An improved level set method for incompressible two-phase flows

Sussman, Mark; Fatemi, Emad; Smereka, Peter; Osher, Stanley

doi:10.1016/s0045-7930(97)00053-4

Cited by 707 publications

(499 citation statements)

References 17 publications

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“…Traditional CFD methods such as the volume-of-fluid (VOF) method [18][19][20][21] and level set (LS) method [22][23][24] simulate multiphase flows by solving the macroscopic Navier-Stokes equations together with a proper technique to track/capture the phase interface. It is challenging to use VOF and LS methods for pore-scale simulations of multiphase flows in porous media because of the difficulties in modelling and tracking the dynamic phase interfaces.…”

Section: Introductionmentioning

confidence: 99%

Multiphase lattice Boltzmann simulations for porous media applications

et al. 2015

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Over the last two decades, lattice Boltzmann methods have become an increasingly popular tool to compute the flow in complex geometries such as porous media. In addition to single phase simulations allowing, for example, a precise quantification of the permeability of a porous sample, a number of extensions to the lattice Boltzmann method are available which allow to study multiphase and multicomponent flows on a pore scale level. In this article, we give an extensive overview on a number of these diffuse interface models and discuss their advantages and disadvantages. Furthermore, we shortly report on multiphase flows containing solid particles, as well as implementation details and optimization issues.

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Section: Introductionmentioning

confidence: 99%

Multiphase lattice Boltzmann simulations for porous media applications

et al. 2015

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“…The equations (13) and (14) together with the condition that the interface should not be affected by the re-initialization, can be then combined into the following compact form proposed in [10],…”

Section: Level Set Re-initialization Equationmentioning

confidence: 99%

“…Although in the DG-based level set method the level set function does not need to be signed distance, this property is required for making a uniform diffusion thickness when a diffuse interface assumption is made, see [8,9]. The signed distance property of a level set function can be maintained by solving an Eikonal equation termed as the level set re-initialization equation, see [10]. Application of the DG method for solving the re-initialization equation has been only considered in [9] yet.…”

Section: Introductionmentioning

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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“…Thresholding is a very abrupt method so it risks to cause discontinuities in the propagation. To avoid this, the Heaviside function defined in [23] is used to get a smoother thresholding.…”

Section: Thresholdingmentioning

confidence: 99%

White Matter Mapping in DT-MRI Using Geometric Flows

Jonasson

Hagmann

Bresson

et al. 2003

Computer Aided Systems Theory - EUROCAST 2003

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Abstract. We present a 3D geometric flow designed to evolve in Diffusion Tensor Magnetic Resonance Images(DT-MRI) along fiber tracts by measuring the diffusive similarity between voxels. Therefore we define a front propagation speed that is proportional to the similarity between the tensors lying on the surface and its neighbor in the propagation direction. The method is based on the assumption that successive voxels in a tract have similar diffusion properties. The front propagation is implemented using level set methods by Osher and Sethian [1] to simplify the handling of topology changes and provides an elegant tool for smoothing the segmented tracts. While many methods demand a regularized tensor field, our geometrical flow performs a regularization as it evolves along the fibers. This is done by a curvature dependent smoothing term adapted for thin tubular structures. The purpose of our approach is to get a quantitative measure of the diffusion in segmented fiber tracts. This kind of information can also be used for white matter registration and for surgical planning.

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An improved level set method for incompressible two-phase flows

Cited by 707 publications

References 17 publications

Multiphase lattice Boltzmann simulations for porous media applications

Multiphase lattice Boltzmann simulations for porous media applications

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

White Matter Mapping in DT-MRI Using Geometric Flows

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