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5 papers · 2 filters
An integral equation method for the simulation of doubly-periodic suspensions of rigid bodies in a shearing viscous flow
Jun Wang, Ehssan Nazockdast, Alex Barnett
With rheology applications in mind, we present a fast solver for the time-dependent effective viscosity of an infinite lattice containing one or more neutrally buoyant smooth rigid…
Solution of Stokes flow in complex nonsmooth 2D geometries via a linear-scaling high-order adaptive integral equation scheme
Bowei Wu, Hai Zhu, Alex Barnett +1
We present a fast, high-order accurate and adaptive boundary integral scheme for solving the Stokes equations in complex---possibly nonsmooth---geometries in two dimensions. The ke…
A fast solver for the narrow capture and narrow escape problems in the sphere
Jason Kaye, Leslie Greengard
We present an efficient method to solve the narrow capture and narrow escape problems for the sphere. The narrow capture problem models the equilibrium behavior of a Brownian parti…
Improving convergence of volume penalised fluid-solid interactions
Eric W. Hester, Geoffrey M. Vasil, Keaton J. Burns
We analyse and improve the volume-penalty method, a simple and versatile way to model objects in fluid flows. The volume-penalty method is a kind of fictitious-domain method that a…
Explicit unconditionally stable methods for the heat equation via potential theory
Alex H. Barnett, Charles L. Epstein, Leslie Greengard +2
We study the stability properties of explicit marching schemes for second-kind Volterra integral equations that arise when solving boundary value problems for the heat equation by…