Isogeometric boundary element formulation for deformable particles in microchannel confinement

Abstract

Numerical simulations of deformable particles are essential to understand quantities that are not possible with experimental techniques. The boundary element method is an advantageous technique to analyze deformable particles in viscous flow conditions since it reduces the dimensionality of the problem by one for linear partial differential equations. Isogeometric boundary element formulation is proposed to model the motion of deformable particles which provides unique ad-vantages in terms of the higher-order continuity of elements and exact geometry representation. Moreover, it enables the calculation of surface normal and curvature analytically. Deformable particles, more specifically droplets, may undergo high deformation which deteriorates the mesh. Moreover, numerical inaccuracies result in a nonphysical change in the volume of the particle. Hence, volume correction and mesh relaxation algorithms are implemented in the isogeometric boundary element method to alleviate the aforementioned numerical artifacts. Without loss of generality, droplets in free and bounded flow cases are formulated and several benchmark problems are solved to assess the accuracy of the proposed formulation. Isogeometric boundary element method supported by stabilization methods explained in the study allows for obtaining stable and accurate results with low-resolution simulations.