

DOI: 10.29235/1561-2430-2024-60-3-216-224

Authors: M M. Chuiko, O. M. Korolyova

Institutions: National Academy of Sciences of Belarus, Institute of Mathematics, Belarusian National Technical University

Language: English

Topic: Differential Equations and Numerical Methods

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4403233776

FWCI: 0.384

Cites: 15

Cited by: 1

Related to: 10