Discrete least squares meshless modeling of shallow water flows for suspended sediment and bed-load transport

The main objective of this study is to extend the Discrete Least Squares Meshless method to a coupled shallow-water, suspended-sediment, and bed-load transport system in a fully implicit meshless framework. The governing equations form a hyperbolic nonlinear system of conservation laws along with source terms. We employ the meshless method of discrete least squares and use moving least squares approximation to determine shape functions and their partial derivatives at any point within the computational domain. This method results in a symmetric coefficient matrix and qualifies as a truly meshless method, eliminating the need for a mesh in approximating field variables and constructing system matrices. The main contribution of the work is the application of a fully coupled DLSM formulation to hydro-morphodynamic modelling involving both suspended sediment and bed-load transport. Several one and two-dimensional test cases are presented to verify and validate the performance of the employed numerical scheme. In addition, an experimental movable-bed dam-break test is included to further assess the model against laboratory measurements. Special focus is directed towards the dam-break problem over fixed and mobile beds. The numerical results highlight the effectiveness of the method in capturing key flow and sediment features.