In this study, a novel meshless stable numerical solver is proposed to solve the non-
conservative form of shallow water equations. Since they form a hyperbolic system of
equations, discontinuous solutions are allowed to transmit during the simulation. The
generalized finite difference-split coefficient matrix method, recently proposed, is applied
and improved using the flux limiter to eliminate the possible-appearing numerical
oscillations. In the proposed scheme, the split-coefficient matrix method is adopted to …