A stabilized SPH method for inviscid shallow water flows

Abstract

SUMMARYIn this paper, the smoothed particle hydrodynamics (SPH) method is applied to the solution of shallow water equations. A brief review of the method in its standard form is ÿrst described then a variational formulation using SPH interpolation is discussed. A new technique based on the Riemann solver is introduced to improve the stability of the method. This technique leads to better results. The treatment of solid boundary conditions is discussed but remains an open problem for general geometries. The dam-break problem with a at bed is used as a benchmark test.

High-order triangle-based discontinuous Galerkin methods for hyperbolic equations on a rotating sphere

“…This case is run for 5.4 days at which point the waves travel to the other side of the sphere where they collide culminating in a strong discontinuity centered at (k, h) = (0, 0). Slight variations of this test have been used recently for shallow water flows by Ata and Soulaimani [1] on the plane, and Rossmanith et al [24] on the sphere.…”

SWE-SPHysics Simulation of Dam Break Flows at South-Gate Gorges Reservoir

“…D m represents the spatial dimensions, with m = 1 for 1-D flows and m = 2 for 2-D flows. Equation (6) implies that the smoothing length is also the function of particle density and thus Equation (5) is implicit, which could be solved by using the Newton-Raphson iterations [18]. Following the SWE-SPHysics User Manual [9,10], the governing Equations (1) and (2) can be efficiently solved by using the leap-frog time integration scheme based on the energy principles with a variational formulation.…”

A numerical study of the SPH method for simulating transient viscoelastic free surface flows

“…Since its invention, it has been extensively studied, extended and applied in many areas such as the dynamic response of elasto-plastic materials [18][19][20], free surface flows [21], low-Reynolds number viscous flows [22][23][24], solid friction [25], incompressible fluids [26,27], heat transfer [28], multi-phase flows [29,30], geophysical flows [31][32][33] and turbulence modeling [34]. Solid friction has often been studied using embedded atom methods, a method very similar in spirit to SPH [35].…”