The MAC method

McKee, Sean; Tomé, Murilo Francisco; Ferreira, Valdemir Garcia; Cuminato, José Alberto; Castelo, A.; Sousa, Fabrício S.; Mangiavacchi, Norberto

doi:10.1016/j.compfluid.2007.10.006

Cited by 170 publications

(95 citation statements)

References 94 publications

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“…Front-tracking methods have been implemented in [30,31] to simulate the deformation of viscoelastic droplets immersed in a Newtonian liquid. Tomé et al [32] developed a variant of the marker-and-cell method [33] for two-and three-dimensional transient simulations of non-Newtonian free-surface flows, where only the non-Newtonian phase is solved (i.e. the flow of the surrounding air is omitted).…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of the planar extrudate swell of pseudoplastic and viscoelastic fluids with the streamfunction and the VOF methods

Comminal

Pimenta

Hattel

et al. 2018

Journal of Non-Newtonian Fluid Mechanics

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. Numerical simulation of the planar extrudate swell of pseudoplastic and viscoelastic fluids with the streamfunction and the VOF methods. Journal of Non-Newtonian Fluid Mechanics, 252, 1-18. DOI: 10.1016/j.jnnfm.2017 A B S T R A C TWe present an Eulerian free-surface flow solver for incompressible pseudoplastic and viscoelastic non-Newtonian fluids. The free-surface flow solver is based on the streamfunction flow formulation and the volume-of-fluid method. The streamfunction solver computes the vector potential of a solenoidal velocity field, which ensures by construction the mass conservation of the solution, and removes the pressure unknown. Pseudoplastic liquids are modelled with a Carreau model. The viscoelastic fluids are governed by differential constitutive models reformulated with the log-conformation approach, in order to preserve the positive-definiteness of the conformation tensor, and to circumvent the high Weissenberg number problem. The volume fraction of the fluid is advected with a geometric conservative unsplit scheme that preserves a sharp interface representation. For the sake of comparison, we also implemented an algebraic advection scheme for the liquid volume fraction. The proposed numerical method is tested by simulating the planar extrudate swell with the Carreau, Oldroyd-B and Giesekus constitutive models. The swell ratio of the extrudates are compared with the data available in the literature, as well as with numerical simulations performed with the open-source rheoTool toolbox in OpenFOAM ® . While the simulations of the generalized Newtonian fluids achieved mesh independence for all the methods tested, the flow simulations of the viscoelastic fluids are more sensitive to mesh refinement and the choice of numerical scheme. Moreover, the simulations of Oldroyd-B fluid flows above a critical Weissenberg number are prone to artificial surface instabilities. These numerical artifacts are due to discretization errors within the Eulerian surface-capturing method. However, the numerical issues arise from the stress singularity at the die exit corner, and the unphysical predictions of the Oldroyd-B model in the skin layer of the extrudate after the die exit, where large extensional deformations occur.

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Section: Introductionmentioning

confidence: 99%

Numerical simulation of the planar extrudate swell of pseudoplastic and viscoelastic fluids with the streamfunction and the VOF methods

Comminal

Pimenta

Hattel

et al. 2018

Journal of Non-Newtonian Fluid Mechanics

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“…Examples of the former approach are the Marker and Cell (MAC) method [22] and the arbitrary Lagranigian-Eulerian (ALE) method ( [23], for example). This approach is very accurate and efficient for tracking moving boundaries with very small deformations but has difficulty addressing complex interface motion such as interface coalescence or breakup, needing continuous re-meshing as the interface shape evolves.…”

Section: Volume Of Fluid (Vof) Methodsmentioning

confidence: 99%

Evaporation analysis in sintered wick microstructures

Bodla

Murthy

Garimella

2013

International Journal of Heat and Mass Transfer

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Heat pipes offer passive transport of heat over long distances without incurring a significant drop in temperature. Topological and microstructural details of the wick material embedded in a heat pipe help determine its thermal performance. A good understanding of pore-scale transport phenomena is crucial to enhancing heat pipe performance. In this study, pore-scale analysis of thin-film evaporation through sintered copper wicks is performed. X-ray microtomography is employed to generate geometrically faithful, feature-preserving meshes. Commercial sintered wicks with particle sizes in the range of 45-60 μm, 106-150 μm and 250-355 μm and with approximately 61% porosity are considered. The capillary pressure, characteristic pore radius, percentage thin film area and evaporative mass and heat fluxes are computed using a Volume of Fluid (VOF) approach. Two different solution strategies are employed to stabilize the numerical solution and to improve convergence. After verifying that these strategies yield the correct solution, the VOF model is used to obtain static meniscus shapes in the pore space of the sintered wick samples. The meniscus shape is then held fixed and steady-state, thin-film evaporation analysis is performed. Liquid-vapor phase change heat transfer is modeled using a modified Schrage equation. Based on the present analysis, the best performing sample (particle size range) is identified along with the optimum contact angle.

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“…The 3D version of the Freeflow simulation system (see [20]), equipped with the MAC methodology and TOPUS scheme, was used in a similar way to previous sections. Details of the free surface boundary conditions can be found in [19].…”

Section: Applications: Full 3d Moving Free Surface Flowsmentioning

confidence: 99%

“…This software, in the context of finite volume methodology, uses the Godunov's method with a correction term; one can provide additional code for initial and boundary conditions and add new limiters. Incompressible viscous flows are simulated by using the primitive variable (front-tracking/finite difference) Marker-And-Cell (MAC) technique: this is a special case of the projection method of Chorin [17] described by Harlow and Welch [18] (see also McKee et al [19]). This method, associated with the upwind TOPUS scheme (and other upwinding schemes), has been incorporated into the Freeflow code of Castelo et al [20] to solve complex incompressible moving free surface flows.…”

Section: Summary Of the Topus Scheme And Its Modificationmentioning

confidence: 99%

Simulation results and applications of an advection bounded scheme to practical flows

Ferreira¹,

Queiroz²,

Candezano³

et al. 2012

Comput. Appl. Math.

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Abstract. This paper reports experiments on the use of a recently introduced advection bounded upwinding scheme, namely TOPUS (Computers & Fluids 57 (2012) 208-224), for flows of practical interest. The numerical results are compared against analytical, numerical and experimental data and show good agreement with them. It is concluded that the TOPUS scheme is a competent, powerful and generic scheme for complex flow phenomena.Mathematical subject classification: Primary: 06B10; Secondary: 06D05.

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The MAC method

Cited by 170 publications

References 94 publications

Numerical simulation of the planar extrudate swell of pseudoplastic and viscoelastic fluids with the streamfunction and the VOF methods

Numerical simulation of the planar extrudate swell of pseudoplastic and viscoelastic fluids with the streamfunction and the VOF methods

Evaporation analysis in sintered wick microstructures

Simulation results and applications of an advection bounded scheme to practical flows

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