|
[Sponsors] |
June 5, 2016, 00:38 |
Diffusion equation with pseudo time step
|
#1 |
New Member
Join Date: Dec 2015
Posts: 6
Rep Power: 10 |
Hi CFD people,
I am trying to solve diffusion equation by using Newtons method and pseudo time sub iterations. I am not sure how to interpolate pseudo time sub iterations. I couldn't find the detailed example for this kind of problem. Any suggestions? |
|
June 5, 2016, 00:58 |
|
#2 |
Senior Member
Michael Prinkey
Join Date: Mar 2009
Location: Pittsburgh PA
Posts: 363
Rep Power: 25 |
The diffusion equation is linear, so why are you using Newton's method?
If this is a nonlinear diffusion problem, then are you looking to use explicit pseudo-timestepping as a preconditioner for (say) a Newton-Krylov method? Or are you using an implicit pseudo-timestepping with a Newton solver to solve for the next pseudo-timestep values? I assume it is the latter, because the former is pretty complicated and probably not something you'd be tackling based on your level of experience. I assume the equation that you are solving is: D(u) = 0 where D is some nonlinear diffusion operator. Pseudo time stepping would replace this equation with: du/dt = D(u) and (pseudo) time integrate to large (pseudo) time. The simplest form is implicit Euler: (u_new - u_old)/dt = D(u_new) You can build the Newton iteration of that system and iterate to solve for u_new. Then take the next pseudo timestep. You could also use other schemes other than Implicit Euler, but (pseudo) time accuracy is usually not important. The focus is on using a stable scheme to wrap around the outside of the Newton method...which is not terribly well behaved when the initial guess is far from the final answer. Good luck. |
|
June 5, 2016, 01:07 |
|
#3 |
New Member
Join Date: Dec 2015
Posts: 6
Rep Power: 10 |
Thank yo for your response. This will be really helpful. I will solve highly non linear and stiff problem. But, before solving that equation, I need to feel comfortable about pseudo time stepping which I never used previously. So, I chose non linear diffusion equation to practice. I will compute jacobian matrices for real and pseudo time stepping. I don't want to use explicit sub iterations.
|
|
June 22, 2016, 08:28 |
NCCS - Authorized SOLIDWORKS Reseller, CAMWORKS Reseller, METACAM Reseller
|
#4 |
New Member
Join Date: Jun 2016
Posts: 1
Rep Power: 0 |
NCCS has built its reputation in Australian & NZ by providing an outstanding service, great knowledge & quality products at low prices. Now SOLIDWORKS.
|
|
Thread Tools | Search this Thread |
Display Modes | |
|
|
Similar Threads | ||||
Thread | Thread Starter | Forum | Replies | Last Post |
[Other] Contribution a new utility: refine wall layer mesh based on yPlus field | lakeat | OpenFOAM Community Contributions | 58 | December 23, 2021 03:36 |
Multiple floating objects | CKH | OpenFOAM Running, Solving & CFD | 14 | February 20, 2019 10:08 |
time step directories naming issue | Andrea_85 | OpenFOAM | 3 | April 3, 2014 09:38 |
Help for the small implementation in turbulence model | shipman | OpenFOAM Programming & Development | 25 | March 19, 2014 11:08 |
How to write k and epsilon before the abnormal end | xiuying | OpenFOAM Running, Solving & CFD | 8 | August 27, 2013 16:33 |