A shock-capturing meshless method for solving the one-dimensional Saint-Venant equations on a highly variable topography

Abstract The Saint-Venant equations are numerically solved to simulate free surface flows in one dimension. A Riemann solver is needed compute the numerical flux for capturing shocks and flow discontinuities occurring situations such as hydraulic jump, dam-break wave propagation, or bore propagation. that captures not yet reported be implemented within framework of a meshless method solving equations. Therefore, wide range problems cannot simulated by available methods. In this study, shock-capturing proposed simulating one-dimensional (1D) on highly variable topography. Harten–Lax–van Leer used computing convective method. Spatial derivatives reconstruction conservative variables terms computed using weighted least square approximation. tested various challenging laboratory experiments different regimes. accurate has potential extended solve two-dimensional (2D) shallow water without any mesh requirements.