Meshfree formulations of kinematic wave for channel flow routing

Abstract

This study concerns the development of various Meshfree formulations, namely Point Interpolation Method (PIM), Radial Point Interpolation Method (RPIM) and Element Free Galerkin (EFG) in solving numerically, St Venant’s kinematic wave equations for the hydrologic modeling of surface runoff and channel flow. It involves problem formulations derivation of governing equations, provision of the corresponding solutions by generating Matlab source codes, verification of results against established data, parametric study and assessment of performance of the newly derived Meshfree formulations against established numerical methods, namely Finite Element Method (FEM) and Finite Difference Method (FDM). The originality and the main contribution of the study are solving the Meshfree formulations of the kinematic wave equations numerically. The formulations are verified when it is found that the results produced by the source codes are in general in close agreement with the benchmark data. Although slight discrepancies have been observed in some cases, these are later validated as due to several factors, namely shape parameters values which are yet to be optimized, different number of nodes used for comparison and manual discretization of input data. In obtaining the best performance of the methods, optimum values of the shape parameters have been determined through a parametric study which once obtained are used in the performance assessment. RPIM and PIM are found to be less sensitive to the optimum values as compared to EFG. Two types of performance are assessed; the convergence rate and the computer resource consumption in terms of CPU time. Based on this study, it can be concluded that, in general, Meshfree methods perform comparably with the established methods in terms of convergence rate despite the fact it does not need the construction of mesh which can save modelling time. This shows the potential of Meshfree as numerical methods for its future development.