A Level Set Method for Simulation of Coalescence of Droplets

2005 ◽  
Author(s):  
A. Salih ◽  
S. Ghosh Moulic
Keyword(s):  
Surface Tension ◽  
Level Set Method ◽  
Level Set ◽  
Stokes Equations ◽  
Surface Tension Force ◽  
Tension Force ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Level Set Function ◽  
Set Function

In the present paper, we discuss a numerical method based on the level set algorithm to simulate two-phase fluid flow systems. Surface tension force at the fluid interface is implemented through the CSF model of Brackbill et al. [1]. The incompressible Navier-Stokes equations were solved on a staggered grid using an explicit projection method. A fifth-order WENO [2] scheme was used for advancing the level set function. We improved the implementation of WENO scheme by staggering the level set function. The Navier-Stokes part of the code was validated by computing the standard lid-driven cavity flow and the free surface part of the code was validated by advecting the interface in a prescribed velocity field. The Young-Laplace law for a static drop has been verified to validate the implementation of surface tension force. We simulated the coalescence of two drops under zero-gravity condition and evaluated the mass conservation property of the level set method.

Simulation of Wave-Body Interaction Using a Single-Phase Level Set Function in the SWENSE Method

2013 ◽  
Author(s):  
Gabriel Reliquet ◽  
Aurélien Drouet ◽  
Pierre-Emmanuel Guillerm ◽  
Erwan Jacquin ◽  
Lionel Gentaz ◽  
...  
Keyword(s):  
Free Surface ◽  
Level Set Method ◽  
Level Set ◽  
Single Phase ◽  
Stokes Equations ◽  
Flow Theory ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Level Set Function ◽  
Set Function

The purpose of this paper is to present combination of the SWENSE (Spectral Wave Explicit Navier-Stokes Equations – [1]) method — an original method to treat fully nonlinear wave-body interactions — and a free surface RANSE (Reynolds Averaged Navier-Stokes Equations) solver using a single-phase Level Set method to capture the interface. The idea is to be able to simulate wave-body interactions under viscous flow theory with strong deformations of the interface (wave breaking in the vicinity of the body, green water on ship decks…), while keeping the advantages of the SWENSE scheme. The SWENSE approach is based on a physical decomposition by combining incident waves described by a nonlinear spectral scheme based on potential flow theory and an adapted Navier-Stokes solver where only the diffracted part of the flow is solved, incident flow parameters seen as forcing terms. In the single-phase Level Set method [2, 3], the air phase is neglected. Thus, only the liquid phase is solved considering a fluid with uniform properties. The location of the free surface is determined by a Level Set function initialised as the signed distance. The accuracy of simulation depends essentially on the pressure scheme used to impose free surface dynamic boundary condition. Comparisons of numerical results with experimental and numerical data for US navy combatant DTMB 5415 in calm water and in head waves are presented.

Numerical Simulation of Breaking Waves Using a Level Set Method

2002 ◽  
Author(s):  
Pablo Go´mez ◽  
Julio Herna´ndez ◽  
Joaqui´n Lo´pez ◽  
Fe´lix Faura
Keyword(s):  
Free Surface ◽  
Level Set Method ◽  
Level Set ◽  
Stokes Equations ◽  
Numerical Study ◽  
Operating Conditions ◽  
Breaking Wave ◽  
Level Set Function ◽  
Set Function ◽  
The Impact

A numerical study of the initial stages of wave breaking processes in shallow water is presented. The waves considered are assumed to be generated by moving a piston in a two-dimensional channel, and may appear, for example, in the injection chamber of a high-pressure die casting machine under operating conditions far from the optimal. A numerical model based on a finite-difference discretization of the Navier-Stokes equations in a Cartesian grid and a second-order approximate projection method has been developed and used to carry out the simulations. The evolution of the free surface is described using a level set method, with a reinitialization procedure of the level set function which uses a local grid refinement near the free surface. The ability of different algorithms to improve mass conservation in the reinitialization step of the level set function has been tested in a time-reversed single vortex flow. The results for the breaking wave profiles show the flow characteristics after the impact of the first plunging jet onto the wave’s forward face and during the subsequent splash-up.

An Improved Three-Dimensional Level Set Method for Gas-Liquid Two-Phase Flows

2004 ◽  
Vol 126 (4) ◽  
pp. 578-585 ◽  
Author(s):  
Hiroyuki Takahira ◽  
Tomonori Horiuchi ◽  
Sanjoy Banerjee
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Stokes Equations ◽  
Interpolation Method ◽  
Density Ratio ◽  
Three Dimensional ◽  
Mass Conservation ◽  
Staggered Grid ◽  
Two Phase ◽  
Level Set Function

For the present study, we developed a three-dimensional numerical method based on the level set method that is applicable to two-phase systems with high-density ratio. The present solver for the Navier-Stokes equations was based on the projection method with a non-staggered grid. We improved the treatment of the convection terms and the interpolation method that was used to obtain the intermediate volume flux defined on the cell faces. We also improved the solver for the pressure Poisson equations and the reinitialization procedure of the level set function. It was shown that the present solver worked very well even for a density ratio of the two fluids of 1:1000. We simulated the coalescence of two rising bubbles under gravity, and a gas bubble bursting at a free surface to evaluate mass conservation for the present method. It was also shown that the volume conservation (i.e., mass conservation) of bubbles was very good even after bubble coalescence.

An Improved Three-Dimensional Level Set Method for Gas-Liquid Two-Phase Flows (Keynote)

2003 ◽  
Author(s):  
Hiroyuki Takahira ◽  
Tomonori Horiuchi ◽  
Sanjoy Banerjee
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Stokes Equations ◽  
Interpolation Method ◽  
Density Ratio ◽  
Three Dimensional ◽  
Mass Conservation ◽  
Staggered Grid ◽  
Two Phase ◽  
Level Set Function

For the present study, we developed a three-dimensional numerical method based on the level set method that is applicable to two-phase systems with high-density ratio. The present solver for the Navier-Stokes equations was based on the projection method with a non-staggered grid. We improved the treatment of the convection terms and the interpolation method that was used to obtain the intermediate volume flux defined on the cell faces. We also improved the solver for the pressure Poisson equations and the reinitialization procedure of the level set function. It was shown that the present solver worked very well even for a density ratio of the two fluids of 1:1000. We simulated the coalescence of two rising bubbles under gravity, and a gas bubble bursting at a free surface to evaluate mass conservation for the present method. It was also shown that the volume conservation (i.e., mass conservation) of bubbles was very good even after bubble coalescence.

Kantorovich-Rubinstein misfit for inverting gravity-gradient data by the level-set method

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. G55-G73
Author(s):  
Guanghui Huang ◽  
Xinming Zhang ◽  
Jianliang Qian
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Random Noise ◽  
Magnetic Data ◽  
Gravity Gradient ◽  
Local Minima ◽  
Target Model ◽  
Level Set Function ◽  
Level Set Evolution ◽  
Set Function

We have developed a novel Kantorovich-Rubinstein (KR) norm-based misfit function to measure the mismatch between gravity-gradient data for the inverse gradiometry problem. Under the assumption that an anomalous mass body has an unknown compact support with a prescribed constant value of density contrast, we implicitly parameterize the unknown mass body by a level-set function. Because the geometry of an underlying anomalous mass body may experience various changes during inversion in terms of level-set evolution, the classic least-squares ([Formula: see text]-norm-based) and the [Formula: see text]-norm-based misfit functions for governing the level-set evolution may potentially induce local minima if an initial guess of the level-set function is far from that of the target model. The KR norm from the optimal transport theory computes the data misfit by comparing the modeled data and the measured data in a global manner, leading to better resolution of the differences between the inverted model and the target model. Combining the KR norm with the level-set method yields a new effective methodology that is not only able to mitigate local minima but is also robust against random noise for the inverse gradiometry problem. Numerical experiments further demonstrate that the new KR norm-based misfit function is able to recover deep dipping flanks of SEG/EAGE salt models even at extremely low signal-to-noise ratios. The new methodology can be readily applied to gravity and magnetic data as well.

Fluid-Structure Simulations for a 2D Fire Applications

2005 ◽  
Author(s):  
Wei Xie ◽  
Changsong Luo ◽  
Paul E. DesJardin
Keyword(s):  
Mass Transfer ◽  
Level Set ◽  
Stokes Equations ◽  
Numerical Algorithms ◽  
Thermal Response ◽  
Navier Stokes ◽  
Fire Plume ◽  
Fluid Structure ◽  
Local Boundary ◽  
Level Set Function

This study is on the development of numerical algorithms and models for simulation of a structure response in a fire. The flow field from the fire plume is modeled using the 2D Navier-Stokes equations supplemented with a transport equation for thermal energy and solved using a vorticity-streamfunction approach. Coupling of the fluid to the FEM based structure model is based on the use of a level set method describing the structure geometry in the fluid domain. The level set function allows for computation of normal gradients at the fluid-solid interface to enforce local boundary conditions of heat and mass transfer at prescribed fluid-structure coupling time increments. Numerical simulations of a two-dimensional composite cantilever beam subject to convection heat loading from a fire plume are presented requiring coupling of both the thermal and mass transfer processes at the fluid-structure interface. Results are presented showing the thermal response of a composite beam to a fire plume and the sensitivity of the heating to fire location.

Computation of a Propagating Interface in Multiphase Flows Using an Adaptive Coupled Level Set Method

2002 ◽  
Author(s):  
Ruquan Liang ◽  
Satoru Komori
Keyword(s):  
Surface Tension ◽  
Level Set Method ◽  
Level Set ◽  
Multiphase Flows ◽  
Surface Tension Force ◽  
Numerical Results ◽  
Passive Transport ◽  
Effect Of Surface ◽  
Good Agreement ◽  
Numerical Strategy

We present a numerical strategy for a propagating interface in multiphase flows using a level set method combined with a local mesh adaptative technique. We use the level set method to move the propagating interface in multiphase flows. We also use the local mesh adaptative technique to increase the grid resolution at regions near the propagating interface and additionally at the regions near points of high curvature with a minimum of additional expense. For illustration, we apply the adaptive coupled level set method to a collection of bubbles moving under passive transport. Good agreement has been obtained in the comparision of the numerical results for the collection of bubbles using an adaptative grid with those using a single grid. We also apply the adaptive coupled level set method to a droplet falling on a step where it is important to accurately model the effect of surface tension force and the motion of the free-surface, and the numerical results agree very closely with available data.

Parametric Shape and Topology Optimization: A New Level Set Approach Based on Cardinal Kernel Functions

2017 ◽  
Author(s):  
Long Jiang ◽  
Shikui Chen ◽  
Xiangmin Jiao
Keyword(s):  
Topology Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Material Property ◽  
Kernel Function ◽  
Level Set Methods ◽  
Level Set Function ◽  
Set Function ◽  
Distance Regularization ◽  
Parametric Level Set Method

The parametric level set method is an extension of the conventional level set methods for topology optimization. By parameterizing the level set function, conventional levels let methods can be easily coupled with mathematical programming to achieve better numerical robustness and computational efficiency. Furthermore, the parametric level set scheme not only can inherit the original advantages of the conventional level set methods, such as clear boundary representation and high topological changes handling flexibility but also can alleviate some un-preferred features from the conventional level set methods, such as needing re-initialization. However, in the RBF-based parametric level set method, it was difficult to determine the range of the design variables. Moreover, with the mathematically driven optimization process, the level set function often results in significant fluctuations during the optimization process. This brings difficulties in both numerical stability control and material property interpolation. In this paper, an RBF partition of unity collocation method is implemented to create a new type of kernel function termed as the Cardinal Basis Function (CBF), which employed as the kernel function to parameterize the level set function. The advantage of using the CBF is that the range of the design variable, which was the weight factor in conventional RBF, can be explicitly specified. Additionally, a distance regularization energy functional is introduced to maintain a desired distance regularized level set function evolution. With this desired distance regularization feature, the level set evolution is stabilized against significant fluctuations. Besides, the material property interpolation from the level set function to the finite element model can be more accurate.

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