| Popis: |
The meshless local Petrov-Galerkin method with weighting function of unit has been applied to the solution of convection-diffusion and fluid problems. In this method, a collection of points is distributed in the computational domain. Subsequently, a control volume is generated around each of the points. The control volumes, which possess simple shapes, intersect each other and overlap. Substituting the interpolation of the dependant variable with each control volume into the weak form of the differential equation and using unity as the test function yields the discretized equation of a control volume. The method is applied to benchmark examples, such as two-dimensional convection-diffusion and liddriven cavity flow. A variation of the SUPG technique based on adding optimal balancing diffusion along the streamlines is employed to obtain stable solutions for convectivedominated cases. The results are compared with analytical solutions and the numerical results obtained by other methods. The L 2 -norm of the error as a function of the distance between the points is presented for some cases and thus the rate of convergence of the method is established. The results of this study show that the proposed method is indeed very promising for solving a variety of heat transfer and fluid flow problems. |
