Numerical solution of bed load transport equations using discrete least squares meshless (DLSM) method

Abstract

The discrete least squares meshless (DLSM) method is extended in this paper for solving coupled bedload sediment transport equations. The mathematical formulation of this model consists of shallow water equations for the hydrodynamical component and an Exner equation expressing sediment continuity for the bedload transport. This method uses the moving least squares (MLS) function approximation to construct the shape functions and the minimizing least squares functional method to discretize the system of equations. The method can be viewed as a truly meshless method as it does not need any mesh for both field variable approximation and the construction of system matrices; it also provides the symmetric coefficient matrix. In the present work, several benchmark problems are studied and compared with the work of other researchers; the proposed method shows good accuracy, high convergence rate, and high efficiency, even for irregularly distributed nodes. At the end, a real test problem is performed to show and verify the main benefit and applicability of the proposed method to cope with complex geometry in practical problems.