scholarly journals A time discretization scheme based on integrated radial basis functions for heat transfer and fluid flow problems

2018 ◽  
Vol 74 (2) ◽  
pp. 498-518 ◽  
Author(s):  
T. T. V. Le ◽  
N. Mai-Duy ◽  
K. Le-Cao ◽  
T. Tran-Cong
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Radial Basis Functions ◽  
Time Discretization ◽  
Basis Functions ◽  
Discretization Scheme ◽  
Flow Problems ◽  
Radial Basis

Meshless Solution of 2D Fluid Flow Problems by Subdomain Variational Method Using MLPG Method With Radial Basis Functions (RBFs)

2006 ◽  
Author(s):  
Mohammad Haji Mohammadi ◽  
A. Shamsai
Keyword(s):  
Fluid Flow ◽  
Variational Method ◽  
Radial Basis Functions ◽  
Basis Functions ◽  
Quadrature Domain ◽  
Two Dimensional ◽  
Matrix Assembly ◽  
Flow Problems ◽  
Mlpg Method ◽  
Radial Basis

This paper deals with the solution of two-dimensional fluid flow problems using the truly meshless Local Petrov-Galerkin (MLPG) method. The present method is a truly meshless method based only on a number of randomly located nodes. Radial basis functions (RBF) are employed for constructing trial functions in the local weighted meshless local Petrov-Galerkin method for two-dimensional transient viscous fluid flow problems. No boundary integration is needed, no element matrix assembly is required and no special treatment is needed to impose the essential boundary conditions due to satisfaction of kronecker delta property in RBFs. Three different radial basis functions (RBFs), i.e. Multiquadrics (MQ), Gaussian (EXP) and Thin Plate Splines (TPS) are examined and the selection of their shape parameters is studied based on closed-form solutions. The effect of quadrature domain size is also studied. The variational method is used for the development of discrete equations. The results are obtained for a two-dimensional model problem using three RBFs and compared with the results of finite element and exact methods. Results show that the proposed method is highly accurate and possesses no numerical difficulties.

scholarly journals Taylor's Meshless Petrov-Galerkin Method for the Numerical Solution of Burger's Equation by Radial Basis Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Maryam Sarboland ◽  
Azim Aminataei
Keyword(s):  
Galerkin Method ◽  
Numerical Solution ◽  
Radial Basis Functions ◽  
Taylor Series Expansion ◽  
Time Discretization ◽  
Basis Functions ◽  
One Dimensional ◽  
Radial Basis ◽  
The One ◽  
Rms Errors

During the last two decades, there has been a considerable interest in developing efficient radial basis functions (RBFs) algorithms for solving partial differential equations (PDEs). In this paper, we introduce the Petrov-Galerkin method for the numerical solution of the one-dimensional nonlinear Burger equation. In this method, the trial space is generated by the multiquadric (MQ) RBF and the test space is generated by the compactly supported RBF. In the time discretization of the equation, the Taylor series expansion is used. This method is applied on some test experiments, and the numerical results have been compared with the exact solutions. The , , and root-mean-square (RMS) errors in the solutions show the efficiency and the accuracy of the method.

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