Boundary regularized integral equation formulation (BRIEF) of Stokes flow

Abstract

Single-phase Stokes flow problems with prescribed boundary conditions can be formulated in terms of a boundary regularized integral equation that is completely free of singularities that exist in the traditional formulation. The usual mathematical singularities that arise from using the fundamental solution in the conventional boundary integral method are removed by subtracting a related auxiliary flow field, $\mathbf{w}$, that can be constructed from one of many known fundamental solutions of the Stokes equation. This approach is exact and does not require the introduction of additional cutoff parameters. The numerical implementation of this boundary regularized integral equation formulation affords considerable savings in coding effort with improved numerical accuracy. The high accuracy of this formulation is retained even in problems where parts of the boundaries may almost be in contact.

References in corpus (4)

• Non-singular boundary integral methods for fluid mechanics applications
• Boundary regularised integral equation formulation of the Helmholtz equation in acoustics
• A robust and non-singular formulation of the boundary integral method for the potential problem
• Stokesian dynamics of pill-shaped Janus particles with stick and slip boundary conditions

Cited by in corpus (4)

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• Helmholtz equation and non-singular boundary elements applied to multi-disciplinary physical problems
• Modeling of Sedimentation of Particles near Corrugated Surface by Boundary Singularity Method
• A non-singular boundary element method for interactions between acoustical field sources and structures