Meshless Local Petrov-Galerkin (MLPG) method for simulation of transient state shallow water flows

The importance of shallow water flow in water engineering has led to the governing equations to be studied in various methods. Numerical techniques like finite element are one of these methods. These methods solve differential equations in simple and complex geometric cases by meshing on the computing domain. Recently, Mesh less methods that need no meshing or re-meshing on the domain are being used to solve differential equations in both simple and complex geometric cases. In this research, shallow water equations were modeled using Mesh less local Petrov- Galerk in with moving least squares approximation function. Then, the convergent in the variable velocity field problem was solved and the model error rate was calculated. it was indicated that the model has a good accuracy, so that the mean error and root mean square error were -0.0326 and 0.15627 respectively..Then, the water flow was calculated from the overflow of Siah Bishe dam and the results of the model were compared with the measured values. Which confirms the accuracy of solving the equations of shallow water using the Petrov- Galerkin method.