NUMERICAL-ANALYSIS OF A 2-D VISCOUS SINTERING PROBLEM WITH NONSMOOTH BOUNDARIES

By viscous sintering it is meant the process of bringing a granular compact to a temperature at which the viscosity of the material becomes low enough for surface tension to cause the particles to deform and coalesce, whereby the material transport can be modelled as a viscous incompressible newtonian volume flow. Here a two-dimensional model is considered. A Boundary Element Method is applied to solve the governing Stokes creeping flow equations for an arbitrarily initial shaped fluid region. In this paper we show that the viscous sintering problem is well-conditioned from an evolutionary point of view. However as boundary value problem at each time step, the problem is ill-conditioned when the contact surfaces of the particles are small, i.e. in the early stages of the coalescence. This is because the curvature of the boundary at those places can be very large. This ill-conditioning is illustrated by an example: the coalescence of two equal circles. This example demonstrates the main evolutionary features of the sintering phenomenon very well. A numerical consequence of this ill-conditioning is that special care has to be taken for distributing and redistributing the nodal points at these boundary parts. Therefore an algorithm for this node redistribution is outlined. Several numerical examples sustain the analysis.