Immersed boundary

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

Ye, T., Mittal, R., Udaykumar, H. S., and Shyy, W. J. Computat. Phys. 156, 209-240 (1999). Yusof, J. M. Combined immersed boundaries/B-splines methods for simulations of flows in complex geometries. CTR Annual Research Briefs, NASA Ames/Stanford University (1997). 

Whenever a cubic grid is mandatory—either due to coding limitations from the part of academic groups or due to the inherent properties of, e.g., LB techniques—and a staircase approach is to be avoided (e.g., for a revolving impeller axis) one can take refuge to some immersed boundary method (see, e.g., Mittal and Iaccarino, 2005). One may distinguish between... 

Which of the various immersed or embedded boundary methods is best— generally or for a particular case—is still an open question. Thornock and Smith (2005) introduced a Cell Adjusted Boundary Force Method for a stirred vessel. All methods proposed so far have their own pros and cons. Immersed boundary methods are also exploited in LB techniques (e.g., Derksen and Van den Akker, 1999). Rohde (2004) investigated the use of triangular facets for representing a spherical particle. 

Yang Ge and Liang-Shih Fan, 3-D Direct Numerical Simulation of Gas-Liquid and Gas-Liquid-Solid Flow Systems Using the Level-Set and Immersed-Boundary Methods M.A. van der Hoef, M. Ye, M. van Sint Armaland, A.T. Andrews IV, S. Sundaresan, and J.A.M. 

The net effects of the immersed boundary technique are that in the interface transition zone the fluid properties change smoothly from the value on one side of the interface to the value on the other side. The artificial interface thickness is fixed as a function of the mesh size applied to provide stability and smoothness, and it does not change during the calculations. Therefore no numerical diffusion is present. The finite thickness also serves to position the interface more accurately on the grid. The surface tension force (normal contribution only) is then calculated estimating the mean curvature based on geometric information obtained from the restructured interface. 

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... 

Francois M, Shyy W (2003) Computations of drop dynamics with the immersed boundary method, part 1 numerical algorithm and buoyancy-induced effect. Numerical Heat Transfer, Part B 44 101-118... 

As already mentioned, an important feature of the membrane assisted fluidized bed to be elucidated is the effect of membranes (and permeation through them) on the bubble behavior (and hence on mass/heat transfer). A DPM can be used in combination with an immersed boundary method to study the behavior of the gas in the immediate vicinity of the membrane. With this... 

J. F. De Jong, H. J. van Gerner, M. van Sint Annaland and J. A. M. Kuipers, Development of a Novel Hybrid Discrete Particle - Immersed Boundary Model for Fluidized Bed Membrane Reactors, Seventh International Conference on CFD in the Minerals and Process Industries. CSIRO, Melbourne, 2009. 

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. 

The immersed boundary method was first introduced by Peskin [1] to simulate the blood flow in... 

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

The downside of the immersed boundary method is that implementation of the boundary conditions is not straightforward since the boundary does not coincide with any grid line. In addition, the immersed boundary method has less flexibility of distributing the grid in the vicinity of the boundary compared to the boundary-conforming methods. 

Figure 1 shows an example where a Cartesian grid is used to discretize the domain including both sides of the boundary. The fluid-fluid boundary or fluid-solid boundary intersects with the grid lines. The governing equations are discretized on the grid using a finite difference method. Near the boundary, special treatment has to be taken in order to incorporate the boundary conditions. Different boundary treatments lead to different variants of the immersed boundary method. 

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... 

Mittal R, laccarino G (2005) Immersed boundary methods. Armu Rev Fluid Mech 37 239-261... 

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

Luo H, Dai H, Ferreira de Sousa P, Yin B (2012) On numerical oscillation of the direct-forcing immersed-boundary method for moving boundaries. Comput Huids 56 61-76... 

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... 

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