Simulation de phénomènes de fonte et solidification à l’aide d’une simulation par particules

Abstract

The simulation of highly viscous fluids using an SPH (Smoothed Particle Hydrodynamics) approach is a tedious task. The viscosity parameter normally varies between 0 (liquid) and +∞, therefore it is difficult to find the value that will produce the desired viscous behaviours. Since the equations are typically posed as stiff problems, simulating highly viscous fluids involves strong forces applied to the particles.With these strong forces, a very small time step is needed to keep the simulation stable and produce good results. The approach detailed in this master’s thesis uses an iterative prediction-correction scheme to optimize rigid forces that act on the fluid, in order to produce a behaviour that varies from liquid to solid. At every time step, each particle position is predicted. The deformation is then compared with a target deformation and rigid forces are adjusted to counteract the deformation. Compared to the typical viscosity parameter which varies from zero to infinity, the proposed rigidity parameter is easier to control, providing a continuous variation from 0 (liquid) to 1 (solid). Since simulating high viscosity fluids is subject to large computation times and instabilities, we complement the proposed model with some important improvements. Firstly, an improved time step adjustment is proposed that results in both reduced computation times and increased stability. Secondly, an implicit temperature diffusion provides stable melting and solidification, regardless of the size of the time step. Thirdly, a constraint propagation provides faster convergence of the rigid forces to realistic behaviours. Together, these improvements and the proposed model allow the simulation of fluids with viscous behaviours that were very difficult, if not impossible, to simulate with current SPH approaches.

Date	9 May 2012
Original language	French
Awarding Institution	École de technologie supérieure
Supervisor	Eric Paquette (Supervisor)