HI,

We have used FEM in developing one CFD code,but I have some doubts in my mind.

1. There are different types of elements in FEM, We have tried both Q1/Q0 and Q1~/Q0. In Q1/Q0 the volocity is located on the vertex of hexahedron and pressure is located in the center of elements, but this type element is slightly unstable which leads to the chessboard of pressure, as a result the pressure equation can only be solved by ICCG method, The problem is what is the reliablity of the chessboard pressure in physical meaning in case that it can derive one resaonable velocity feild.

2. We are not satisfied with the chessboard pressure in Q1/Q0 element, even in the case we can get one smooth pressure distribution after numerical filter. So we turn into Q1~/Q0 element. In Q1~/Q0 element, the velocity is located on the center of surface( facet), and pressure is located in the center of element, this kind if element removed the chessboard of pressure away, but there still existed another problem which is that, the tangential velocity at the facet doesn't have a direct relation with pressure gradient in case of rectangular element, here exists one big clue to catastrophe, the velocity variables around one element is not smooth after limited iterations, which means the solution of momentum equations is not a smooth field after limited iterations, this will cause a great trouble in the implementation of multigrid method.

3. my problem is that: what is going on in the FEM/CFD? There always exists some kind of purturbation in some corner. Is there anyone who knows one *perfect FEM/CFD*, I would be very appreciated.

Hongliang Yang

A quite successful implementations and reports on many calculations of incompressible flows with Q1~/Q0 element you can found on http://www.featflow.de including the use of multigrids.

Olshanskii

Hi I suggest you to dig for the papers by K.S. surana on p-version least squares finite element method. This methd is proven to be applicable to almost every regime of fluid dynamics flows. This method might help you. Proffessor Surana is in Kansas university mechanical enginering department. Good luck Reza

try this book: "INCOMPRESSIBLE FLOW AND THE FINITE ELEMENT

METHOD" By P.M. Gresho and R.L.Sani, John Wiley & Sons, 1999;