An accurate integral equation method for simulating multi-phase Stokes flow

Integral Equation Methods for Unsteady Stokes Flow in Two Dimensions

We present an integral equation formulation for the unsteady Stokes equations in two dimensions. This problem is of interest in its own right, as a model for slow viscous flow, but perhaps more importantly, as an ingredient in the solution of the full, incompressible Navier-Stokes equations. Using the unsteady Green’s function, the velocity evolves analytically as a divergence-free vector field...

An integral equation method for epitaxial step-flow growth simulations

In this paper, we describe an integral equation approach for simulating diffusion problems with moving interfaces. The solutions are represented as moving layer potentials where the unknowns are only defined on the interfaces. The resulting integro-differential equation (IDE) system is solved using spectral deferred correction (SDC) techniques developed for general differential algebraic equati...

A multi-Gaussian quadrature method of moments for simulating high Stokes number turbulent two-phase flows

An Indirect Boundary Integral Method for an Oscillatory Stokes Flow Problem

The purpose of this paper is to present an indirect boundary integral method for the oscillatory Stokes flow provided by the translational oscillations of two rigid spheres in an incompressible Newtonian fluid of infinite expanse. 1. Introduction. The study of oscillatory Stokes flows has a key role in the understanding of the biomechanics of blood flow, the Brownian motion, the motion of swimm...

A Numerical Method for Solving Stochastic Volterra-Fredholm Integral Equation

In this paper, we propose a numerical method based on the generalized hat functions (GHFs) and improved hat functions (IHFs) to find numerical solutions for stochastic Volterra-Fredholm integral equation. To do so, all known and unknown functions are expanded in terms of basic functions and replaced in the original equation. The operational matrices of both basic functions are calculated and em...