scholarly journals Application of Element Free Galerkin Method to Navier-Stokes Equation

2009 ◽  
Vol 3 (1) ◽  
pp. 95-115 ◽  
Author(s):  
Kazuki Ubukata ◽  
Mutsuto Kawahara
Keyword(s):  
Galerkin Method ◽  
Stokes Equation ◽  
Navier Stokes ◽  
Element Free Galerkin Method ◽  
Navier Stokes Equation ◽  
Element Free Galerkin ◽  
Element Free

scholarly journals Numerical Simulation of Nonlinear Flow Based on Element-Free Galerkin Method

2019 ◽  
Vol 37 (1) ◽  
pp. 70-79
Author(s):  
Junnan Meng ◽  
Guang Pan ◽  
Yonghui Cao ◽  
Linfeng Li ◽  
Zhencen Li ◽  
...  
Keyword(s):  
Galerkin Method ◽  
Flow Problem ◽  
Rectangular Domain ◽  
Nonlinear Flow ◽  
Penalty Function Method ◽  
Element Free Galerkin Method ◽  
Navier Stokes Equation ◽  
Essential Boundary Condition ◽  
Element Free Galerkin ◽  
Element Free

This paper focuses on the studying on some flow problems of nonlinear based on the Element Free Galerkin method. First the Navier-Stokes equation is discretized with the Galerkin method. The inertial term in the equation is discretized with the method of the speed term and direct deduction respectively. And the penalty function method is used to deal with the pressure and the essential boundary condition in the equation, and the discretization of two-dimensional N-S equation based on the EFG method is established. Then the flow problem of stationary nonlinear is studied. The flow problem of water in the rectangular domain squeezed by the two plates distributed above and below the calculated domain is studied with the method of EFG. The accuracy of the direct linear alternating interation method is shown by contrast with the analytical solution. Then the flow problem of unsteady nonlinear is studied. The θ-weighted method is used to discrete the time term of the N-S equation and the unsteady nonlinear solution matrix of EFG is established. The flow problem of flow around the square column is studied with the method of EFG and the flows under a series of low Reynolds are stimulated.

Element-Free Galerkin method for dynamic boundary flow problems

2020 ◽  
Vol 34 (24) ◽  
pp. 2050257
Author(s):  
Jun-Nan Meng ◽  
Guang Pan ◽  
Yong-Hui Cao
Keyword(s):  
Galerkin Method ◽  
Penalty Function Method ◽  
Element Free Galerkin Method ◽  
Navier Stokes Equation ◽  
Essential Boundary Condition ◽  
Boundary Flow ◽  
Flow Problems ◽  
Element Free Galerkin ◽  
Dynamic Boundary ◽  
Element Free

This paper focuses on the study of dynamic boundary flow problems based on the Element-Free Galerkin method. First, Navier–Stokes equation is discretized with the Galerkin method. The inertial term in the equation is discretized with the method of the speed term and direct deduction, respectively. The penalty function method is used to deal with the pressure and the essential boundary condition in the equation, and the discretization of two-dimensional N–S equation based on the EFG method is established. However, irregular changes in boundary conditions are often encountered in practical fluid problems. For example, the motion of flapping-foil is not uniform relative to the flow. In this paper, numerical experiments are carried out for the flow problems with non-uniform boundary motions. The problem which a plate with non-uniform drag movement above a rectangular tank filled with water is studied with the EFG method. The feasibility of the proposed algorithm is verified by comparison with the FEM method. Then, the procession of the water in the tank is stimulated. In the end, the influence of different calculation time steps on the accuracy of the solution is discussed.

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.

Implementing of Displacement Boundary Conditions of Element-Free Galerkin Method and its Applications Used in Fracture Mechanics

2012 ◽  
Vol 629 ◽  
pp. 606-610
Author(s):  
Gang Cheng ◽  
Wei Dong Wang ◽  
Dun Fu Zhang
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Reproducing Kernel ◽  
Particle Method ◽  
Transformation Method ◽  
Computational Method ◽  
Reproducing Kernel Particle Method ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Element Free

The main draw back of the Moving Least Squares (MLS) approximate used in element free Galerkin method (EFGM) is its lack the property of the delta function. To alleviate difficulties in the treatment of essential boundary conditions in EFGM, the local transformation method and the boundary singular weight method, which are used in the reproducing kernel particle method, is combined with the element free Galerkin method. The computational method is given to analyze the stress intensity factors and the numerical simulation of crack propagation of two-dimentional problems of the elastic fracture analysis. The application examples reveal the effectiveness and feasibility of the present methods.

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