[batabek]

hi,
I want to know why Finite difference schemes are mostly preferred when numerically simulating fluid dynamics instead of using Finite Element Methods(FEM). Is it computationally expensive to use a discretization schema like FEM due to their large number of discrete element requirements ?

[Rami]

Hi batabek,

To start with, the most common practice in CFD is the Finite Volume Method (FVM) rather than the Finite Difference Method.

The reasons the Finite Element Method (FEM) is less common in CFD, in my view are mainly two:

1. It is more complex, mainly if convection dominates, so some sort of upwind is required, and also due to difficulties arising when consistency with the shape functions assumed is to be preserved throughout (e.g., for the fluid properties, the BCs, etc.). These are simpler in the FVM, since usually everything is assumed constant withing each control volume (cell or cell face).
2. Conformism - this is what was done for years...

I see no difference in cost between FEM and FVM for unstructured grid, since the calculations in both cases require some connectivity arrays (indirect addressing). In both cases, the accuracy with the same grid is similar or better for FEM (after all, the FVM is more-or-less a degenerated FEM, with constant shape functions and some additional assumptions). FVM can be more efficient if a structured grid is adequate, but this is hardly the case in real-life problems.

Rami

[batabek]

yeah volume preservation is a good point to consider, specifically in the incompressible flow. But I have not known FVM is dominant in the field until you said so. I thought FDM is more easy to implement in a computer.