A local domain BEM for solving transient convection-diffusion-reaction problems

The convection-diffusion-reaction (CDR) equation has been extensively used to simulate a variety of phys-ical phenomena. A robust numerical method for solving linear CDR problems is the Boundary Element Method (BEM). However, the conventional BEM leads to dense coefficient matrices and as a result the memory requirements grow quadratically with respect to the number of degrees of freedom. In this work, a Local Domain BEM (LD-BEM) for solving the transient CDR equation with a constant velocity field is presented. The domain of interest is fragmented into small subdomains and the integral repre-sentation of the solution is considered separately for each of the subdomains. Eliminating the fluxes at all subdomain interfaces, the proposed LD-BEM leads to sparse linear system coefficient matrices and a reduced number of degrees of freedom. Eight numerical examples are solved to assess the efficiency and accuracy of the proposed method.(c) 2022 Elsevier Ltd. All rights reserved.

Automated summary

This paper presents a numerical method, called Local Domain Boundary Element Method (LD-BEM), for solving the convection-diffusion-reaction (CDR) equation. The method divides the domain of interest into small subdomains and considers the integral representation of the solution separately for each subdomain. By eliminating the fluxes at the subdomain interfaces, the proposed LD-BEM leads to sparse linear system coefficient matrices and reduced degrees of freedom.