Fluid flow modeling in channel using meshless local Petrov-Galerkin (MLPG) method by Radial Basis Function

In this study first the meshless local Petrov-Galerkin (MLPG) method by Radial Basis Function (RBF) has been explained entirely. In this way the governing channel flow expression that is based on the Laplace equation is expanded. In MLPG method, the problem domain is represented by a set of arbitrarily distributed nodes and Quadrature radial basis function is used for field function approximation and local integration is used to calculate the integrals. In the following, MLPG method is verified by exact solution in a numerical example. The Results show that MLPG method presented high accuracy and capability for solving the governing equation of the problem. Finally the velocity field is approximated in middle of nodes by RBF (MatLab code was adopted) in the uniform flow in a sloped channel problem. The MLPG results are compared with the isogeometric analysis (IA) method in the tutorial numerical example of Fluid flow modeling in channel, the velocity contours is detected, and their accuracy is demonstrated by means of several examples. The results showed good conformity compared to available analytical solution. The obtain results explain that Application of meshless method in Fluid flow modeling in channel show the applicability and efficiency of the meshless local Petrov-Galerkin method by Radial Basis Function method.