# Immersed Boundary Method (IBM)

Although found some reemergence in the past few years, the general concept was actually developed by Peskin in 1972 for the simulation of blood flow and cardiac mechanics coupling.
In IBM a non-body conformal Cartesian grid is employed. The immersed boundary would still be represented by a surface grid, but the Cartesian volume grid is generated without regarding the immersed boundary surface grid resulting in the solid boundary “cutting” through this Cartesian volume grid.

IBM mesh

Because of the non-conformity of the solid boundary and the Cartesian grid, applying boundary conditions requires modifying the equations in the vicinity of the solid boundary by means of a forcing function that reproduces the effect of the boundary.

The methodologies for generating a forcing function are the Continuous Forcing approach and the Discrete Forcing Approach.

### Continuous Forcing approach

In the continuous forcing approach the forcing function is included in the continuous momentum and continuity set of equations for the entire domain to be subsequently discretized on a Cartesian grid leading to a system of forced discrete equations.
In contrast, in the discrete forcing approach the equations are first discretized on a Cartesian grid disregarding the immersed boundary and subsequently the discretization in the cells near the immersed boundary is adjusted to account for its presence.
The main advantage of the method is in its ability to simplify tremendously the task of grid generation.

### Discrete Forcing approach

In contrast to structured method grid generation no additional operations are required to account for the terms associated with grid transformation. As to unstructured methods for grid generation, the main advantage of IBM is its ability to efficiently invoke geometric multigrid methods and line-iterative techniques which leads to a per-grid reduction in operations, reducing the computational cost.
Another application of which IBM stands above others is when moving boundaries are present. approaching such a case study with unstructured method grid generation would require the generation of new mesh to conform with the moving surface of the body as the calculation progresses. In IBM on the other hand, the non-body conforming mesh would alleviate such a problematic feature.

#### To conclude…

IBM method could prove very beneficial, especially when it’s utilised for boundary-layer LES calculations, where LES has severe limitations in the near wall regions, as the computational effort required to reliably model the innermost portion of the boundary layer (sometimes constituting more than 90% of the mesh) where turbulence length scale becomes very small is far from the resources available to the industry.

On the other hand, devising  and validating accepted forcing functions for such advanced LES calculation requires novelty which is somewhat state-of-the-art (example below) that is still out of reach for most industry CFD practitioners.

snapshot of Large Eddy Simulation of a 5-bladed rotor wake in hover with a novel multiblock IBM
(by Technion CFD Lab)

Highly recommended for further in-depth reading and implementation: