Discrete Least Squares Meshless (DLSM) method for simulation of steady state shallow water flows

In this paper, a meshless method, namely, Discrete Least Squares Meshless (DLSM) method is used for the solution of shallow water problems. In this method, the computational domain is discretized by some nodes and then a set of simultaneous equations are built using Moving Least Squares (MLS) shape functions and the least squares technique. The proposed method does not need any background mesh and therefore is a truly meshless method. The stability and accuracy of the DLSM method is improved using some sampling points. Some 2D benchmark problems and a two dimensional flow over an ogee spillway are used to illustrate the performance of the present DLSM method. Numerical results are compared with experimental or analytical ones. Both regular and irregular meshes of nodes are used to show the potential of the DLSM method in solving problems with more complex domains.