CFD Online Logo CFD Online URL
Home > Forums > Main CFD Forum

S u + k B p = g, B^T u = 0

Register Blogs Members List Search Today's Posts Mark Forums Read

LinkBack Thread Tools Display Modes
Old   January 22, 2001, 08:03
Default S u + k B p = g, B^T u = 0
Rolf Reinelt
Posts: n/a
In the book "Efficient Solvers for Incompressible Flow Problems" by Turek the resulting algebraic equation system of the discretised Navier-Stokes equations is given as

S u + k B p = g

B^T u = 0


u = (u1,u2,...,um,v1,v2,...,vm)^T


p = (p1,p2,...,pn)^T

are vectors and S and B are matrices. An equivalent form for steady flows would be

S u + B1 p = g1

S v + B2 p = g2

B1^T u + B2^T v = 0


u = (u1,u2,...,um)^T

v = (v1,v2,...,vm)^T

The crucial point is that we can use B^T in the continuity equation. My questions are:

1) Are there other books that use this formulation?

2) Is it true that this formulation is valid for finite difference, finite volume and finite element methods?

3) Are the known and unknown boundary values supposed to be part of the vectors u,v,p?

4) When using finite volume method, what are the restrictions that the formulation remains valid?

5) If m=n, i.e. the number of pressure nodes = number of u-velocity nodes, can the continuity equation be written as B1 u + B2 v = 0 ?

Kind regards, Rolf
  Reply With Quote


Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On

All times are GMT -4. The time now is 05:38.