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Incompressible SPH Model for Simulating Violent Free-Surface Fluid Flows

Staroszczyk R.

Archives of Hydro-Engineering and Environmental Mechanics

2014

Vol. 61, nr 1-2

61--83

In this paper the problem of transient gravitational wave propagation in a viscous incompressible fluid is considered, with a focus on flows with fast-moving free surfaces. The governing equations of the problem are solved by the smoothed particle hydrodynamics method (SPH). In order to impose the incompressibility constraint on the fluid motion, the so-called projection method is applied in which the discrete SPH equations are integrated in time by using a fractional-step technique. Numerical performance of the proposed model has been assessed by comparing its results with experimental data and with results obtained by a standard (weakly compressible) version of the SPH approach. For this purpose, a plane dam-break flow problem is simulated, in order to investigate the formation and propagation of a wave generated by a sudden collapse of a water column initially contained in a rectangular tank, as well as the impact of such a wave on a rigid vertical wall. The results of simulations show the evolution of the free surface of water, the variation of velocity and pressure fields in the fluid, and the time history of pressures exerted by an impacting wave on a wall.

Application of an Element-free Galerkin Method to Water Wave Propagation Problems

Staroszczyk R.

Archives of Hydro-Engineering and Environmental Mechanics

2013

Vol. 60, nr 1-4

87--105

The paper is concerned with the problem of gravitational wave propagation in water of variable depth. The problem is solved numerically by applying an element-free Galerkin method. First, the proposed model is validated by comparing its predictions with experimental data for the plane flow in water of uniform depth. Then, as illustrations, results of numerical simulations performed for plane gravity waves propagating through a region with a sloping bed are presented. These results show the evolution of the free-surface elevation, displaying progressive steepening of the wave over the sloping bed, followed by its attenuation in a region of uniform depth. In addition, some of the results of the present model are compared with those obtained earlier by using the conventional finite element method.

A Lagrangian Finite Element Analysis of Gravity Waves in Water of Variable Depth

Staroszczyk R.

Archives of Hydro-Engineering and Environmental Mechanics

2009

Vol. 56, nr 1-2

43-61

The paper is concerned with the problem of gravitational wave propagation in water of variable depth. The problem is formulated in the Lagrangian description, and the ensuing equations are solved numerically by a finite element method. In computations a convecting mesh that follows the material fluid particles is used. As illustrations, results of numerical simulations carried out for plane gravity waves propagating over bottoms of simple geometry are presented. For parameters typical of a laboratory flume, the transformation of a transient wave, generated by a single movement of a piston-like wave maker, is investigated. The results show the evolution of the free-surface elevation, displaying steepening of the wave over sloping beds and its gradual attenuation in regions of uniform depth.