Adaptive level set method applied to drag minimization problems constrained by Stokes equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Xianbao Duan ◽  
Yichen Li ◽  
Hongxia Tan ◽  
Yangyang Li
Keyword(s):  
Level Set ◽  
Stokes Equations ◽  
Computational Cost ◽  
Uniform Mesh ◽  
Computational Domain ◽  
Coarse Mesh ◽  
Fine Mesh ◽  
Level Set Function ◽  
Drag Minimization ◽  
Set Function

Abstract We present a level set based adaptive mesh method for solving the drag minimization problem of incompressible flow governed by Stokes equations. Shape sensitivity analysis of the cost functional is derived. During the optimization process, two levels of meshes are adopted. A uniform coarse mesh for evolving the level set function is defined over the whole computational domain. The level set function also serves as the refinement indicator with an easy strategy. The coarse mesh that contains the interfaces then further divided into a uniform fine mesh and the computation is mainly near the interfaces. Therefore, the computational cost is significantly reduced compared with the uniform mesh over the whole domain that achieves the same resolution. Above all, the value of the shape derivative on the boundary can be obtained implicitly, which is a very difficult task in classical optimal shape design problems. The overall optimization procedure is presented and verified with benchmark examples.

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.

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.

scholarly journals A New Analytical Procedure to Solve Two Phase Flow in Tubes

2018 ◽  
Author(s):  
Terry Moschandreou
Keyword(s):  
Level Set ◽  
Stokes Equations ◽  
Vertical Tube ◽  
Interfacial Waves ◽  
Two Phase ◽  
Level Set Function ◽  
Dependent Part ◽  
New Formulation ◽  
Additive Solution ◽  
Set Function

A new formulation for a proposed solution to the 3D Navier-Stokes Equations in cylindrical co-ordinates coupled to the continuity and level set convection equation is presented in terms of an additive solution of the three principle directions in the radial, azimuthal and z directions of flow and a connection between the level set function and composite velocity vector for the additive solution is shown. For the case of a vertical tube configuration with small inclination angle, results are obtained for the level set function defining the interface in both the radial and azimuthal directions. It is found that the curvature dependent part of the problem alone induces sinusoidal azimuthal interfacial waves wheras when the curvature together with the equation for the composite velocity is considered oscillating radial interfacial waves occur. The implications of two extremes indicate the importance of looking at the full equations including curvature.

scholarly journals Image Segmentation Using Signed Pressure Force Based Active Contour Model

2013 ◽  
Vol 12 (1) ◽  
pp. 3195-3200
Author(s):  
Sagar Chouksey ◽  
Mayur Ghadle ◽  
Shreya Sharma ◽  
Rohan Puranik
Keyword(s):  
Level Set ◽  
Active Contour ◽  
Active Contour Model ◽  
Computational Cost ◽  
Initial Contour ◽  
Pressure Force ◽  
Binary Function ◽  
Level Set Function ◽  
Contour Model ◽  
Set Function

A novel signed pressure force (SPF) based active contour model (ACM) is proposed in this work. It is implemented with help of Gaussian filtering regularized level set method, which first selectively penalizes the level set function to be binary, and then uses a Gaussian smoothing kernel to regularize it. The advantages of this method are as follows. First, a new region-based signed pressure force (SPF) function is proposed, which can efficiently stop the contours at weak or blurred edges. Second, the exterior and interior boundaries can be automatically detected with the initial contour being anywhere in the image. Third, the proposed SPF with ACM has the property of selective local or global segmentation. It can segment not only the desired object but also the other objects. Fourth, the level set function can be easily initialized with a binary function, which is more efficient. The computational cost for traditional re-initialization can also be reduced.

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.

scholarly journals A New Analytical Procedure to Solve Two Phase Flow in Tubes

2018 ◽  
Author(s):  
Terry Moschandreou
Keyword(s):  
Level Set ◽  
Stokes Equations ◽  
Vertical Tube ◽  
Interfacial Waves ◽  
Two Phase ◽  
Level Set Function ◽  
Dependent Part ◽  
New Formulation ◽  
Additive Solution ◽  
Set Function

A new formulation for a proposed solution to the 3D Navier-Stokes Equations in cylindrical co-ordinates coupled to the continuity and level set convection equation is presented in terms of an additive solution of the three principle directions in the radial, azimuthal and z directions of flow and a connection between the level set function and composite velocity vector for the additive solution is shown. For the case of a vertical tube configuration with small inclination angle, results are obtained for the level set function defining the interface in both the radial and azimuthal directions. It is found that the curvature dependent part of the problem alone induces sinusoidal azimuthal interfacial waves wheras when the curvature is small oscillating radial interfacial waves occur. The implications of two extremes indicate the importance of looking at the full equations including curvature.

Image Segmentation Using Binary Level Set Method Based on Region-Based GAC Model

2011 ◽  
Vol 480-481 ◽  
pp. 1206-1209 ◽  
Author(s):  
Ge Ren ◽  
Xing Qin Cao ◽  
Wei Min Pan ◽  
Yong Yang
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Active Contour ◽  
Active Contour Model ◽  
Computational Cost ◽  
Geodesic Active Contour ◽  
Level Set Function ◽  
Contour Model ◽  
Set Function ◽  
Better Than

A new Region-based GAC (geodesic active contour) model was presented, which is the improvement of traditional GAC model. A new region-based signed pressure forces function was presented, which takes the place of the edge stopping function, and can efficiently solve the problem of segmentation of objects with weak edges or without edges. The model is implemented by level set method with a binary level set function to reduce the expensive computational cost of re-initialization of the traditional level set function. The proposed algorithm has been applied to images of different modalities with promising results, which are better than that of traditional GAC model and C-V model.

A Developed Numerical Method for Turbulent Unsteady Fluid Flow in Two-Phase Systems with Moving Interface

2017 ◽  
Vol 14 (06) ◽  
pp. 1750063 ◽  
Author(s):  
A. M. Hegab ◽  
S. A. Gutub ◽  
A. Balabel
Keyword(s):  
Numerical Model ◽  
Gas Phase ◽  
Level Set ◽  
The Body ◽  
Phase System ◽  
Computational Domain ◽  
Two Phase ◽  
Moving Interface ◽  
Level Set Function ◽  
Gas System

This paper presents the development of an accurate and robust numerical modeling of instability of an interface separating two-phase system, such as liquid–gas and/or solid–gas systems. The instability of the interface can be refereed to the buoyancy and capillary effects in liquid–gas system. The governing unsteady Navier–Stokes along with the stress balance and kinematic conditions at the interface are solved separately in each fluid using the finite-volume approach for the liquid–gas system and the Hamilton–Jacobi equation for the solid–gas phase. The developed numerical model represents the surface and the body forces as boundary value conditions on the interface. The adapted approaches enable accurate modeling of fluid flows driven by either body or surface forces. The moving interface is tracked and captured using the level set function that initially defined for both fluids in the computational domain. To asses the developed numerical model and its versatility, a selection of different unsteady test cases including oscillation of a capillary wave, sloshing in a rectangular tank, the broken-dam problem involving different density fluids, simulation of air/water flow, and finally the moving interface between the solid and gas phases of solid rocket propellant combustion were examined. The latter case model allowed for the complete coupling between the gas-phase physics, the condensed-phase physics, and the unsteady nonuniform regression of either liquid or the propellant solid surfaces. The propagation of the unsteady nonplanar regression surface is described, using the Essentially-Non-Oscillatory (ENO) scheme with the aid of the level set strategy. The computational results demonstrate a remarkable capability of the developed numerical model to predict the dynamical characteristics of the liquid–gas and solid–gas flows, which is of great importance in many civilian and military industrial and engineering applications.

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