Application of Radial Base Function Method to Investigate Seepage under the Dam in Steady and Unsteady Flow Conditions

Solving the problem with the meshless method is based on selecting a series of points from inside the computational area and boundaries without meshing. In the present study, the phenomenon of seepage below the dam under steady and unsteady flow conditions has been investigated by combining the Meshless method and the Finite Difference Method. Problem solving and calibrating operations were done by coding in MATLAB software. The Meshless method was used for spatial sentences and the Finite Difference Method was used for the discretization of temporal sentences. The results showed that the shape factor (α) for low points is 0.85 and for high points is 0.52, which indicates the proximity of the initial approximations to the main answer. Considering that, the shape factor depends on the geometry and the governing equation, so the same shape factor was obtained for the steady and unsteady conditions equal to 0.52. In the unsteady condition, with the water level behind the dam remaining constant, the water head below the dam also reaches a constant value over time. Also, examination of the results showed that in numerical problem solving, a low error is not a criterion and among the various basic functions, only the MQ function has the better hydraulic performance to draw equipotential lines, so that for 133 points, the shape factor and root mean square error index are 0.52 and 0.0108, respectively.