Mathematical modelling and numerical simulation of viscous sintering processes

The objective of this research is to develop reliable numerical methods to predict the deformation of an incompressible Newtonian viscous fluid region (Stokes flow) driven by the surface tension. In particular this mathematical model describes the physical processes that appear when a compact of glassy particles is heated to such a high temperature that the glass becomes a viscous creeping fluid. As a result the particles are joining together so that the cohesion of the compact is increasing with time. This phenomenon is usually called viscous sintering and appears, e.g . in the production of high-quality glasses. From the methods developed, theoretical insights can be obtained about the densification kinetics of such a compact. Therefore, a numerical simulation program is developed which calculates the deformation of a representative two-dimensional or an axisymmetric unit cell of the compact. A boundary element method is applied to solve the integral equations arising frorn the Stokes problem and the time integration is carried out by a variable-step, variable-order backward differences formulae method.