Solution of the mixed boundary problem for the Poisson equation on two-dimensional irregular domains-Reference-Cited by-同舟云学术

Solution of the mixed boundary problem for the Poisson equation on two-dimensional irregular domains

Published:2023-06-29 Issue:2 Volume:20 Page:111-120
ISSN:2617-6963
Container-title:Informatics
language:
Short-container-title:Informatika (Minsk)

Author:

Chuiko M. M.¹,Korolyova O. M.²

Affiliation:

1. Institute of Mathematics of the National Academy of Sciences of Belarus

2. Belarusian National Technical University

Abstract

Objectives. A finite-difference computational algorithm is proposed for solving a mixed boundary-value problem for the Poisson equation given in two-dimensional irregular domains.Methods. 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 non-uniform boundary-fitted difference grid in the physical domain.Results. The second order approximations of mixed Neumann-Dirichlet boundary conditions for the Poisson equation in the space of generalized curvilinear coordinate are constructed. To increase the order of Neumann condition approximations, an approximation of the Poisson equation on the boundary of the domain is used.Conclusions. To solve a mixed boundary value problem for the Poisson equation in two-dimensional irregular domains, the computational algorithm of second-order accuracy is constructed. The generalized curvilinear coordinates are used. The results of numerical experiments, which confirm the second order accuracy of the computational algorithm, are presented.

Publisher

United Institute of Informatics Problems of the National Academy of Sciences of Belarus

Subject

General Earth and Planetary Sciences,General Environmental Science

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