Interface Capturing in Dual-Flow Microfluidics

Shapiro, Evgeniy; Drikakis, Dimitris; Gargiuli, Joseph; Vadgama, Pankaj

doi:10.1166/jctn.2007.2371

Cited by 7 publications

(5 citation statements)

References 15 publications

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“…The discretized system of governing equations is solved via a dual-time stepping numerical procedure, therefore a pseudo-time stepping strategy is required for stability reasons. The accuracy and convergence properties of CB schemes were investigated by Shapiro and Drikakis [22] based on an eigenvalue analysis to estimate the locally computed pseudo-time step size. The relationship between the pseudo-time step and characteristic condition numbers provides the stability of the numerical procedure [20] as…”

Section: Pseudo-time Stepping Strategymentioning

confidence: 99%

“…where CFL Inviscid and CFL Viscous are the Courant-Friedrichs-Lewy (CFL) numbers of the inviscid and viscous fluxes, respectively, and dl n represents the cell dimension according to the coordinate directions. The CFL numbers are characteristic condition numbers relating to the stiffness of the numerical solution [22]. For stability reasons, the locally computed pseudo-time step is defined by the minimum value of the locally determined pseudo-time steps for the inviscid and viscous fluxes as…”

Section: Pseudo-time Stepping Strategymentioning

confidence: 99%

“…Eberle [16] developed a CB scheme method for the three-dimensional compressible Euler equations, and the scheme was further extended by Drikakis et al [17] for solving the incompressible Navier-Stokes equations. This scheme was also extended to three-dimensional incompressible flows [18,19] in conjunction with a nonlinear, FMG-FAS algorithm, as well as to variable density flows [20][21][22]. Recently, Za-mzamian and Razavi [23] further investigated the numerical behaviour of a multidimensional, characteristics-based (MCB) upwind scheme on different benchmarks.…”

Section: Introductionmentioning

confidence: 99%

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A Unified Fractional-Step, Artificial Compressibility and Pressure-Projection Formulation for Solving the Incompressible Navier-Stokes Equations

Könözsy

Drikakis

2014

Commun. comput. phys.

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This paper introduces a unified concept and algorithm for the fractional-step (FS), artificial compressibility (AC) and pressure-projection (PP) methods for solving the incompressible Navier-Stokes equations. The proposed FSAC-PP approach falls into the group of pseudo-time splitting high-resolution methods incorporating the characteristics-based (CB) Godunov-type treatment of convective terms with PP methods. Due to the fact that the CB Godunov-type methods are applicable directly to the hyperbolic AC formulation and not to the elliptical FS-PP (split) methods, thus the straightforward coupling of CB Godunov-type schemes with PP methods is not possible. Therefore, the proposed FSAC-PP approach unifies the fully-explicit AC and semi-implicit FS-PP methods of Chorin including a PP step in the dual-time stepping procedure to a) overcome the numerical stiffness of the classical AC approach at (very) low and moderate Reynolds numbers, b) incorporate the accuracy and convergence properties of CB Godunov-type schemes with PP methods, and c) further improve the stability and efficiency of the AC method for steady and unsteady flow problems. The FSAC-PPmethod has also been coupled with a non-linear, full-multigrid and fullapproximation storage (FMG-FAS) technique to further increase the efficiency of the solution. For validating the proposed FSAC-PP method, computational examples are presented for benchmark problems. The overall results show that the unified FSAC-PP approach is an efficient algorithm for solving incompressible flow problems.

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Section: Pseudo-time Stepping Strategymentioning

confidence: 99%

Section: Pseudo-time Stepping Strategymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Unified Fractional-Step, Artificial Compressibility and Pressure-Projection Formulation for Solving the Incompressible Navier-Stokes Equations

Könözsy

Drikakis

2014

Commun. comput. phys.

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“…Eulerian one flow model [26,27], or a multiphase entity, i.e. Eulerian-Eulerian two-flow model [28][29][30]. This paper adopts the global modelling approach, in which two flows modelled are single phase.…”

Section: I)mentioning

confidence: 99%

Progress towards the design and numerical analysis of a 3D microchannel biochip separator

Xue¹,

Marson²,

Patel³

et al. 2011

Numer Methods Biomed Eng

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This paper reports the design and numerical analysis of a three‐dimensional biochip plasma blood separator using computational fluid dynamics techniques. Based on the initial configuration of a two‐dimensional (2D) separator, five three‐dimensional (3D) microchannel biochip designs are categorically developed through axial and plenary symmetrical expansions. These include the geometric variations of three types of the branch side channels (circular, rectangular, disc) and two types of the main channel (solid and concentric). Ignoring the initial transient behaviour and assuming that steady‐state flow has been established, the behaviour of the blood fluid in the devices is algebraically analysed and numerically modelled. The roles of the relevant microchannel mechanisms, i.e. bifurcation, constriction and bending channel, on promoting the separation process are analysed based on modelling results. The differences among the different 3D implementations are compared and discussed. The advantages of 3D over 2D separator in increasing separation volume and effectively depleting cell‐free layer fluid from the whole cross section circumference are addressed and illustrated. Copyright © 2011 John Wiley & Sons, Ltd.

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“…The high-resolution methods applied in the context of the artificial compressibility approach have been shown to better capture discontinuities in multicomponent microfluidic flows. 44 The continuum level solution for flow in micro-and nanofluidic devices can be obtained using in-house or open-source codes (e.g., OpenFOAM) based on methods listed above. Whenever feasible, this approach provides great advantages, out of which extensibility is probably the most important one.…”

Section: Numerical Approachesmentioning

confidence: 99%