Abstract
A simple method is proposed, for incremental static analysis of a set of inter-colliding particles, simulating 2D flow. Within each step of proposed algorithm, the particles perform small displacements, proportional to the out-of-balance forces, acting on them. Numerical experiments show that if the liquid is confined within boundaries of a set of inter-communicating vessels, then the proposed method converges to a final equilibrium state. This incremental static analysis approximates dynamic behavior with strong damping and can provide information, as a first approximation to 2D movement of a liquid. In the initial arrangement of particles, a rhombic element is proposed, which assures satisfactory incompressibility of the fluid. Based on the proposed algorithm, a simple and short computer program (a “pocket” program) has been developed, with only about 120 Fortran instructions. This program is first applied to an amount of liquid, contained in a single vessel. A coarse and refined discretization is tried. In final equilibrium state of liquid, the distribution on hydro-static pressure on vessel boundaries, obtained by proposed computational model, is found in satisfactory approximation with corresponding theoretical data. Then, an opening is formed, at the bottom of a vertical boundary of initial vessel, and the liquid is allowed to flow gradually to an adjacent vessel. Almost whole amount of liquid is transferred, from first to second vessel, except of few drops-particles, which remain, in equilibrium, at the bottom of initial vessel. In the final equilibrium state of liquid, in the second vessel, the free surface level of the liquid confirms that the proposed rhombing element assures a satisfactory incompressibility of the fluid.
Highlights
In Computational Fluid Mechanics, recently, a combination of grid method with a mesh-free particle method is recommended [1]-[3] or a purely particle method [4][6]
The movement of a fluid is treated by incremental static analysis [11], by which dynamic behavior with strong damping is approximated and the computation is significantly simplified. This incremental static analysis is adopted in present work
Current work has two motivations: 1) To develop a simple algorithm for incremental static analysis of intercolliding particles, which approximates dynamic behavior with strong damping and is simpler than particle dynamics, which creates artificial high frequency oscillations which have to be suppressed by an additional technique
Summary
In Computational Fluid Mechanics, recently, a combination of grid method (in Eulerian co-ordinates) with a mesh-free particle method (in Lagrangian co-ordinates) is recommended [1]-[3] or a purely particle method [4][6]. The movement of a fluid is treated by incremental static analysis [11], by which dynamic behavior with strong damping is approximated and the computation is significantly simplified. This incremental static analysis is adopted in present work. Current work has two motivations: 1) To develop a simple algorithm for incremental static analysis of intercolliding particles, which approximates dynamic behavior with strong damping and is simpler than particle dynamics, which creates artificial high frequency oscillations which have to be suppressed by an additional technique. These point-particles are much simpler than finite size particles [6]
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