Abstract: Meshfree methods could be used to deliberately distribute nodes freely and simply in the computational domain  free from constraints. Compared with traditional methods, meshfree methods have greater ability to deal with complex boundary. In this paper, a Meshfree Least-Square-based Finite Difference (MLSFD) method is applied to the calculation 2-D non-conservative shallow water equations. Two solutions are presented for nodes selection. In order to avoid cumbersome examination process, the least square technique is introduced to optimize the approximation of the vector. The MLSFD method is employed to simulate a circular dam-break model. To treat boundary condition better, three-layer right-angle grids are distributed from the boundary to the inside around the meshfree nodes. Numerical simulation results are analyzed and compared. The results show that the MLSFD method has a high accuracy of simulating 2-D shallow water flow. It’s indicated that the MLSFD method is feasible for solving shallow water equations.

Key words: MLSFD method, 2-D shallow water equation, circular dam-break model