Immersed Interface Method

Li Z (1997) Immersed interface methods for moving interface problems. Numerical Algorithms 14 269-293... 

Lee L, Leveque RJ (2003) An immersed interface method for incompressible Navier-Stokes equations. SIAM J Sci Comput 25 832-856... 

The NACE Landrum Wheel velocity test, originally TM0270-72, is typical of several mechanical-action immersion test methods to evaluate the effects of corrosion. Unfortunately, these laboratory simulation techniques did not consider the fluid mechanics of the environment or metal interface, and service experience very seldom supports the test... 

The immersed boundary method is a numerical method in computational fluid dynamics where the flow boundary, e.g., the surface of a solid body in contact with the fluid or the interface between two immiscible fluids, is immersed in the mesh that does not conform with the boundary. In the immersed boundary method, special treatment has to be taken at the boundary to incorporate the boundary conditions. 

Fig. 1 Schematic the fluid-fluid or fluid-solid interface and the Cartesian grid used for the immersed boundary method...

The basic idea of Peskin s immersed botmdary method is to choose an approximate delta function to smear the interface, and therefore, the physical properties of the fluid and the interfacial traction undergo a smooth transition across the interface. One example of such approximation in the two-dimensional space is... 

Immersed Boundary Method, Fig. 2 (a) A snapshot of an evolving interface between two fluids, computed using the immersed boundary method, and (b) the corresponding mollifying function c(x) (simulation done by the author)... 

In some variants of the immersed boundary method dealing with the boundary between a fluid and a solid body, the fictitious fluid is introduced inside the solid body, and a boundary force, F, in place of Af in Eq. 4, is distributed into the augmented flow field in the same way as described for the fluid-fluid interface (e.g., Goldstein et al. [6]). To impose the no-slip and no-penetration boundary conditions at the interface, F is modeled as... 

In some other immersed boundary methods for a fluid-solid interface, the no-slip/no-penetration conditions are enforced via an interpolation scheme (e.g., Mittal [2]). To carry out the interpolation, the variables on the grid points near the interface are used, and the interpolation may involve the ghost nodes defined outside the flow domain. In these methods, the boundary conditions are satisfied at the exact location of... 

Ghias R, Mittal R, Dong H (2007) A sharp interface immersed boundary method for compressible viscous flows. J Comput Phys 225(l) 528-553... 

Seo JH, Mittal R (2011) A sharp interface immersed boundary method with improved mass conservation and reduced spurious pressure oscillations. J Comput Phys 230(19) 7347-7363... 

Interface Tracking in Immersed Boundary Method The immersed boundary or interface denoted by C(f) (a curve in two dimensions or a surface in three dimensions) (see Fig. 11a) is represented by K markers of coordinates x (i) with k = The markers are uniformly... 

There are a number of hybrid techniques which integrate different methodologies. These include (a) coupled level set-volume of fluid (CLSVOF) which combines mass-conserving properties with accurate normal and curvature calculation of level set (b) particle level set which uses particles to enhance mass conservation (c) mixed markers and volume of fluid with which one obtains a smooth motion of the interface, typical of the marker approach, with a good volume conservation, as in standard VOF methods and (d) hybrid immersed interface-level set which, instead of tracking the interface explicitly, captures the interface similar to level set method (purely Eulerian technique). There are a number of other hybrid techniques which have been less widely used. 

Immersed Boundary (IB) and Immersed Interface (II) Techniques The immersed boundary technique [28] is a combined Eulerian-Lagrangian method in the sense that the flow is solved using a Eulerian approach on a fixed Cartesian mesh, and the interface is represented by a discrete set of points and advected in a Lagrangian way. In this method, a single set of conservation equations valid for both phases is solved. The interface conditions are incorporated into the governing field equa-... 

Interface Tracking in Immersed Boundary Method The immersed boundary or interface denoted by C t) (a curve in two dimensions or a surface in three dimensions), see Fig. 1 la, is represented by K markers of coordinates Xk s) with k= 1,2, The markers are uniformly distributed along C(f) at some fraction of the grid spacing, 0.5h < ds < 1.5h. The interface is parameterized as a function of the arclength s by fitting quadratic polynomials Xjt(s) = -I- bj(S + Ck through three consecutive marker points of coordinates... 

Numerical Techniques for Free Surface Flows Interface Capturing and Interface Tracking, Figure 11 Immersed boundary method (a) computational domain composed of two immiscible fluids (b) grid points considered for the interface velocity around the marker X [12]... 

Interfdci l Composite Membra.nes, A method of making asymmetric membranes involving interfacial polymerization was developed in the 1960s. This technique was used to produce reverse osmosis membranes with dramatically improved salt rejections and water fluxes compared to those prepared by the Loeb-Sourirajan process (28). In the interfacial polymerization method, an aqueous solution of a reactive prepolymer, such as polyamine, is first deposited in the pores of a microporous support membrane, typically a polysulfone ultrafUtration membrane. The amine-loaded support is then immersed in a water-immiscible solvent solution containing a reactant, for example, a diacid chloride in hexane. The amine and acid chloride then react at the interface of the two solutions to form a densely cross-linked, extremely thin membrane layer. This preparation method is shown schematically in Figure 15. The first membrane made was based on polyethylenimine cross-linked with toluene-2,4-diisocyanate (28). The process was later refined at FilmTec Corporation (29,30) and at UOP (31) in the United States, and at Nitto (32) in Japan. 

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