A meshless boundary method for Stokes flows with particles: Application to canalithiasis

Abstract

We propose to couple the method of fundamental solutions (MFS) to the force coupling method (FCM). The resulting method is an efficient, easy to program, meshless method for flows at low Reynolds numbers with finite-size particles. In such an approach, the flow domain is extended across the solid particle phase, and the flow is approximated by a superposition of singular Stokeslets positioned outside the flow domain and finite-size multipoles collocated with the particle. To improve the efficiency of the coupling, we propose new MFS quadratures for the computation of the volume integrals required for the FCM. These are exact and do not require the expensive evaluation of Stokeslets. The proposed method has been developed in the context of investigations of the fluid dynamics of canalithiasis, that is, a pathological condition of the semicircular canals of the inner ear. Numerical examples are presented to illustrate the applicability of the method.

Meshfree and Particle Methods in Biomechanics: Prospects and Challenges

“…Boselli and his colleagues [166,167] employed a combination of the multilayer MFS approach and the force coupling method for numerical investigation of the fluid dynamics of benign paroxysmal positional vertigo or canalithiasis conditions affecting the semicircular canals of the inner ear by solving the Stoke flow equations with finite-size particles. In [168], the authors employed a block greedy-QR algorithm that exploits the robustness of the multilayer MFS approach in a multilevel fashion and alleviates the over-head of multiple source layers thereby allowing the multilayer MFS to outperform the monolayer MFS.…”