On the Boundary Condition for the Level Set Function in the Numerical Simulation of Moving Contact Lines

2020 ◽  
Author(s):  
Pablo Gómez ◽  
Adolfo Esteban ◽  
Claudio Zanzi ◽  
Joaquín López ◽  
Julio Hernández
Keyword(s):  
Boundary Condition ◽  
Contact Angle ◽  
Level Set ◽  
Contact Line ◽  
Solid Wall ◽  
Interfacial Flows ◽  
Moving Contact ◽  
Level Set Function ◽  
Static Contact ◽  
Set Function

Abstract We present a method based on a level set formulation to reproduce the behavior of the contact line on solid walls in the simulation of 3D unsteady interfacial flows characterized by large density ratios. The level set method poses a particular difficulty, related to the reinitialization procedure, when used in the simulation of interfacial flows in which the interface intersects a solid wall, due to the appearance of a blind zone where standard reinitialization procedures produce inconsistent results. The proposed method overcomes this difficulty by introducing a boundary condition for the level set function on the solid surface based on the normal extension of the contact angle from the interface along the solid wall. In order to reproduce the dynamics of the contact line we use a simplified model that imposes a boundary condition on the interface curvature based on the static contact angle, and define a thin slip zone at the solid wall around the contact line. To assess the accuracy and robustness of the proposed method, we conducted several preliminary numerical tests in three dimensions, whose results are compared with analytical solutions and other results available in the literature.

Reinitialization of the Level-Set Function in 3d Simulation of Moving Contact Lines

2016 ◽  
Vol 20 (5) ◽  
pp. 1163-1182 ◽  
Author(s):  
Shixin Xu ◽  
Weiqing Ren
Keyword(s):  
Boundary Condition ◽  
Contact Angle ◽  
Level Set ◽  
Contact Line ◽  
Dynamic Contact Angle ◽  
Coupled System ◽  
Dynamic Contact ◽  
Moving Contact ◽  
Level Set Function ◽  
Set Function

AbstractThe level set method is one of the most successful methods for the simulation of multi-phase flows. To keep the level set function close the signed distance function, the level set function is constantly reinitialized by solving a Hamilton-Jacobi type of equation during the simulation. When the fluid interface intersects with a solid wall, a moving contact line forms and the reinitialization of the level set function requires a boundary condition in certain regions on the wall. In this work, we propose to use the dynamic contact angle, which is extended from the contact line, as the boundary condition for the reinitialization of the level set function. The reinitialization equation and the equation for the normal extension of the dynamic contact angle form a coupled system and are solved simultaneously. The extension equation is solved on the wall and it provides the boundary condition for the reinitialization equation; the level set function provides the directions along which the contact angle is extended from the contact line. The coupled system is solved using the 3rd order TVD Runge-Kutta method and the Godunov scheme. The Godunov scheme automatically identifies the regions where the angle condition needs to be imposed. The numerical method is illustrated by examples in three dimensions.

Contact Line Dynamics in Liquid-Vapor Flows Using Lattice Boltzmann Method

2006 ◽  
Author(s):  
Shi-Ming Li ◽  
Danesh K. Tafti
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Contact Line ◽  
Lattice Boltzmann ◽  
Solid Wall ◽  
Hydrodynamic Theory ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Boltzmann Method ◽  
Contact Line Dynamics

A mean-field free-energy lattice Boltzmann method (LBM) is applied to simulate moving contact line dynamics. It is found that the common bounceback boundary condition leads to an unphysical velocity at the solid wall in the presence of surface forces. The magnitude of the unphysical velocity is shown proportional to the local force term. The velocity-pressure boundary condition is generalized to solve the problem of the unphysical velocity. The simulation results are compared with three different theories for moving contact lines, including a hydrodynamic theory, a molecular kinetic theory, and a linear cosine law of moving contact angle versus capillary number. It is shown that the current LBM can be used to replace the three theories in handling moving contact line problems.

HYDRODYNAMIC BOUNDARY CONDITION AT THE FLUID-SOLID INTERFACE

2007 ◽  
Vol 21 (23n24) ◽  
pp. 4131-4143 ◽  
Author(s):  
PING SHENG ◽  
TIEZHENG QIAN ◽  
XIAOPING WANG
Keyword(s):  
Boundary Condition ◽  
Contact Line ◽  
Solid Wall ◽  
Equations Of Motion ◽  
Minimum Energy ◽  
Dissipative System ◽  
Two Phase ◽  
Moving Contact Line ◽  
Solid Interface ◽  
Moving Contact

While the no-slip boundary condition (no relative motion at the fluid-solid interface) has been universally accepted as a cornerstone of hydrodynamics, it was known for some time that it is incompatible with the moving contact line, defined as the motion of the line of intersection of the immiscible (two phase) fluid-fluid interface with the solid wall. By employing Onsager's principle of minimum energy dissipation, we show in this work that a continuum hydrodynamics, comprising the equations of motion as well as the relevant boundary conditions, can be obtained which resolves the moving contact line problem. Our derivation reveals that just as other dissipative system dynamics, the fluid-solid interfacial boundary condition should be consistent with the framework of linear response theory. Implications of our results are discussed.

scholarly journals An Image Segmentation Method Based on Improved Regularized Level Set Model

2018 ◽  
Vol 8 (12) ◽  
pp. 2393 ◽  
Author(s):  
Lin Sun ◽  
Xinchao Meng ◽  
Jiucheng Xu ◽  
Shiguang Zhang
Keyword(s):  
Image Segmentation ◽  
Level Set ◽  
Energy Functional ◽  
External Energy ◽  
Regularization Term ◽  
Level Set Function ◽  
New Energy ◽  
Segmentation Approach ◽  
Set Function ◽  
Distance Regularization

When the level set algorithm is used to segment an image, the level set function must be initialized periodically to ensure that it remains a signed distance function (SDF). To avoid this defect, an improved regularized level set method-based image segmentation approach is presented. First, a new potential function is defined and introduced to reconstruct a new distance regularization term to solve this issue of periodically initializing the level set function. Second, by combining the distance regularization term with the internal and external energy terms, a new energy functional is developed. Then, the process of the new energy functional evolution is derived by using the calculus of variations and the steepest descent approach, and a partial differential equation is designed. Finally, an improved regularized level set-based image segmentation (IRLS-IS) method is proposed. Numerical experimental results demonstrate that the IRLS-IS method is not only effective and robust to segment noise and intensity-inhomogeneous images but can also analyze complex medical images well.

A Method for Tracking a Solid Body in a Fluid Field in Immersed Boundary Methods

2018 ◽  
Author(s):  
Guangfa Yao
Keyword(s):  
Level Set ◽  
Solid Body ◽  
Volume Fraction ◽  
Transformation Matrix ◽  
The Body ◽  
New Method ◽  
Immersed Boundary ◽  
Body Interaction ◽  
Level Set Function ◽  
Set Function

Immersed boundary method has got increasing attention in modeling fluid-solid body interaction using computational fluid dynamics due to its robustness and simplicity. It usually simulates fluid-solid body interaction by adding a body force in the momentum equation. This eliminates the body conforming mesh generation that frequently requires a very labor-intensive and challenging task. But accurately tracking an arbitrary solid body is required to simulate most real world problems. In this paper, a few methods that are used to track a rigid solid body in a fluid domain are briefly reviewed. A new method is presented to track an arbitrary rigid solid body by solving a transformation matrix and identifying it using a level set function. Knowing level set function, the solid volume fraction can be derived if needed. A three-dimensional example is used to study a few methods used to represent and solve the transformation matrix, and demonstrate the presented new method.

Low-Dimensional Components of Flows With Large Free/Moving-Surface Motion

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Yi Zhang ◽  
Solomon C. Yim
Keyword(s):  
Flow Field ◽  
Level Set ◽  
Wave Impact ◽  
Moving Surface ◽  
Surface Motion ◽  
Level Set Function ◽  
Highly Nonlinear ◽  
Flow Systems ◽  
Low Dimensional ◽  
Set Function

Flow systems with highly nonlinear free/moving surface motion are common in engineering applications, such as wave impact and fluid-structure interaction (FSI) problems. In order to reveal the dynamics of such flows, as well as provide a reduced-order modeling (ROM) for large-scale applications, we propose a proper orthogonal decomposition (POD) technique that couples the velocity flow field and the level-set function field, as well as a proper normalization for the snapshots data so that the low-dimensional components of the flow can be retrieved with a priori knowledge of equal distribution of the total variance between velocity and level-set function data. Through numerical examples of a sloshing problem and a water entry problem, we show that the low-dimensional components obtained provide an efficient and accurate approximation of the flow field. Moreover, we show that the velocity contour and orbits projected on the space of the reduced basis greatly facilitate understanding of the intrinsic dynamics of the flow systems.

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