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Boundary integral numerical methods are among the most accurate methods for interfacial Stokes flow, and are widely applied. They have the advantage that only the boundary of the domain must be discretized, which reduces the number of…
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 key ingredient is a set of panel quadrature rules capable of…
Boundary integral equation methods are widely used in the solution of many partial differential equations. The kernels that appear in these surface integrals are nearly singular when evaluated near the boundary, and straightforward…
We present a numerical method for computing the single layer (Stokeslet) and double layer (stresslet) integrals in Stokes flow. The method applies to smooth, closed surfaces in three dimensions, and achieves high accuracy both on and near…
The immersed boundary method is a numerical and mathematical formulation for solving fluid-structure interaction problems. It relies on solving fluid equations on an Eulerian fluid grid and interpolating the resulting velocity back onto…
This work presents a robust and efficient sharp interface immersed boundary (IBM) framework, which is applicable for all-speed flow regimes and is capable of handling arbitrarily complex bodies (stationary or moving). The work deploys an…
Performing highly accurate simulations of droplet systems is a challenging problem. This is primarily due to the interface dynamics which is complicated further by the addition of surfactants. This paper presents a boundary integral method…
Many problems in fluid dynamics are effectively modeled as Stokes flows - slow, viscous flows where the Reynolds number is small. Boundary integral equations are often used to solve these problems, where the fundamental solutions for the…
A highly accurate method for simulating surfactant-covered droplets in two-dimensional Stokes flow with solid boundaries is presented. The method handles both periodic channel flows of arbitrary shape and stationary solid constrictions. A…
We propose an efficient threshold dynamics method for topology optimization for fluids modeled with the Stokes equation. The proposed algorithm is based on minimization of an objective energy function that consists of the dissipation power…
This paper describes a trapezoidal quadrature method for the discretization of singular and hypersingular boundary integral operators (BIOs) that arise in solving boundary value problems for elliptic partial differential equations. The…
Boundary integral methods are highly suited for problems with complicated geometries, but require special quadrature methods to accurately compute the singular and nearly singular layer potentials that appear in them. This paper presents a…
Immersed methods discretize boundary conditions for complex geometries on background Cartesian grids. This makes such methods especially suitable for two-way coupled flow-body problems, where the body mechanics are partially driven by…
The presence of surfactants alters the dynamics of viscous drops immersed in an ambient viscous fluid. This is specifically true at small scales, such as in applications of droplet based microfluidics, where the interface dynamics become of…
An immersed-boundary method for the incompressible Navier--Stokes equations is presented. It employs discrete forcing for a sharp discrimination of the solid-fluid interface, and achieves second-order accuracy, demonstrated in examples with…
The interaction of fibers in a viscous (Stokes) fluid plays a crucial role in industrial and biological processes, such as sedimentation, rheology, transport, cell division, and locomotion. Numerical simulations generally rely on slender…
A non-local slender body approximation for slender flexible fibers in Stokes flow can be derived, yielding an integral equation along the center lines of the fibers that involves a slenderness parameter. The formulation contains a so-called…
Two-dimensional Stokes flow through a periodic channel is considered. The channel walls need only be Lipschitz continuous, in other words they are allowed to have corners. Boundary integral methods are an attractive tool for numerically…
We present a new derivation of a boundary integral equation (BIE) for simulating the three-dimensional dynamics of arbitrarily-shaped rigid particles of genus zero immersed in a Stokes fluid, on which are prescribed forces and torques. Our…
Inexpensive numerical methods are key to enable simulations of systems of a large number of particles of different shapes in Stokes flow. Several approximate methods have been introduced for this purpose. We study the accuracy of the…