# Augmented Lagrangian method for FEM-CFD

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

 October 28, 2001, 14:25 Augmented Lagrangian method for FEM-CFD #1 sylvain Guest   Posts: n/a Hi, i am looking for someone who uses the augmented lagrangian method with a finite element method to simulate incompressible fluid flow. I am actualy using a penalty method and i am wondering if this method is better. Thank you best regards

 October 29, 2001, 05:08 Re: Augmented Lagrangian method for FEM-CFD #2 Anthony Wachs Guest   Posts: n/a Hi, I have used Augmented Lagrangian Method (ALM) for solving incompressible fluid flows (especially non-Newtonian) in the past. The discretization method was a Finite Volume method, but that is likely not to make any difference with your FEM since at the end you get symmetric matrix system that looks like [ A B ](v)=(f) [ Bt 0 ](p) (g) (the two lines are together and represent a single matrix system, e.g. it corresponds to : A.v+B.p=f and Bt.v=g) where A is the velocity matrix, B pressure matrix, v velocity vector, p pressure vector, f and g the second members of your system With the ALM, you replace this problem by the following one [ A+rBBt B ](v)=(f+rBg) [ Bt 0 ](p) (g) where r stands for the Lagrangian parameter. The larger r, the faster the convergence is achieved. But since in the algorithm, you are to solve matrix sub-systems like : (A+rBBt)(x)=b Those systems become bad-conditioned as r increases. Therefore, if u use a direct method to solve this sub-system (as for instance Cholevski factorization), then you don't have to take care of the magnitude of r. On the other hand, if u choose to solve this sub-system using iterative solver (conjugate gradient), then the larger r, the poorer the convergence rate. Finally, the ALM is a very powerful method provided you can factortize the augmented matrix A+rBBt once at the beginning of the procedure in its Cholevski form. Otherwise, you can still use it but it requires to pay attention to the magnitude of r. Do not hesitate to contact me if you need additional informations I hope it might help u Best regards, Anthony

 August 16, 2015, 22:08 Augmented Lagrangian method for Viscoplastic fluids. #3 New Member   John Smith Join Date: Feb 2010 Posts: 13 Rep Power: 8 ............... Last edited by hami9293; August 17, 2015 at 17:45.

 Thread Tools Display Modes Linear Mode

 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 OffTrackbacks are On Pingbacks are On Refbacks are On Forum Rules

 Similar Threads Thread Thread Starter Forum Replies Last Post seyedashraf Main CFD Forum 0 June 20, 2011 15:41 D.S.Nasan Main CFD Forum 6 September 4, 2008 02:08 Shyam Main CFD Forum 0 January 20, 2004 00:44 Chris R. Kleijn Main CFD Forum 0 September 8, 1998 08:19 Chris R. Kleijn Main CFD Forum 0 September 3, 1998 08:45

All times are GMT -4. The time now is 10:18.