TY - JOUR
T1 - Integral method for a two-dimensional Stokes flow with shrinking holes applied to viscous sintering
AU - Vorst, van de, G.A.L.
PY - 1993
Y1 - 1993
N2 - An integral method is developed to solve the two-dimensional Stokes problem with Neumann boundary conditions for multiply connected domains in which the inside hole area can shrink and disappear. The method is applied to simulate viscous sintering. In particular the sintering of glasses can be modelled as such, i.e. a viscous incompressible Newtonian volume flow driven solely by surface tension. A Boundary Element Method is applied to solve the integral equations of Stokes flow involved, and the time integration is carried out by a variable-step, variable-order Backward Differences Formulae method. The derived numerical algorithm is demonstrated for several arbitrarily shaped multiply connected sintering domains. In particular some cylindrical packings are considered. The latter simulations provide a justification for the use of ‘unit problems’ in the theory of sintering.
AB - An integral method is developed to solve the two-dimensional Stokes problem with Neumann boundary conditions for multiply connected domains in which the inside hole area can shrink and disappear. The method is applied to simulate viscous sintering. In particular the sintering of glasses can be modelled as such, i.e. a viscous incompressible Newtonian volume flow driven solely by surface tension. A Boundary Element Method is applied to solve the integral equations of Stokes flow involved, and the time integration is carried out by a variable-step, variable-order Backward Differences Formulae method. The derived numerical algorithm is demonstrated for several arbitrarily shaped multiply connected sintering domains. In particular some cylindrical packings are considered. The latter simulations provide a justification for the use of ‘unit problems’ in the theory of sintering.
U2 - 10.1017/S002211209300326X
DO - 10.1017/S002211209300326X
M3 - Article
SN - 0022-1120
VL - 257
SP - 667
EP - 689
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
ER -