Journal
JOURNAL OF HYDROINFORMATICS
Volume 25, Issue 4, Pages 1235-1255Publisher
IWA PUBLISHING
DOI: 10.2166/hydro.2023.164
Keywords
Harten-Lax-van Leer Riemann solver; meshless method; Saint-Venant equations; shock-capture; weighted least square
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In this study, a shock-capturing meshless method is proposed for simulating one-dimensional flows with highly variable topography. The proposed method uses the HLL Riemann solver for computing the convective flux and a weighted least square approximation for spatial derivatives. The method is tested for various challenging problems and experiments, demonstrating its high accuracy.
The Saint-Venant equations are numerically solved to simulate free surface flows in one dimension. A Riemann solver is needed to compute the numerical flux for capturing shocks and flow discontinuities occurring in flow situations such as hydraulic jump, dam-break wave propagation, or bore wave propagation. A Riemann solver that captures shocks and flow discontinuities is not yet reported to be implemented within the framework of a meshless method for solving the Saint-Venant equations. Therefore, a wide range of free surface flow problems cannot be simulated by the available meshless methods. In this study, a shock-capturing meshless method is proposed for simulating one-dimensional (1D) flows on a highly variable topography. The Harten-Lax-van Leer Riemann solver is used for computing the convective flux in the proposed meshless method. Spatial derivatives in the Saint-Venant equations and the reconstruction of conservative variables for flux terms are computed using a weighted least square approximation. The proposed method is tested for various numerically challenging problems and laboratory experiments on different flow regimes. The proposed highly accurate shock-capturing meshless method has the potential to be extended to solve the two-dimensional (2D) shallow water equations without any mesh requirements.
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