Level set method

Based on the flame-hole dynamics [59], dynamic evolutions of flame holes were simulated to yield the statistical chance to determine the reacting or quenched flame surface under the randomly fluctuating 2D strain-rate field. The flame-hole d5mamics have also been applied to turbulent flame stabilization by considering the realistic turbulence effects by introducing fluctuating 2D strain-rate field [22] and adopting the level-set method [60]. 

J. Kim, S. H. Chung, K. Y. Ahn, and J. S. Kim, Simulation of a diffusion flame in turbulent mixing layer by the flame hole dynamics model with level-set method. Combust. Theory Model. 10(2) 219-240, 2006. 

Simulations of multiphase flow are, in general, very poor, with a few exceptions. Basically, there are three different kinds of multiphase models Euler-Lagrange, Euler-Euler, and volume of fluid (VOF) or level-set methods. The Euler-Lagrange and Euler-Euler models require that the particles (solid or fluid) are smaller than the computational grid and a finer resolution below that limit will not give a... 

This paper is intended to describe recent progress on the development of the level-set method and IBM in the context of the advanced front-capturing and front-tracking methods. The paper is also intended to discuss the application of them for the 3-D DNS of two complex three-phase flow systems as described earlier. 

To compute the motion of two immiscible and incompressible fluids such as a gas liquid bubble column and gas-droplets flow, the fluid-velocity distributions outside and inside the interface can be obtained by solving the incompressible Navier-Stokes equation using level-set methods as given by Sussman et al. (1994) ... 

Ge and Fan (2005) developed a 3-D numerical model based on the level-set method and finite-volume technique to simulate the saturated droplet impact on a superheated flat surface. A 2-D vapor-flow model was coupled with the heat-transfer model to account for the vapor-flow dynamics caused by the Leidenfrost evaporation. The droplet is assumed to be spherical before the collision and the liquid is assumed to be incompressible. 

The flow field of the impacting droplet and its surrounding gas is simulated using a finite-volume solution of the governing equations in a 3-D Cartesian coordinate system. The level-set method is employed to simulate the movement and deformation of the free surface of the droplet during impact. The details of the hydrodynamic model and the numerical scheme are described in Sections... 

Immersed-Boundary I Level-Set Method for Particle-Flow Interaction... 

In system 1, the 3-D dynamic bubbling phenomena in a gas liquid bubble column and a gas liquid solid fluidized bed are simulated using the level-set method coupled with an SGS model for liquid turbulence. The computational scheme in this study captures the complex topological changes related to the bubble deformation, coalescence, and breakup in bubbling flows. In system 2, the hydrodynamics and heat-transfer phenomena of liquid droplets impacting upon a hot flat surface and particle are analyzed based on 3-D level-set method and IBM with consideration of the film-boiling behavior. The heat transfers in... 

Since ordinary zero finders fail us often in root-finding problems with multiple roots, we now set out to develop a more reliable graphical level-set method for finding all... 

Let us therefore proceed by a different route, using a level-set method approach that is ultimately more promising for this problem. We proceed in two stages. 

Figure 3.11 makes it obvious that the level-set method for equation (3.6) gives much more meaningful numerical results and clearer graphical representations of the multiple steady state solutions of the CSTR problem (3.3). 

In conclusion, the graphical output of the level-set method is far superior to the bifurcation data obtained via any of the more standard root-finding algorithms. 

Instead, we shall rely again on graphical solvers and the level-set method, but with the added twist and complication of the two additional parameters Kc and yc. 

To gain further and broader insights into the bifurcation behavior of nonadiabatic, nonisothermal CSTR systems, we again use the level-set method for nonalgebraic surfaces such as z = /(K,., y). This particular surface is defined via equation (3.14) as follows for a given constant value of yc with the bifurcation parameter Kc ... 

To solve equation (4.86) for y and K > 0 we use the graphical level set method that we have introduced in Chapter 3 for the adiabatic and nonadiabatic CSTRs and draw the surface z = F(y, K), as well as the y versus K curve of solutions to equation (4.86) in order to exhibit and study the bifurcation behavior of the underlying system. 

Sethian, J. A., Level Set Methods . Cambridge University Press, New York (1996). 

Wheeler, D., Josell, D. and Moffat, T.P. (2003) Modeling Superconformal Electrodeposition using the Level Set Method./. Electrochem. Soc., 150, C302-C310. 

J. A. Sethian, in Level set methods and fast marching methods, Cambridge University Press, Cambridge, 1999. 

In reactor engineering the level-set method is generally too computationally demanding for direct applications to industrial scale units. The level set method can be applied for about the same cases as the VOF method and works best analyzing flows where the macroscopic interface motion is independent of the microscopic phenomena. These concepts are not primarily intended for multi-component reactive flows, so no interfacial heat- and mass transfer fluxes or any variations in the surface tension are normally considered. 

Beux F, Banerjee S (1996) Numerical Simulation of Three-Dimensional Two-Phase Flows by Means of a Level Set Method. ECCOMAS 96 Proceedings, John Wiley. 

J.A. Sethian, P. Smereka, Level Set Methods for Fluid Interfaces, Annu. Rev. Fluid Mech, 35 (2003). 

As mentioned above, a parallel line of research has been carried out by Dzubiella, Hansen, McCammon, and Li. Early work by Dzubiella and Hansen demonstrated the importance of the self-consistent treatment of polar and nonpolar interactions in solvation models [137, 138]. These observations were then incorporated into a self-consistent variational framework for polar and nonpolar solvation behavior by Dzubiella, Swanson, and McCammon [131, 139] which shared many common elements with our earlier geometric flow approach but included an additional term to represent nonpolar energetic contributions from surface curvature. Li and co-workers then developed several mathematical methods for this variational framework based on level-set methods and related approaches [140-142] which they demonstrated and tested on a... 

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