Related papers: Boundary regularized integral equation formulation…
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 show that the standard boundary integral operators, defined on the unit sphere, for the Stokes equations diagonalize on a specific set of vector spherical harmonics and provide formulas for their spectra. We also derive analytical…
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…
An efficient, accurate, and flexible numerical method is proposed for the solution of the swimming problem of one or more autophoretic particles in the purely-diffusive limit. The method relies on successive boundary element solutions of…
The incompressible Stokes equations can classically be recast in a boundary integral (BI) representation, which provides a general method to solve low-Reynolds number problems analytically and computationally. Alternatively, one can solve…
A new reformulation of a free boundary problem for the Stokes equations governing a viscous flow with overdetermined condition on the free boundary is proposed. The idea of the method is to transform the governing equations to a boundary…
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…
Inspired by the numerical immersed boundary method, we introduce regularized Stokes immersed boundary problems in two dimensions to describe regularized motion of a 1-D closed elastic string in a 2-D Stokes flow, in which a regularized…
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…
A formulation of the boundary integral method for solving partial differential equations has been developed whereby the usual weakly singular integral and the Cauchy principal value integral can be removed analytically. The broad…
New analytical representations of the Stokes flows due to periodic arrays of point singularities in a two-dimensional no-slip channel and in the half-plane near a no-slip wall are derived. The analysis makes use of a conformal mapping from…
Since their development in 2001, regularised stokeslets have become a popular numerical tool for low-Reynolds number flows since the replacement of a point force by a smoothed blob overcomes many computational difficulties associated with…
A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated…
We deal with a steady Stokes-type problem, associated with a flow of a Newtonian incompressible fluid through a spatially periodic profile cascade. The used mathematical model is based on the reduction to one spatial period, represented by…
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…
In transient simulations of particulate Stokes flow, to accurately capture the interaction between the constituent particles and the confining wall, the discretization of the wall often needs to be locally refined in the region approached…
This work introduces a stabilised finite element formulation for the Stokes flow problem with a nonlinear slip boundary condition of friction type. The boundary condition is enforced with the help of an additional Lagrange multiplier and…
Simulation of unsteady creeping flows in complex geometries has traditionally required the use of a time-stepping procedure, which is typically costly and unscalable. To reduce the cost and allow for computations at much larger scales, we…
A discontinuous viscosity coefficient makes the jump conditions of the velocity and normal stress coupled together, which brings great challenges to some commonly used numerical methods to obtain accurate solutions. To overcome the…