Application of localized meshless methods to 2D shallow water equation problems

This study aims to apply the meshless local radial-basis-function differential quadrature (LRBFDQ) method to solve the shallow water equations (SWE). This localized approach is developed from the differential quadrature (DQ) method by employing the radial-basis functions (RBFs) as the trial functions. Comparing with global-type meshless methods, the present method is more appropriate to large-scale problems with complex shapes. Moreover the drawbacks rising from the poor selection of shape parameter and also the full resultant matrix with high condition number are reduced. For real hydraulic-engineering applications located in irregular domains, the LRBFDQ method is very suitable to solve these kinds of shallow-water problems. In this work, the numerical models are applied to simulate three typical 2D SWE problems: (1) a tidal-wave propagation, (2) a dam-break problem and (3) an inverse engineering problem: the numerical analysis of the inflow discharge of the Yuanshantze Flood Diversion (YFD) project in Taiwan. As a result, the adopted meshless method not only shows its algorithm superiority over other mesh-dependent numerical schemes, but also brings more efficiency than several conventional mesh or meshless methods. The application of YFD project also delivers its applicability of this meshless scheme to solve real-world engineering projects.