Quadrature methods for periodic singular and weakly singular Fredholm integral equations
Journal of Scientific Computing
Application of adaptive quadrature to axi-symmetric vortex sheet motion
Journal of Computational Physics
Axisymmetric Vortex Sheet Motion: Accurate Evaluation of the Principal Value Integral
SIAM Journal on Scientific Computing
Computation of axisymmetric suction flow through porous media in the presence of surface tension
Journal of Computational Physics
Interfacial dynamics for Stokes flow
Journal of Computational Physics
Singularity formation in a cylindrical and a spherical vortex sheet
Journal of Computational Physics
Introduction to Scientific Computing: A Matrix-Vector Approach Using MATLAB
Introduction to Scientific Computing: A Matrix-Vector Approach Using MATLAB
Numerical simulations of inviscid capillary pinchoff
Journal of Computational Physics
Removing the stiffness from interfacial flows with surface tension
Journal of Computational Physics
Hi-index | 31.45 |
We propose new high order accurate methods to compute the evolution of axi-symmetric interfacial Stokes flow. The velocity at a point on the interface is given by an integral over the surface. Quadrature rules to evaluate these integrals are developed using asymptotic expansions of the integrands, both locally about the point of evaluation, and about the poles, where the interface crosses the axis of symmetry. The local expansions yield methods that converge to the chosen order pointwise, for fixed evaluation point. The pole expansions yield corrections that remove maximal errors of low order, introduced by singular behaviour of the integrands as the evaluation point approaches the poles. An interesting example of roundoff error amplification due to cancellation is also addressed. The result is a uniformly accurate fifth order method. Second order, pointwise fifth order, and uniform fifth order methods are applied to compute three sample flows, each of which presents a different computational difficulty: an initially bar-belled drop that pinches in finite time, a drop in a strain flow that approaches a steady state, and a continuously extending drop. In each case, the fifth order methods significantly improve the ability to resolve the flow. The examples furthermore give insight into the effect of the corrections needed for uniformity. We determine conditions under which the pointwise method is sufficient to obtain resolved results, and others under which the corrections significantly improve the results.