13 citations · 16 across the 4 of their papers we have counts for
6 papers
On the preservation of second integrals by Runge-Kutta methods
Benjamin K Tapley
One can elucidate integrability properties of ordinary differential equations (ODEs) by knowing the existence of second integrals (also known as weak integrals or Darboux polynomia…
Computational geometric methods for preferential clustering of particle suspensions
Benjamin K. Tapley, Helge I. Andersson, Elena Celledoni +1
A geometric numerical method for simulating suspensions of spherical and non-spherical particles with Stokes drag is proposed. The method combines divergence-free matrix-valued rad…
A slender body model for thin rigid fibers: validation and comparisons
Laurel Ohm, Benjamin K. Tapley, Helge I. Andersson +2
In this paper we consider a computational model for the motion of thin, rigid fibers in viscous flows based on slender body theory. Slender body theory approximates the fluid veloc…
Using discrete Darboux polynomials to detect and determine preserved measures and integrals of rational maps
E Celledoni, C Evripidou, D I McLaren +4
In this Letter we propose a systematic approach for detecting and calculating preserved measures and integrals of a rational map. The approach is based on the use of cofactors and…
Computing cost-effective particle trajectories in numerically calculated incompressible fluids using geometric methods
Benjamin K Tapley
We present an novel algorithm for tracking massless solid particles in a divergence-free velocity field that is only available at discrete points in space and time such as those ar…
A novel approach to rigid spheroid models in viscous flows using operator splitting methods
Benjamin Tapley, Elena Celledoni, Brynjulf Owren +1
Calculating cost-effective solutions to particle dynamics in viscous flows is an important problem in many areas of industry and nature. We implement a second-order symmetric split…