Radial basis function-based differential quadrature for dam break problems

This study presents a new approach for simulating dam break flows with the two-dimensional shallow water equations (SWE), incorporating wet and dry beds, as well as irregular and frictional topography. The proposed method employs local radial basis function-based differential quadrature (LRBF-DQM) meshless techniques for space-derivative operators, while utilizing an explicit first-order finite difference scheme for the temporal derivatives. To evaluate the effectiveness of the proposed method, several two-dimensional numerical experiments were conducted to simulate the flow resulting from a dam break. The numerical experiments were specifically designed to assess the performance of the suggested approach and compare it against existing benchmarks. The results demonstrate the promising accuracy of the LRBF-DQM meshless technique in solving SWE problems, specifically in simulating dam break flows, despite the inherent complexities of these problems. The method is easy to program and mesh-free, but requires careful selection of suitable shape parameters, as with previous RBF applications.