A 3D isogeometric BE–FE analysis with dynamic remeshing for the simulation of a deformable particle in shear flows

Maestre, Jorge; Pallarès, Jordi; Cuesta, Ildefonso; Scott, Michael A.

doi:10.1016/j.cma.2017.08.003

Cited by 20 publications

(5 citation statements)

References 115 publications

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“…Its superior accuracy as compared to previous methods to compute geometric properties like curvature was confirmed in [36]. A coupled IGA-BEM and shell approach is seen as a promising way to study the interaction between thin elastic structures and Stokes flows and is attracting growing attention in the soft particle's community [40,32,41].…”

Section: Introductionmentioning

confidence: 93%

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An isogeometric boundary element method for soft particles flowing in microfluidic channels

Lyu,

Chen,

Boedec

et al. 2020

Preprint

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Understanding the flow of deformable particles such as liquid drops, synthetic capsules and vesicles, and biological cells confined in a small channel is essential to a wide range of potential chemical and biomedical engineering applications. Computer simulations of this kind of fluid-structure (membrane) interaction in low-Reynolds-number flows raise significant challenges faced by an intricate interplay between flow stresses, complex particles' interfacial mechanical properties, and fluidic confinement. Here, we present an isogeometric computational framework by combining the finite-element method (FEM) and boundary-element method (BEM) for an accurate prediction of the deformation and motion of a single soft particle transported in microfluidic channels. The proposed numerical framework is constructed consistently with the isogeometric analysis paradigm; Loop's subdivision elements are used not only for the representation of geometry but also for the membrane mechanics solver (FEM) and the interfacial fluid dynamics solver (BEM). We validate our approach by comparison of the simulation results with highly accurate benchmark solutions to two well-known examples available in the literature, namely a liquid drop with constant surface tension in a circular tube and a capsule with a very thin hyperelastic membrane in a square channel. We show that the numerical method exhibits second-order convergence in both time and space. To further demonstrate the accuracy and long-time numerically stable simulations of the algorithm, we perform hydrodynamic computations of a lipid vesicle with bending stiffness and a

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Section: Introductionmentioning

confidence: 93%

“…( 9) for the NH and Sk laws, we also have µ αβ = 0. Following [47,40], the membrane stress tensor can be written as…”

Section: Membrane Constitutive Lawsmentioning

confidence: 99%

An isogeometric boundary element method for soft particles flowing in microfluidic channels

Lyu,

Chen,

Boedec

et al. 2020

Preprint

View full text Add to dashboard Cite

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“…This paper focus on Stokes flow, but the presented quadrature schemes are also applicable to other BE applications like heat transfer (Mera et al, 2002;Zang et al, 2021), acoustics (Amini and Harris, 1990;Venås and Kvamsdal, 2020), elastostatics (Simpson et al, 2012;Taus et al, 2019), mechanical contact (Yac et al, 1970;Zirakashvili, 2020) and electromagnetics (Rajski et al, 2019;Takahashi et al, 2022). The quadrature schemes are further applicable to coupled BE and surface FE formulations that can be used to study droplets (Brown et al, 1980;Sauer, 2014), bubbles (Wang et al, 2003;Boedec et al, 2017), shells (Heltai et al, 2017;Maestre et al, 2017) and wetting (Osman and Sauer, 2015;Luginsland and Sauer, 2017). They can be used to solve unsteady BE problems since the singular integrals investigated here also occur there.…”

Section: Application To Be Analysismentioning

confidence: 99%

New hybrid quadrature schemes for weakly singular kernels applied to isogeometric boundary elements for 3D Stokes flow

Harmel¹,

Sauer²

2022

Preprint

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This work proposes four novel hybrid quadrature schemes for the efficient and accurate evaluation of weakly singular boundary integrals (1/r kernel) on arbitrary smooth surfaces. Such integrals appear in boundary element analysis for several partial differential equations including the Stokes equation for viscous flow and the Helmholtz equation for acoustics. The proposed quadrature schemes apply a Duffy transform-based quadrature rule (Duffy, 1982) to surface elements containing the singularity and classical Gaussian quadrature to the remaining elements. Two of the four schemes additionally consider a special treatment for elements near to the singularity, where refined Gaussian quadrature and a new moment-fitting quadrature rule are used. The hybrid quadrature schemes are systematically studied on flat B-spline patches and on NURBS spheres considering two different sphere discretizations: An exact single-patch sphere with degenerate control points at the poles and an approximate discretization that consist of six patches with regular elements. The efficiency of the quadrature schemes is further demonstrated in boundary element analysis for Stokes flow, where steady problems with rotating and translating curved objects are investigated in convergence studies for both, mesh and quadrature refinement. Much higher convergence rates are observed for the proposed new schemes in comparison to classical schemes.

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“…Since the advent of isogeometric analysis (IGA) [29,30], spline-based discretizations of immersed approaches for FSI problems have proliferated [31,32,33,34,35,36,37,38,39,40,41,42]. This includes NURBS-based and T-spline-based generalizations of the IB method [32,34] and the FD method [33,35,38], which are two of the most widespread immersed approaches for challenging FSI applications.…”

Section: Introductionmentioning

confidence: 99%

The divergence-conforming immersed boundary method: Application to vesicle and capsule dynamics

Casquero,

Bona-Casas,

Toshniwal

et al. 2020

Preprint

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We extend the recently introduced divergence-conforming immersed boundary (DCIB) method [1] to fluid-structure interaction (FSI) problems involving closed co-dimension one solids. We focus on capsules and vesicles, whose discretization is particularly challenging due to the higher-order derivatives that appear in their formulations. In two-dimensional settings, we employ cubic B-splines with periodic knot vectors to obtain discretizations of closed curves with C 2 inter-element continuity. In three-dimensional settings, we use analysis-suitable bi-cubic T-splines to obtain discretizations of closed surfaces with at least C 1 inter-element continuity. Large spurious changes of the fluid volume inside closed codimension one solids is a well-known issue for IB methods. The DCIB method results in volume changes orders of magnitude lower than conventional IB methods. This is a byproduct of discretizing the velocity-pressure pair with divergence-conforming B-splines, which lead to negligible incompressibility errors at the Eulerian level. The higher interelement continuity of divergence-conforming B-splines is also crucial to avoid the quadrature/interpolation errors of IB methods becoming the dominant discretization error. Benchmark and application problems of vesicle and capsule dynamics are solved, including meshindependence studies and comparisons with other numerical methods.

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A 3D isogeometric BE–FE analysis with dynamic remeshing for the simulation of a deformable particle in shear flows

Cited by 20 publications

References 115 publications

An isogeometric boundary element method for soft particles flowing in microfluidic channels

An isogeometric boundary element method for soft particles flowing in microfluidic channels

New hybrid quadrature schemes for weakly singular kernels applied to isogeometric boundary elements for 3D Stokes flow

The divergence-conforming immersed boundary method: Application to vesicle and capsule dynamics

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