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

Linearization and continuation for upwind FVM schemes

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

LinkBack Thread Tools Search this Thread Display Modes
Old   October 15, 2012, 11:34
Default Linearization and continuation for upwind FVM schemes
New Member
Olle Trollberg
Join Date: Oct 2012
Posts: 1
Rep Power: 0
Troll is on a distinguished road
Hello all,

The question in short: Is it common to get a discontinuous Jacobian at steady state solutions when using upwind schemes and what can be done about it?

The long version: I have a time-dependent advection-diffusion-reaction problem in one dimension which I need to be able to:

1) simulate
2) linearize
3) compute a steady-state mapping for a varying parameter.

I first tried out the simplest thing I could think of (MOL with a first-order finite-difference scheme for spatial discretization) which turned out to be unstable. After some study, I ended up with implementing a first order upwind finite volume method. This model is stable and I can perform simulations. However, I run into problems with linearization. Since the advective flow can switch sign in the problem, it was necessary to introduce logic for the upwind-scheme. This in turn cause the Jacobian to become discontinuous at the steady-state solution. Is this a common problem and how do I solve it?

One of the reasons I need to linearize is that I want to use continuation in order to compute the steady-state mapping between some states and a control-parameter. Due to the discontinuity, the nullspace of the Jacobian get too many dimensions which cause my continuation algorithm to fail...

I'm now thinking about abandoning the FVM-method and try some collocation method for the spatial discretization. Do you think that is a feasible path?

/Best regards

Ps. I'm rather new to CFD so please, If you know any good litterature for advective-diffusive-reactive problems, I would greatly appreciate tips.
Troll is offline   Reply With Quote


continuation, fvm, linearization, upwind

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 01:15.