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Simulation of Solitary Wave Mechanics by a Corrected Smoothed Particle Hydrodymamics Method

Staroszczyk R.

Archives of Hydro-Engineering and Environmental Mechanics

2011

Vol. 58, nr 1-4

23-45

The paper is devoted to numerical modelling of solitary wave propagation phenomena in shallow water of uniform depth. The problem governing equations are solved by applying a corrected smoothed particle hydrodynamics (SPH) method in which standard smoothing kernel functions are modified in such a way that so-called linear reproducing conditions for kernel approximations and their first-order spatial derivatives are satisfied. Numerical performance of the proposed SPH model has been verified by comparing its predictions with analytical results for a solitary wave travelling over the horizontal bottom. Also, the results obtained by applying the corrected SPH method and those given by the standard SPH method, with no kernel correction, are compared. Further, an impact of the solitary wave on a vertical rigid wall is investigated, and finally an interaction of two colliding solitary waves is considered.

Simulation of Dam-Break Flow by a Corrected Smoothed Particle Hydrodynamics Method

Staroszczyk R.

Archives of Hydro-Engineering and Environmental Mechanics

2010

Vol. 57, nr 1

61-79

The paper deals with numerical modelling of water flow which is generated by the break of a dam. The problem is solved by applying a smoothed particle hydrodynamics (SPH) method in which standard smoothing kernel functions are corrected in such a way that so-called linear reproducing conditions for kernel approximations and their gradients are satisfied. The proposed SPH model has been used to simulate a two-dimensional problem of the collapse of a water column inside a rectangular tank. The simulations illustrate the formation and subsequent propagation of a wave over the horizontal plane. It is shown that the model predictions of the changes of the advancing wave-front position, and of the changes of the free surface elevation of water, compare well with experimental data. Also, the results obtained with the corrected SPH method are compared with those given by the standard SPH method with no kernel correction. In addition, an impact of the surging wave against a vertical rigid wall is illustrated.