A Lagrangian particle level set method

Hieber, Simone; Koumoutsakos, Petros

doi:10.1016/j.jcp.2005.04.013

Cited by 148 publications

(117 citation statements)

References 47 publications

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“…These numbers are much less than the particle level set method [6,8]. The method in [6] requires approximately 5.9 × 10 4 particles at t = 0 to sample the initial circle with grid resolution of only 256 2 in the particle level set method [6], and at least 5.5 × 10 4 particles at t = 0 with grid resolution of 1000 2 using the lagrangian particle level set method [8]. [6] did not report any numbers on the Lagrangian particles used, but we expect more and more particles were required to fix the interface as it rolls-up.…”

Section: Motions Under Single Vortex Flowmentioning

confidence: 93%

“…The following example on vortex flow has been widely used [6,8,11] as an important test case for various numerical methods. It was originally proposed by Bell et al [2] to test if a numerical method is able to resolve very thin filaments.…”

Section: Motions Under Single Vortex Flowmentioning

confidence: 99%

“…We are using approximately 2.4 × 10 4 Lagrangian particles to sample the interface at t = 3 using a uniform underlying grid, while approximately 2 × 10 4 particles to sample the interface at the same value of t using an adaptive grid with the coarsest resolution of 129 2 and the finest resolution of 1025 2 . These numbers are much less than the particle level set method [6,8]. The method in [6] requires approximately 5.9 × 10 4 particles at t = 0 to sample the initial circle with grid resolution of only 256 2 in the particle level set method [6], and at least 5.5 × 10 4 particles at t = 0 with grid resolution of 1000 2 using the lagrangian particle level set method [8].…”

Section: Motions Under Single Vortex Flowmentioning

confidence: 99%

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A grid based particle method for moving interface problems

Leung

Zhao

2009

Journal of Computational Physics

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We propose a novel algorithm for modeling interface motions. The interface is represented and is tracked using quasi-uniform meshless particles. These particles are sampled according to an underlying grid such that each particle is associated to a grid point which is in the neighborhood of the interface. The underlying grid provides an Eulerian reference and local sampling rate for the particles on the interface. It also renders neighborhood information among the meshless particles for local reconstruction of the interface. The resulting algorithm, which is based on Lagrangian tracking using meshless particles with Eulerian reference grid, can naturally handle/control topological changes. Moreover, adaptive sampling of the interface can be achieved easily through local grid refinement with simple quad/oct-tree data structure. Extensive numerical examples are presented to demonstrate the capability of our new algorithm.

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Section: Motions Under Single Vortex Flowmentioning

confidence: 93%

Section: Motions Under Single Vortex Flowmentioning

confidence: 99%

Section: Motions Under Single Vortex Flowmentioning

confidence: 99%

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A grid based particle method for moving interface problems

Leung

Zhao

2009

Journal of Computational Physics

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“…Indeed, solving the level set equations (4) and (5) does not guarantee conservation of the fluid mass, as formally conservation of does not imply conservation of mass. Typically, in transient level set simulations, the fluid mass varies with time; however, these variations can be significantly minimized by using special numerical procedures [3,28,29].…”

Section: Resultsmentioning

confidence: 99%

On surface tension modelling using the level set method

Shepel¹,

Smith

2008

Numerical Methods in Fluids

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SUMMARYThe paper describes and compares the performance of two options for numerically representing the surface tension force in combination with the level set interface-tracking method. In both models, the surface tension is represented as a body force, concentrated near the interface, but the technical implementation is different: the first model is based on a traditional level set approach in which the force is distributed in a band around the interface using a regularized delta function, whereas in the second, the force is partly distributed in a band around the interface and partly localized to the actual computational cells containing the interface. A comparative study, involving analysis of several two-phase flows with moving interfaces, shows that in general the two surface tension models produce results of similar accuracy. However, in the particular case of merging and pinching-off of interfaces, the traditional level set model of surface tension produces an error that results in non-converging solutions for film-like interfaces (i.e. ones involving large contact areas). In contrast, the second model, based on the localized representation of the surface tension force, displays consistent first-order convergence.

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“…These works take advantage of the exact Lagrangian solution to advection equation in order to limit the numerical diffusion of grid-based method and enforce mass conservation. In [15,10], on the other hand, the use of regular remeshed particle methods was advocated to ensure an efficient treatment of advection equations. By remeshed particles methods, we mean particle methods where particles are simply advected and remeshed on a regular grid through high order interpolation kernels.…”

Section: Introductionmentioning

confidence: 99%

Accurate, non-oscillatory, remeshing schemes for particle methods

Magni

Cottet

2012

Journal of Computational Physics

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PreprintInternational audienceIn this article we propose and validate new remeshing schemes for the simulation of transport equations by particle methods. Particle remeshing is a common way to control the regularity of the particle distribution which is necessary to guarantee the accuracy of particle methods in presence of strong strain in a flow. Using a grid-based analysis, we derive remeshing schemes that can be used in a consistent way at every time-step in a particle method. The schemes are obtained by local corrections of classical third order and fth order interpolation kernels. The time-step to be used in the resulting push-and-remesh particle method is determined on the basis of rigorous bounds and can signi cantly exceed values obtained by CFL conditions in usual grid-based Eulerian methods. In addition, we extend the analysis of [5] to obtain TVD remeshing schemes that avoid oscillations of remeshing formulas near sharp variations of the solution. These methods are illustrated in several flow conditions in 1D, 2D and 3D

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A Lagrangian particle level set method

Cited by 148 publications

References 47 publications

A grid based particle method for moving interface problems

A grid based particle method for moving interface problems

On surface tension modelling using the level set method

Accurate, non-oscillatory, remeshing schemes for particle methods

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