CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > General Forums > Main CFD Forum

Fractional step-Theta time stepping and SUPG stabilized FEM

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

Reply
 
LinkBack Thread Tools Search this Thread Display Modes
Old   May 5, 2017, 19:51
Question Fractional step-Theta time stepping and SUPG stabilized FEM
  #1
New Member
 
David
Join Date: Aug 2016
Posts: 6
Rep Power: 10
dajuno is on a distinguished road
Dear all,

I am working on a FEM based incompressible Navier-Stokes solver.
I have implemented the second order Fractional step-Theta time discretization (see [1], [2]; only time-stepping, NO splitting! has slightly better stability properties than Crank-Nicolson) for inf-sup stable elements (P2P1), which corresponds roughly to staggered grids in FVM.

I also use an unstable P1/P1 discretization, stabilized with SUPG/PSPG or Galerkin/Least-squares (GLS), as in [3], [4], that I want to apply the FS-Theta method to.
However, I wonder how to bring both parts together: How to use the Fractional step-Theta discretization on the GLS stabilization terms.
The problem is that different parts of the FS-Theta discretized Navier-Stokes equations are multiplied by different constants (thetas), i.e., du/dt, convection + diffusion term, and the pressure gradient, respectively.
It seems logical to add weightings correspondingly to the GLS formulation, but I am really not sure (what and where) and I have not found any references for that.

I realize that this is a very particular question... any advice would be very much appreciated!!


[1] Turek 1999, Efficient solvers for incompressible flow problems: an algorithmic and computational approach (Book)
[2] John 2006, A comparison of time-discretization/linearization approaches
for the incompressible Navier–Stokes equations
[3] Tezduyar 1992, Stabilized finite element formulations for incompressible flow computations
[4] Shakib & Hughes, 1991, Part X

Kind regards
David
dajuno is offline   Reply With Quote

Reply

Tags
fem, fractional step method, gls, stabilization, supg

Thread Tools Search this Thread
Search this Thread:

Advanced Search
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 Off
Pingbacks are On
Refbacks are On



All times are GMT -4. The time now is 11:40.