Abstract
Smoothed particle hydrodynamics (SPH) is a Lagrangian mesh free particle method which has been developed and widely applied to different areas in engineering. Recently, the SPH method has also been used to solve the shallow water equations, resulting in (SPH-SWEs) formulations. With the significant developments made, SPH-SWEs provide an accurate computational tool for solving problems of wave propagation, flood inundation, and wet-dry interfaces. Capabilities of the SPH method to solve Saint-Venant equations have been tested using a SPH-SWE code to simulate different hydraulic test cases. Results were compared to other established and commercial hydraulic modelling packages that use Eulerian approaches. The test cases cover non-uniform steady state profiles, wave propagation, and flood inundation cases. The SPH-SWEs simulations provided results that compared well with other established and commercial hydraulic modeling packages. Nevertheless, SPH-SWEs simulations experienced some drawbacks such as loss of inflow water volume of up to 2%, for 2D flood propagation. Simulations were carried out using an open source solver, named SWE-SPHysics.
Highlights
Smoothed particle hydrodynamics (SPH) is a mesh-free Lagrangian particle method originally designed for continuum scale applications
In order to maintain the solution accuracy, SPH-shallow water equations (SWEs) uses a varying smoothing length hi related to the density, as shown in hi = h0 ρ0 1/Dm ρi In Equation (5), Dm is the number of the space dimensions, and h0 and ρ0 are the initial smoothing length and density, respectively
In order to march the particle in time, particle positions and velocities are integrated in time using an explicit Leap-frog scheme [20], where the time step must satisfy a Courant– Friedrichs–Levy (CFL) condition given by Equation (9)
Summary
Smoothed particle hydrodynamics (SPH) is a mesh-free Lagrangian particle method originally designed for continuum scale applications. The numerical simulations of different natural phenomena such as flood waves due to dam breaks [10], river flood waves, and tidal flows are important for flood risk analysis [4] These types of simulations have been conducted using solution of shallow water equations (SWEs) on classical grid-based discretization of the computational domain. The bed gradient source term is addressed in two ways; [17] describes the bed gradient using an analytical function whereas [15] introduces an approach to address irregular bathymetries In this last technique, the bed is discretized into a new set of interpolation points called bottom particles over which an SPH-based interpolation is performed to calculate the bed gradient and tensor. These equations are formulated and implemented as a system of equations of density and momentum
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