FREE SURFACE SIMULATION BY A COMPRESSIBLE SPH METHOD

Smoothed particle hydrodynamics was begun by Lucy (1977) and Gingold and Monaghan (1977) for use in astrophysics. Over past twenty years SPH has been applied to various areas incontinuum mechanics and fluid mechanics. In 1994 Monaghan showed that SPH could be usedfor free surface flows and it needs no special treatment to simulate free surface problems such asnear shore problems [1,2]. In SPH, a computational domain is represented by a set of interpolation points called particles. The governing equations for the system are then solved at each of the particles. The particlescarry the information on position, velocity, density and other problem dependent variables. The value of a scalar at a particle i within the domain is computed as a weighted average, usingkernel function, of the scalar at the neighboring particles j that are within a pre-determinedradius of influence from particle i . In SPH, derivatives at the interpolation points are estimated using analytical expressions. This means fixed computational grids, such as those used in finitedifference and finite element methods are not required. The nature of Lagrangian formulation ofSPH ensures that advection is modeled exactly. This also makes it quite attractive to handle complex physics such as fragmentation problems and breaking water waves.In this paper the free surface is simulated by a weakly compressible SPH for a dam break andwave run-up problem and two kinds of boundary conditions called, Monaghan BC and dynamic boundary conditions are introduced. The fluid is considered viscous by considering artificial viscosity and laminar flow theories [3,4].

کلیدواژه ها:

Smoothed Particle Hydrodynamics (SPH) ، Free Surface ، Weakly Compressible