What is the basic difference between Finite Volume Method (FVM), Finite Difference Method (FDM) and Finite Element Method(FEM)? Why is FVM & FDM preferred for CFD analysis where as FEM for Structural analysis?

A bunch of interesting unanswered questions here... I think that it is time that we all start answering them. It seems like Wen Long has given up and needs some help

First, thanks to everybody. I have just passed the qualify exams last week, and had a trip to Univesity of Virginia, good place to go.

I found the answer of some questions, some others, I don't.

1) Peter's question of blunt body flow:

I'm not very sure, but I guess it's due to transition from to supersonic to subsonic flow near the body head. The transition tends to be unstable, right? I'm studying hydrodynamics, seems samething happened in hydraulic jumps, when the Fr number near 1, the flow is very unstable, and sensitive to noises.

2) John Bradley's question of Chimney spiraling pattern:

Sorry, I don't understand the question.

3) John Bradley's question of tea rotation:

Yes, I got it, as also pointed out by Jan Rusas. Mainly due to oblique pressure gradient, and secondary flow circulation.

4) Jasen's question:

a)laminar separation from a curved surface

This one is relatively easier, but not after the separation. The curvature of the surface gives rise of adverse pressure gradient.

b)turbulent separation from a curved surface

This one is harder than the upper one, first, outer flow is turbulent, second, we need adress turbulence closures in the boundary layer. Log law may not work for curved surface.

c)by-pass transition:

d)natural transition

I don't know what's by-pass transition and natural transition. But I guess, by pass transition means putting some obstacle upsteam to cause transition to turbulence. and natural transition is just the wall and keep increasing velocity. then c) is harder than d). For we have to resolve the by-pass obstacle for details.

e)skin friction:

This depends on whether you want the total friction or detailed friction. For total friction on wall, can use Karman Boundary Layer Integration Method. For detailed distribution skin, friction, it's very hard. I really want to know more about simulation of turbulent boundary layers, especially under unsteady outer flow condition. I will appreciate very much, if you can provide more guideline or information for me.

d)heat transfer:

we have to use more equations, i.e. equation of state , and first thermodynmaic law. so it's not a trival problem at all. For perfect gas, it's well established. For liquid or two-phase flow, I don't know if there is much advance.

e)Pressure distribution:

f)total pressure loss

e) is harder than f). As. total pressure loss can be predicted by integral equations, but distribution requires detailed simuation. for irrotational flow, can use Bernoulli equation, for rotational flow, viscous flow, it's not easy at all, especially for unsteady cases.

5)Prasad's question about FEM, FVM, FDM:

FEM and FVM are more popular is because it can use unstructured grids to fit complex geometry. Also FVM is based on local balance conservation of mass + momentum of cells, it's straightforward.

FEM needs assumption of shape functions, I think it's more suitable for elliptic problems, for unsteady strong convection flow, it will sort of fail, if anyone can point me more about it, I'll appreciate you very much.

FDM: It's simple, but everything based on Taylor expansion, also linear stability analysis is well established. Lots of schemes are proposed, and I'm sort of confused with which one to use. I think there is a disgusting trade off between stability and accuracy. It's very hard to achieve both. Also very hard to deal shock problems such as breaking waves.

I appreciate everybody's problems, and pls explain to me you think I missed your points,

thanks!

wen

1) Peter's question of blunt body flow: The questions refers to space-marching methods. You cannot use them for blunt bodies because of the presence of a subsonic region at the nose. Space marching requires that the equations be hyperbolic.

2) John Bradley's question of Chimney spiraling pattern: The spirals are put in to prevent periodic vortex shedding which can lead to unstable oscillations of the chimney, and final destruction.

Very good!!! You pass : )