Numerical Analysis of Seepage in Steady and Transient Flow State by the Radial Basis Function Method

Here, the meshless method with the finite difference method has been used to discretize the governing equations of the seepage phenomenon from under the dam in the steady and transient flow. The seepage problem was solved by considering the 6656 triangular mesh and 3449 nodes by the Finite Element Method and was used for validation. The radial basis function method (RBF) was considered one of the methodological methods to solve the seepage problem by considering several points. The results showed that by increasing the number of points, the accuracy of the solution increases, and the error decreases. The results of statistical indicators in the RBF method are reduced compared to the Finite Element Method. The results showed the proximity of the initial approximations to the original answer. The shape factor of the base function depends on the geometry and the governing equation, so the exact shape factor was used for the steady and transient state. In the transient condition, with the water level behind the dam remaining constant, the water head below the dam also reaches a constant value over time. The calculation of statistical indicators showed that the solution by the RBF method has acceptable accuracy.