Advecting normal vectors: A new method for calculating interface normals and curvatures when modeling two-phase flows

Raessi, Mehdi; Mostaghimi, J.; Bussmann, Markus

doi:10.1016/j.jcp.2007.04.023

Cited by 41 publications

(39 citation statements)

References 34 publications

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“…According to this condition, a signed-distance level set function remains signed-distance if u n does not have any spatial variation in the direction normal to the level set function, see [22]. If the advection field does not meet the condition (8), the signed distance property can be recovered by performing a re-initialization procedure that of course must not move the interface.…”

Section: Level Set Re-initialization Equationmentioning

confidence: 99%

See 1 more Smart Citation

Level Set Method for Simulating the Interface Kinematics: Application of a Discontinuous Galerkin Method

Mousavi¹,

Kummer²,

Oberlack³

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Section: Level Set Re-initialization Equationmentioning

confidence: 99%

“…Multiplying ϵ by |∇ϕ| in the formulation (22), modifies the smoothing width in order to prevent the numerical instability. As it was mentioned before, in the present research we prefer to use a smoothed Signum function with a finite width.…”

Section: Level Set Re-initialization Equationmentioning

confidence: 99%

Level Set Method for Simulating the Interface Kinematics: Application of a Discontinuous Galerkin Method

Mousavi¹,

Kummer²,

Oberlack³

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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show abstract

“…In the work of Raessi et al [16], the normal vector is imposed with the unit normal constraint. Although the normalization of an SN vector does not change the orientation and the curvature of an interface, it destroys the solution in the neighborhood of the vector of zero magnitude and creates one or more discontinuities there.…”

Section: Sunmentioning

confidence: 99%

“…The idea is to treat the SN vector as independent variables that are integrated along with the advection algorithm, instead of calculating them from (3). The equations for the SN vector imposed with the unit normal constraint (|n| = 1) were tested by Raessi et al [16], and accurate surface curvatures for resolvable circular interfaces Figure 1. A PLIC-VOF method may reconstruct a subgrid particle, given the phase volume and the normal vector.…”

Section: Introductionmentioning

confidence: 99%

Volume‐tracking of subgrid particles

Sun

2011

Numerical Methods in Fluids

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SUMMARYA new PLIC-VOF method is proposed to track deformable particles, such as bubbles and liquid droplets, that can be smaller than the grid spacing. The idea is to replace the surface normal (SN) calculation used in the PLIC, by the SN vector obtained from partial differential equations that are solved together with the advection algorithm. The equations for the evolution of SN vector are derived, and examined by using the first-order and the second-order upwind schemes. Since the normal vector is defined in every cell, the method generally improves the accuracy at low grid resolution. It is found that a normal vector of zero magnitude is located at the centroid of a particle, to second-order accuracy for small particles. The motion of a subgrid particle is controlled by the arrival of the zero vector in the present PLIC/SN method, so that the particle can be translated at the right speed without any additional treatment. This has been numerically verified by simulating a particle of one-tenth of grid spacing traveling in three different directions, in addition to a few typical test cases.

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“…These principles can be expressed mathematically at every point in space and time by local, instantaneous field equations as reported by Attia (2003), Kumar and Prasad (2014), Chutia and Deka (2015). Some other researchers used computational simulation, using both, the volume-of-fluid method and level set method to analyze two phase flow, like Raessi et al (2007). On other hand, Ghasemi et al (2015) developed simulation procedure for system power output, vorticity flow field, and hydrodynamic coefficients.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling of the Flow of Diesel-CNG Fuel Mixture in a Pipe under the Influence of a Magnetic Field

Wahhab¹,

Aziz²,

Al-Kayiem³

et al. 2017

JAFM

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Horizontal bubbly flow is encountered in various gas and oil facilities and industrial systems. Bubbly flow is characterized by the ability to provide large interfacial areas for heat and mass transfer. Nonetheless, horizontal bubbly flow orientation has received less attention when compared to vertical bubbly flow. This paper presents development of mathematical model and discusses the results obtained from the simulation of hydro-magnetic flow of Diesel-CNG fuel mixture in a horizontal pipe, as predicted by the developed model. The fundamental equations of unsteady, two-phase liquid-gas under an imposed magnetic field were derived and presented. Derivation procedure of the velocity distribution of the liquid and gas phases and the inverse Stokes' number of a bubbly flow are presented. These governing nonlinear partial-differential equations have been solved numerically using a Fourier-Bessel series. Results obtained from the model solution show that the axial velocities of liquid and gas, in laminar flow, have decreased and the slip ratio has increased with the increase of the magnetic field intensity. While, the magnetic field parameter, Ha increased the probability of decreasing the bubbles radii and increasing the bubbles number (n.Rb).

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Advecting normal vectors: A new method for calculating interface normals and curvatures when modeling two-phase flows

Cited by 41 publications

References 34 publications

Level Set Method for Simulating the Interface Kinematics: Application of a Discontinuous Galerkin Method

Level Set Method for Simulating the Interface Kinematics: Application of a Discontinuous Galerkin Method

Volume‐tracking of subgrid particles

Mathematical Modeling of the Flow of Diesel-CNG Fuel Mixture in a Pipe under the Influence of a Magnetic Field

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