Critical Study on Incremental Static Analysis of 2D Flow, by Inter-Colliding Point-Particles, by Use of In-Compressible Rhombic Element

A simple method is proposed, for incremental static analysis of a set of inter-colliding particles,
simulating 2D flow. 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 in-compressibility 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. 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 rhombic element assures
a satisfactory in-compressibility of the fluid.