I am using a first order approximation at my Navier-Stokes code and want to know if an IBM (Immersed boundary method) is useful for it to represent a wall or an object, since the approximation of derivation only needs one point to be solved. I am wondering if it influences the poisson equation that solves the pressure.
I would say that IB method should be useful for representing a wall or an other object. Note that the fluid mesh around the wall or object should be uniform, since that is generally the requirement by discrete delta functions used in IB methods. Otherwise the IB method is not depending on specific order of the fluid solver.
There are many IB versions available, for example, in the direct forcing IB method the poisson equation is not modified. Only an explicit forcing is added to the right-hand-side of Navier-Stokes equation. I think it would be possible to add direct forcing IB method to your fluid code.
Article An Immersed Boundary Method with Direct Forcing for the Simu...
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