On a two-level element-free Galerkin method for incompressible fluid flow

2009 ◽  
Vol 59 (8) ◽  
pp. 1894-1904 ◽  
Author(s):  
Lin Zhang ◽  
Jie Ouyang ◽  
Xiao-Hua Zhang
Keyword(s):  
Fluid Flow ◽  
Incompressible Fluid ◽  
Galerkin Method ◽  
Incompressible Fluid Flow ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Element Free

scholarly journals Numerical Modeling of Stokes Flow in a Circular Cavity by Variational Multiscale Element Free Galerkin Method

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Ping Zhang ◽  
Xiaohua Zhang
Keyword(s):  
Galerkin Method ◽  
Stokes Flow ◽  
Simple Technique ◽  
Circular Cavity ◽  
Incompressible Fluid Flow ◽  
Element Free Galerkin Method ◽  
Variational Multiscale ◽  
Flow Problems ◽  
Element Free Galerkin ◽  
Element Free

The variational multiscale element free Galerkin method is extended to simulate the Stokes flow problems in a circular cavity as an irregular geometry. The method is combined with Hughes’s variational multiscale formulation and element free Galerkin method; thus it inherits the advantages of variational multiscale and meshless methods. Meanwhile, a simple technique is adopted to impose the essential boundary conditions which makes it easy to solve problems with complex area. Finally, two examples are solved and good results are obtained as compared with solutions of analytical and numerical methods, which demonstrates that the proposed method is an attractive approach for solving incompressible fluid flow problems in terms of accuracy and stability, even for complex irregular boundaries.

Application of an Element-free Galerkin Method to Water Wave Propagation Problems

2014 ◽  
Vol 60 (1-4) ◽  
pp. 87-105 ◽  
Author(s):  
Ryszard Staroszczyk
Keyword(s):  
Wave Propagation ◽  
Galerkin Method ◽  
Present Model ◽  
Free Surface Elevation ◽  
Element Free Galerkin Method ◽  
Plane Flow ◽  
Element Free Galerkin ◽  
Proposed Model ◽  
Sloping Bed ◽  
Element Free

Abstract The paper is concerned with the problem of gravitational wave propagation in water of variable depth. The problem is solved numerically by applying an element-free Galerkin method. First, the proposed model is validated by comparing its predictions with experimental data for the plane flow in water of uniform depth. Then, as illustrations, results of numerical simulations performed for plane gravity waves propagating through a region with a sloping bed are presented. These results show the evolution of the free-surface elevation, displaying progressive steepening of the wave over the sloping bed, followed by its attenuation in a region of uniform depth. In addition, some of the results of the present model are compared with those obtained earlier by using the conventional finite element method.

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