Fast multipole singular boundary method for Stokes flow problems

2018 ◽  
Vol 146 ◽  
pp. 57-69 ◽  
Author(s):  
Wenzhen Qu ◽  
Wen Chen ◽  
Zhuojia Fu ◽  
Yan Gu
Keyword(s):  
Stokes Flow ◽  
Singular Boundary ◽  
Fast Multipole ◽  
Flow Problems ◽  
Boundary Method ◽  
Singular Boundary Method

Solution of Two-Dimensional Stokes Flow Problems Using Improved Singular Boundary Method

2015 ◽  
Vol 7 (1) ◽  
pp. 13-30 ◽  
Author(s):  
Wenzhen Qu ◽  
Wen Chen
Keyword(s):  
Fundamental Solution ◽  
Stokes Flow ◽  
Singular Boundary ◽  
Two Dimensional ◽  
Intensity Factors ◽  
Flow Problems ◽  
Modified Method ◽  
Boundary Method ◽  
Singular Boundary Method

AbstractIn this paper, an improved singular boundary method (SBM), viewed as one kind of modified method of fundamental solution (MFS), is firstly applied for the numerical analysis of two-dimensional (2D) Stokes flow problems. The key issue of the SBM is the determination of the origin intensity factor used to remove the singularity of the fundamental solution and its derivatives. The new contribution of this study is that the origin intensity factors for the velocity, traction and pressure are derived, and based on that, the SBM formulations for 2D Stokes flow problems are presented. Several examples are provided to verify the correctness and robustness of the presented method. The numerical results clearly demonstrate the potentials of the present SBM for solving 2D Stokes flow problems.

A wideband fast multipole accelerated singular boundary method for three-dimensional acoustic problems

2018 ◽  
Vol 206 ◽  
pp. 82-89 ◽  
Author(s):  
Wenzhen Qu ◽  
Changjun Zheng ◽  
Yaoming Zhang ◽  
Yan Gu ◽  
Fajie Wang
Keyword(s):  
Three Dimensional ◽  
Singular Boundary ◽  
Fast Multipole ◽  
Boundary Method ◽  
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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