Mathematical Modelling and Numerical Simulation of Viscous Sintering Processes

摘要

The objective of this research is to develop reliable numerical methods topredict the deformation of an incompressible Newtonian viscous fluid region (Stokes Flow) driven by 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. 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 from the Stokes problem and the time integration is carried out by a variable step, variable order Backward Differences Formulae method.