Localized Singular Boundary Method for Solving the Convection–diffusion Equation With Variable Velocity Field

Abstract

This paper focuses on deriving the local variant of the singular boundary method (SBM) to solve the convection-diffusion equation. Adopting the combination of an SBM and finite collocation, one obtains the localized variant of SBM. Unlike the global variant, local SBM leads to a sparse matrix of the resulting system of equations, making it much more efficient to solve large-scale tasks. It also allows solving velocity vector variable tasks, which is a problem with global SBM. The article presents the steady numerical example for the convection-diffusion problem with variable velocity field and examines the dependence of the accuracy of the solution on the nodal grid's density and the subdomain's size.