GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A fast algorithm for particle simulations
Journal of Computational Physics
Second kind integral equation formulation of Stokes' flows past a particle of arbitary shape
SIAM Journal on Applied Mathematics
How fast are nonsymmetric matrix iterations
SIAM Journal on Matrix Analysis and Applications
High-order and efficient methods for the vorticity formulation of the Euler equations
SIAM Journal on Scientific Computing
An efficient numerical method for studying interfacial motion in two-dimensional creeping flows
Journal of Computational Physics
Numerical methods for multiple inviscid interfaces in creeping flows
Journal of Computational Physics
A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains
Journal of Computational Physics
A fast multipole method for the three-dimensional Stokes equations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Dynamics of multicomponent vesicles in a viscous fluid
Journal of Computational Physics
Shape optimization of peristaltic pumping
Journal of Computational Physics
A spectral boundary integral method for flowing blood cells
Journal of Computational Physics
Hi-index | 31.45 |
A second-kind integral equation for the tractions on a rigid body moving in a Stokesian fluid is established using the Lorentz reciprocal theorem and an integral equation for a double-layer density. A second-order collocation method based on the trapezoidal rule is applied to the integral equation after appropriate singularity reduction. For translating prolate spheroids with various aspect ratios, the scheme is used to explore the effects of the choice of completion flow on the error in the numerical solution, as well as the condition number of the discretized integral operator. The approach is applied to obtain the velocity and viscous dissipation of rotating helices of circular cross-section. These results are compared with both local and non-local slender-body theories. Motivated by the design of artificial micro-swimmers, similar computations are performed on previously unstudied helices of non-circular cross-section to determine the dependence of the velocity and propulsive efficiency on the cross-section aspect ratio and orientation. Overall, we find that this formulation provides a stable numerical approach with which to solve the flow problem while simultaneously obtaining the surface tractions and that the appropriate choice of completion flow provides both increased accuracy and efficiency. Additionally, this approach naturally avails itself to known fast summation techniques and higher-order quadrature schemes.