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.

Singular Boundary Method for Various Exterior Wave Applications

2015 ◽  
Vol 12 (02) ◽  
pp. 1550011 ◽  
Author(s):  
Zhuo-Jia Fu ◽  
Wen Chen ◽  
Ji Lin ◽  
Alexander H.-D. Cheng
Keyword(s):  
Fundamental Solution ◽  
Helmholtz Equation ◽  
Laplace Equation ◽  
International Workshop ◽  
Fundamental Solutions ◽  
Singular Boundary ◽  
Intensity Factors ◽  
Trefftz Method ◽  
Boundary Method ◽  
Singular Boundary Method

This paper presents an improved singular boundary method (ISBM) to various exterior wave applications. The SBM is mathematically simple, easy-to-program, meshless and introduces the concept of source intensity factors to eliminate the singularity of the fundamental solutions. In this study, we first derive the source intensity factors of the exterior Helmholtz equation by means of the source intensity factors of the exterior Laplace equation due to the same order of the singularities on their fundamental solutions. The source intensity factors of the exterior Laplace equation can be determined using the reference technique [Chen, W. and Gu, Y. [2011] "Recent advances on singular boundary method," Joint international workshop on Trefftz method VI and method of fundamental solution II, Taiwan]. Numerical illustrations demonstrate the efficiency and accuracy of the proposed scheme on four benchmark exterior wave examples.

scholarly journals The singular boundary method for two-dimensional static thermoelasticity analysis

2016 ◽  
Vol 72 (11) ◽  
pp. 2716-2730 ◽  
Author(s):  
Bin Chen ◽  
Wen Chen ◽  
Alexander H.D. Cheng ◽  
Xing Wei
Keyword(s):  
Singular Boundary ◽  
Two Dimensional ◽  
Boundary Method ◽  
Singular Boundary Method

scholarly journals Numerical Investigation on Convergence Rate of Singular Boundary Method

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Junpu Li ◽  
Wen Chen ◽  
Zhuojia Fu
Keyword(s):  
Short Communication ◽  
Convergence Rates ◽  
Fundamental Solutions ◽  
Benchmark Problems ◽  
Singular Boundary ◽  
Intensity Factors ◽  
Collocation Points ◽  
Boundary Method ◽  
Collocation Scheme ◽  
Singular Boundary Method

The singular boundary method (SBM) is a recent boundary-type collocation scheme with the merits of being free of mesh and integration, mathematically simple, and easy-to-program. Its essential technique is to introduce the concept of the source intensity factors to eliminate the singularities of fundamental solutions upon the coincidence of source and collocation points in a strong-form formulation. In recent years, several numerical and semianalytical techniques have been proposed to determine source intensity factors. With the help of these latest techniques, this short communication makes an extensive investigation on numerical efficiency and convergence rates of the SBM to an extensive variety of benchmark problems in comparison with the BEM. We find that in most cases the SBM and BEM have similar convergence rates, while the SBM has slightly better accuracy than the direct BEM. And the condition number of SBM is lower than BEM. Without mesh and numerical integration, the SBM is computationally more efficient than the BEM.

Analysis of Two-Dimensional Thin Structures (From Micro- to Nano-Scales) Using the Singular Boundary Method

2015 ◽  
Vol 7 (5) ◽  
pp. 597-609 ◽  
Author(s):  
Dejian Shen ◽  
Yan Gu
Keyword(s):  
Smart Materials ◽  
Boundary Element Methods ◽  
Singular Boundary ◽  
Two Dimensional ◽  
Thin Structures ◽  
Micro Electro Mechanical Systems ◽  
Structural Problems ◽  
Boundary Method ◽  
Potential Applications ◽  
Singular Boundary Method

AbstractThis study investigates the applicability of the singular boundary method (SBM), a recent developed meshless boundary collocation method, for the analysis of two-dimensional (2D) thin structural problems. The troublesome nearly-singular kernels, which are crucial in the applications of SBM to thin shapes, are dealt with efficiently by using a non-linear transformation technique. Promising SBM results with only a small number of boundary nodes are obtained for thin structures with the thickness-to-length ratio is as small as 1E-9, which is sufficient for modeling most thin layered coating systems as used in smart materials and micro-electro-mechanical systems. The advantages, disadvantages and potential applications of the proposed method, as compared with the finite element (FEM) and boundary element methods (BEM), are also discussed.

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