Solution of Stokes flow in complex nonsmooth 2D geometries via a linear-scaling high-order adaptive integral equation scheme

Wu, Bowei; Zhu, Hai; Barnett, Alex H.; Veerapaneni, Shravan

doi:10.1016/j.jcp.2020.109361

Cited by 27 publications

(22 citation statements)

References 64 publications

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“…In this study, the channel size between bundles of fiber cloth was less than 100 um, so the Stokes flow equation could be used for numerical simulation [ 54 , 55 ]. The Stokes flow equation is mainly applied to micro-fluid flow with extremely small geometry size, which is another manifestation of the Navier–Stokes equation [ 56 , 57 , 58 ], ignoring the inertia term.…”

Section: Methodsmentioning

confidence: 99%

A General and Efficient Approach for the Dual-Scale Infiltration Flow Balancing in In Situ Injection Molding of Continuous Fiber Reinforced Thermoplastic Composites

Liang

2021

Polymers

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In situ injection molding of continuous fiber reinforced thermoplastic composites is challenged by unbalanced dual-scale infiltration flow due to the pronounced capillary effect. In this paper, a general and efficient approach was proposed for dual-scale infiltration flow balancing based on numerical simulation. Specifically, Stokes and Brinkman equations were used to describe the infiltration flow in inter- and intra-fiber bundles. In particular, capillary pressure drop was integrated in the Brinkmann equation to consider the capillary effect. The infiltration flow front is tracked by the level set method. Numerical simulation and experimental results indicate that the numerical model can accurately demonstrate the unbalanced infiltration flow in inter- and intra-fiber bundles caused by the changes of the injection rate, the resin viscosity, the injection rate, the fiber volume fraction and the capillary number. In addition, the infiltration flow velocity in inter- and intra-fiber bundles can be efficiently tuned by the capillary number, which is mainly determined by the injection rate for a specified resin system. The optimal capillary numbers obtained by simulation and experiment are 0.022 and 0.026, which are very close to each other. Finally, one-dimensional in situ injection molding experiments with constant injection pressure were conducted to prepare fiber reinforced polymerized cyclic butylene terephthalate composite laminate with various flow rates along the infiltration direction. The experimental results confirmed that the lowest porosity and the highest interlaminar shear strength of the composite can only be obtained with the optimized capillary number, which is basically consistent with the simulation results.

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Section: Methodsmentioning

confidence: 99%

A General and Efficient Approach for the Dual-Scale Infiltration Flow Balancing in In Situ Injection Molding of Continuous Fiber Reinforced Thermoplastic Composites

Liang

2021

Polymers

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“…The operators in (43) are discretized by splitting Γ and γ uniformly into M Γ and M γ disjoint panels respectively. In each panel, a p-th order Gauss-Legendre quadrature is employed to evaluate smooth integrals while a local panel-wise close evaluation scheme of [26] is employed to accurately handle corrections for the singularities of S(x, y), T D (x, y) and P D (x, y). A forward Euler time-stepping scheme is used to evolve the particle position and the solution procedure outlined above is repeated at each time-step.…”

Section: Boundary Integral Formulationmentioning

confidence: 99%

Shape optimization of peristaltic pumps transporting rigid particles in Stokes flow

Bonnet¹,

Liu²,

Veerapaneni³

et al. 2021

Preprint

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This paper presents a computational approach for finding the optimal shapes of peristaltic pumps transporting rigid particles in Stokes flow. In particular, we consider shapes that minimize the rate of energy dissipation while pumping a prescribed volume of fluid, number of particles and/or distance traversed by the particles over a set time period. Our approach relies on a recently developed fast and accurate boundary integral solver for simulating multiphase flows through periodic geometries of arbitrary shapes. In order to fully capitalize on the dimensionality reduction feature of the boundary integral methods, shape sensitivities must ideally involve evaluating the physical variables on the particle or pump boundaries only. We show that this can indeed be accomplished owing to the linearity of Stokes flow. The forward problem solves for the particle motion in a slip-driven pipe flow while the adjoint problems in our construction solve quasi-static Dirichlet boundary value problems backwards in time, retracing the particle evolution. The shape sensitivies simply depend on the solution of one forward and one adjoint (for each shape functional) problems. We validate these analytic shape derivative formulas by comparing against finite-difference based gradients and present several examples showcasing optimal pump shapes under various constraints.

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“…However, if the density has regions where refinement is needed (such as corners or close interactions with other bodies), a composite ("panel") scheme is better, as is common with Galerkin boundary-element methods [44]. On each panel a high-order representation (such as the Lagrange basis for a set of Gauss-Legendre nodes) is used; panels may then be split in either a graded [24,36,44] or adaptive [37,41,50] fashion.…”

Section: Introductionmentioning

confidence: 99%

Accurate quadrature of nearly singular line integrals in two and three dimensions by singularity swapping

Klinteberg

Barnett

2020

Bit Numer Math

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The numerical method of Helsing and co-workers evaluates Laplace and related layer potentials generated by a panel (composite) quadrature on a curve, efficiently and with high-order accuracy for arbitrarily close targets. Since it exploits complex analysis, its use has been restricted to two dimensions (2D). We first explain its loss of accuracy as panels become curved, using a classical complex approximation result of Walsh that can be interpreted as “electrostatic shielding” of a Schwarz singularity. We then introduce a variant that swaps the target singularity for one at its complexified parameter preimage; in the latter space the panel is flat, hence the convergence rate can be much higher. The preimage is found robustly by Newton iteration. This idea also enables, for the first time, a near-singular quadrature for potentials generated by smooth curves in 3D, building on recurrences of Tornberg–Gustavsson. We apply this to accurate evaluation of the Stokes flow near to a curved filament in the slender body approximation. Our 3D method is several times more efficient (both in terms of kernel evaluations, and in speed in a C implementation) than the only existing alternative, namely, adaptive integration.

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Solution of Stokes flow in complex nonsmooth 2D geometries via a linear-scaling high-order adaptive integral equation scheme

Cited by 27 publications

References 64 publications

A General and Efficient Approach for the Dual-Scale Infiltration Flow Balancing in In Situ Injection Molding of Continuous Fiber Reinforced Thermoplastic Composites

A General and Efficient Approach for the Dual-Scale Infiltration Flow Balancing in In Situ Injection Molding of Continuous Fiber Reinforced Thermoplastic Composites

Shape optimization of peristaltic pumps transporting rigid particles in Stokes flow

Accurate quadrature of nearly singular line integrals in two and three dimensions by singularity swapping

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