Dear Pablo,

It greatly depends on the type of the Immersed Boundary method you are using,

If you are using a sharp interface method then the internal fellow should not effect the fellow field around the object as long as you ensure there is no mass fellow across the boundary, However note that if you are planning to calculate lift, drag, Cp ect. you should be very careful, there are many suggestion to simplify the force calculations which depend on the problem (moving, stationary, internal flows etc) but I would suggest if the body is stationary just use direct interpolation/integration of the stress tensor ensuring only external points are used in the interpolation. see [1,2] for some suggestions on how to do this

For some immersed boundary methods the internal flow can be detrimental at high Reynolds number (see for example in Virtual Boundary or feedback forcing methods of Goldstein 93) and you need to put forcing terms inside the object.

But If you are planning to enforce a physical field there are Fictitious domain methods see [2] that you might want to consider (this is done by apply rigidity constraint inside the solid object), The idea is not much different from immersed boundary methods but the internal flow is physically meaningful in FD methods which specially speeds up the calculation in the moving boundary cases. Also to predict the motion you don't generally need to calculate the surface forces.

I suggest you have a look at my review paper [1] where you can find many references and discussions,

1. On the application of immersed boundary, fictitious domain and body-conformal mesh methods to many particle multiphase flows, IJMF (2012) 38–55

2. A new implicit fictitious domain method for the simulation of flow in complex geometries with heat transfer , JCP (2013) 21-45

Hello,

I assume you are simulating a flow around an NACA airfoil. As long as your airfoil (I assume it is one piece) is sealed, then there is no need to mesh the inside of the airfoil. This is an "external" problem, so you should only mesh the boundary.

If there are solid mechanics involved in your analysis of the airfoil, then you should consider meshing it.

Best of luck