A fast algorithm for simulating multiphase flows through periodic geometries of arbitrary shape
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Publication:2821776
DOI10.1137/15M1043066zbMATH Open1381.76229arXiv1510.05616MaRDI QIDQ2821776
Author name not available (Why is that?)
Publication date: 23 September 2016
Published in: (Search for Journal in Brave)
Abstract: This paper presents a new boundary integral equation (BIE) method for simulating particulate and multiphase flows through periodic channels of arbitrary smooth shape in two dimensions. The authors consider a particular system---multiple vesicles suspended in a periodic channel of arbitrary shape---to describe the numerical method and test its performance. Rather than relying on the periodic Green's function as classical BIE methods do, the method combines the free-space Green's function with a small auxiliary basis, and imposes periodicity as an extra linear condition. As a result, we can exploit existing free-space solver libraries, quadratures, and fast algorithms, and handle a large number of vesicles in a geometrically complex channel. Spectral accuracy in space is achieved using the periodic trapezoid rule and product quadratures, while a first-order semi-implicit scheme evolves particles by treating the vesicle-channel interactions explicitly. New constraint-correction formulas are introduced that preserve reduced areas of vesicles, independent of the number of time steps taken. By using two types of fast algorithms, (i) the fast multipole method (FMM) for the computation of the vesicle-vesicle and the vesicle-channel hydrodynamic interaction, and (ii) a fast direct solver for the BIE on the fixed channel geometry, the computational cost is reduced to per time step where is the spatial discretization size. Moreover, the direct solver inverts the wall BIE operator at , stores its compressed representation and applies it at every time step to evolve the vesicle positions, leading to dramatic cost savings compared to classical approaches. Numerical experiments illustrate that a simulation with can be evolved in less than a minute per time step on a laptop.
Full work available at URL: https://arxiv.org/abs/1510.05616
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