scholarly journals Singular boundary method for heat conduction problems with certain spatially varying conductivity

2015 ◽  
Vol 69 (3) ◽  
pp. 206-222 ◽  
Author(s):  
Xing Wei ◽  
Wen Chen ◽  
Bin Chen ◽  
Linlin Sun
Keyword(s):  
Heat Conduction ◽  
Singular Boundary ◽  
Boundary Method ◽  
Spatially Varying ◽  
Singular Boundary Method

The Local Singular Boundary Method for Solution of Two-Dimensional Advection–Diffusion Equation

2021 ◽  
pp. 2150041
Author(s):  
Karel Kovářík ◽  
Juraj Mužík
Keyword(s):  
Diffusion Equation ◽  
Large Scale ◽  
Sparse Matrix ◽  
Singular Boundary ◽  
Tracer Transport ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Boundary Method ◽  
Local Variant ◽  
Singular Boundary Method

This work focuses on the derivation of the local variant of the singular boundary method (SBM) for solving the advection-diffusion equation of tracer transport. Localization is based on the combination of SBM and finite collocation. 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. This paper compares the results on several examples for the steady and unsteady variant of the advection-diffusion equation and also examines the dependence of the accuracy of the solution on the density of the nodal grid and the size of the subdomain.

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