Front tracking method

I.L. Chern and P. Colella, A Conservative Front Tracking Method for Hyperbolic Conservation Laws, UCRL-97200, Lawrence Livermore National Laboratory, Livermore, CA, 1987. 

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. 

Discussions in Chapter 2 may be referred to for explanations of the various symbols. It is straightforward to apply such conservation equations to single-phase flows. In the case of multiphase flows also, in principle, it is possible to use these equations with appropriate boundary conditions at the interface between different phases. In such cases, however, density, viscosity and all the other relevant properties will have to change abruptly at the location of the interface. These methods, which describe and track the time-dependent behavior of the interface itself, are called front tracking methods. Numerical solution of such a set of equations is extremely difficult and enormously computation intensive. The main difficulty arises from the interaction between the moving interface and the Eulerian grid employed to solve the flow field (more discussion about numerical solutions is given in Chapters 6 and 7). 

Unverdi SO, Tryggvason G (1992) A Front-Tracking Method for Viscous, Incompressible, Multi-Fluid Flows. J Comput Phys 100 25-37. 

The purpose of this section is to give an overview of the pertinent high resolution methods often referred in the literature on multiphase reactor modeling. These are The Maker and Cell (MAC) method [96], the Simplified MAC method [6], the volume of fluid (VOF) method[108], the level set (LS) front capturing method [214, 20, 186], and finally the front tracking method [227, 221[. 

It is noticed that after some re-evaluation Tryggvason and co-workers [228, 222] classified their front tracking method [227] as an embedded interface method, since it is best described as a hybrid between a front tracking and a front capturing method. 

In this sub-section the embedded interface method (frequently referred to as a front tracking method) developed for direct numerical simulations of viscous multi-fluid flows is outlined and discussed. The unsteady model is based on the whole held formulation in which a sharp interface separates immiscible fluids, thus the different phases are treated as one fluid with variable material properties. Therefore, equations (3.14) and (3.15) account for both the differences in the material properties of the different phases as well as surface tension effects at the phase boundary. The bulk fluids are incompressible. The numerical surface tension force approximation used is consistent with the VOF and LS techniques [222] [32], hence the major novelty of the embedded interface method is in the way the density and viscosity fields are updated when the fluids and the interface evolve in time and space. 

Esmaeeli A, Tryggvason G (2004) A front tracking method for computations of boiling in complex geometries. Int J Multiphase Flow 30 1037-1050... 

Qian J, Tryggvason G, Law CK (1998) A Front Tracking Method for the Motion of Premixed Flames. J Comput Phys 144 52-69... 

Tryggvason G, Buimer B, Esmaeeh A, Juric D, Al-Rawahi N, Tauber W, Han J, Nas S, Jan Y-J (2001) A Front-Tracking Method for the Computations of Multiphase Flow. J Comput Phys 169 708-759... 

Here, we describe a method that has been particularly successful for a wide range of multifluid and multiphase flow problems. The front-tracking method is based on a single-field formulation of the flow equations for the entire computational domain and so treats different phases as a single fluid with variable material properties [3, 13]. In fact, the front-tracking method discussed here is an application of the immersed boundary method of Peskin... 

In this chapter, the fundamentals of the front-tracking method are described as a computational method that can be used as a design tool in microfluidic systems. 

The finite-difiference/front-tracking method has been validated for a wide variety of test cases in simple geometries as reviewed by Trgyyvason et al. 

The front-tracking method has been developed by Trgyyvason and coworkers and been successfully used for computational modeling of interfacial flows... 

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