Front Tracking

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

Hult, J., Josefsson, G., Alden, M., and Kaminski, C.F., Flame front tracking and simultaneous flow field visualisation in turbulent combustion, in 10th International Symposium and Applications of Laser Techniques to Fluid Mechanics, Paper No. 26-2, Lisbon, 2000. 

Front-tracking model for in situ combustion oil recovery [1515]... 

P. S. Rocha, M. A. Miller, and K. Sepehmoori. A succession-of-states front-tracking model for the in-situ combustion recovery process. In Situ, 21(1) 65-100, February 1997. 

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. 

Tai, Y.-C. (2000) Dynamics of Granular Avalanches and their Simulations with Shock-Capturing and Front-Tracking Numerical Schemes. Ph.D. thesis, Department of Applied Mechanics, Darmstadt University of Technology, Germany... 

An alternative and complementary method is to follow the deformation of the material by following the boundaries of a fluid domain, by either the front capturing or front tracking technique. In the former, marker particles are distributed over the fluid domain volume and tracked over time, with the surface of the domain being restored by interpolation techniques in the latter, a separate moving mesh is used to describe the interface between the subdomain and the rest of the volume (86-89). 

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). 

Shape change algorithms vary from simple analytical descriptions to a variety of numerical models of increasing sophistication. For example, numerical front tracking or string models [12, 62] and surface triangularization (3D-simulations [303])... 

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. 

After the discrete points on the interface are moved with the flow, the continuous interface is reconstructed by connecting these points by appropriate linear or triangular elements (i.e., a finite element technique). It is noticed that explicit front tracking is generally more complex than the advection of a maker function as in the VOF and LS methods, nevertheless this technique is also considered more accurate [224]. 

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... 

---