On the properties and limitations of the height function method in two-dimensional Cartesian geometry

Bornia, Giorgio; Cervone, A.; Manservisi, Sandro; Scardovelli, Ruben; Zaleski, Stéphane

doi:10.1016/j.jcp.2010.11.029

Cited by 54 publications

(42 citation statements)

References 20 publications

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“…After the reconstruction, direction-split geometrical fluxes are computed to advect the interface (DeBar, 1974;Rudman, 1997). The VOF method has been shown to preserve sharp interfaces and be close to second-order accuracy for practical applications (Aulisa et al, 2007;Popinet, 2009;Bornia et al, 2011).…”

Section: Governing Equationsmentioning

confidence: 99%

Multiscale simulation of atomization with small droplets represented by a Lagrangian point-particle model

Ling

Zaleski

Scardovelli

2015

International Journal of Multiphase Flow

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130

107

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a b s t r a c tModeling and simulation of atomization is challenging due to the existence of a wide range of length scales. This multiscale nature of atomization introduces a fundamental challenge to numerical simulation. A pathway to comprehensive modeling is still to be found. The present study proposes a multiscale multiphase flow model for atomization simulations, where the large-scale interfaces are resolved by the Volume-of-Fluid (VOF) method and the small droplets by the Lagrangian point-particle (LPP) model. Particular attention is focused on the momentum coupling between LPP and resolved flow and the conversion between droplets represented by VOF and LPP. A series of multiphase flow problems are considered to validate the model. The results obtained by a number of simulations are compared against direct numerical simulation (DNS) results and experimental data. In particular, the model is applied to simulate the gas-assisted atomization experiment, and the numerical results are compared to the experimental measurements for a quantitative validation.

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Section: Governing Equationsmentioning

confidence: 99%

Multiscale simulation of atomization with small droplets represented by a Lagrangian point-particle model

Ling

Zaleski

Scardovelli

2015

International Journal of Multiphase Flow

Self Cite

130

107

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“…Finally, quantities at the locations x d andx are approximated using the non-oscillatory interpolation procedure given in equation (19).…”

Section: Discretization Of the Level-set Equationmentioning

confidence: 99%

“…In additions, adaptive framework have been introduced (see e.g. [138,15,3,14,143,76,51,19,137,10,92,4,111,41,25,58,128,66] and the references therein).…”

Section: Improvement On Mass Conservationmentioning

confidence: 99%

High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries

2012

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We present a review of some of the state-of-the-art numerical methods for solving the Stefan problem and the Poisson and the diffusion equations on irregular domains using (i) the level-set method for representing the (possibly moving) irregular domain's boundary, (ii) the ghost-fluid method for imposing the Dirichlet boundary condition at the irregular domain's boundary and (iii) a quadtree/octree nodebased adaptive mesh refinement for capturing small length scales while significantly reducing the memory and CPU footprint. In addition, we highlight common misconceptions and describe how to properly implement these methods. Numerical experiments illustrate quantitative and qualitative results.

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“…The HF method has been shown to be second-order convergent in n and κ numerically [15,19,24]. The second-order accuracy was corroborated analytically provided that the function describing the interface could be approximated to second order with H [18].…”

Section: Overview Of the Height-function Technique On A Structured Gridmentioning

confidence: 87%

“…When this constraint is not satisfied, like in cell (i, j + 1) of Fig. 2(c), the interface crosses multiple cells along the middle HF column, degrading the accuracy of this method [18,19,24]. For the interface cells, 0 < F < 1, that do not satisfy this criterion, n and κ are determined through an interpolation of the neighboring interface cells that do satisfy this criterion.…”

Section: Overview Of the Height-function Technique On A Structured Gridmentioning

confidence: 99%

Accurate interface normal and curvature estimates on three-dimensional unstructured non-convex polyhedral meshes

Ivey

Moin

2015

Journal of Computational Physics

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This paper presents a framework for extending the height-function technique for the calculation of interface normals and curvatures to unstructured non-convex polyhedral meshes with application to the piecewise-linear interface calculation volume-of-fluid method. The methodology is developed with reference to a collocated node-based finitevolume two-phase flow solver that utilizes the median-dual mesh, requiring a set of data structures and algorithms for non-convex polyhedral operations: truncation of a polyhedron by a plane, intersection of two polyhedra, joining of two convex polyhedra, volume enforcement of a polyhedron by a plane, and volume fraction initialization by a signed-distance function. By leveraging these geometric tools, a geometric interpolation strategy for embedding structured height-function stencils in unstructured meshes is developed. The embedded height-function technique is tested on surfaces with known interface normals and curvatures, namely cylinder, sphere, and ellipsoid. Tests are performed on the median duals of a uniform cartesian mesh, a wedge mesh, and a tetrahedral mesh, and comparisons are made with conventional methods. Across the tests, the embedded height-function technique outperforms contemporary methods and its accuracy approaches the accuracy that the traditional height-function technique exemplifies on uniform cartesian meshes.

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On the properties and limitations of the height function method in two-dimensional Cartesian geometry

Cited by 54 publications

References 20 publications

Multiscale simulation of atomization with small droplets represented by a Lagrangian point-particle model

Multiscale simulation of atomization with small droplets represented by a Lagrangian point-particle model

High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries

Accurate interface normal and curvature estimates on three-dimensional unstructured non-convex polyhedral meshes

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