Is the resulting set of discretised equations for a general CFD problem nonlinear?

Baum · August 13, 2020, 12:35

Hi, I was just wondering this while reading up about it: As far as I understand, the PDEs/Navier-Stokes equations in each cell are discretised via different schemes and then solved iteratively in a huge system of equations (matrix). From this, you get the mass, momentum, temperature, pressure etc. in each cell, and you use those to calculate new source terms, densities etc. for the next iteration.

Now, my question is the following: Is the resulting equation system that Fluent/OF/whatever solver solves linear, due to the discretisation schemes being used? In other words, are nonlinear equation system solvers necessary for the solution of a CFD problem?

Cheers,
Baum

FMDenaro · August 13, 2020, 13:09

Quote:

Originally Posted by Baum

Hi, I was just wondering this while reading up about it: As far as I understand, the PDEs/Navier-Stokes equations in each cell are discretised via different schemes and then solved iteratively in a huge system of equations (matrix). From this, you get the mass, momentum, temperature, pressure etc. in each cell, and you use those to calculate new source terms, densities etc. for the next iteration.

Now, my question is the following: Is the resulting equation system that Fluent/OF/whatever solver solves linear, due to the discretisation schemes being used? In other words, are nonlinear equation system solvers necessary for the solution of a CFD problem?

Cheers,
Baum

Generally the resulting discrete equations are linearized in some way but the NSE are non-linear and the discrete equations can be non-linear, too.

Baum · August 14, 2020, 04:08

Hi Filippo, thanks for the reply. Of course the NSE are non-linear, but if I choose a simple first order discretisation scheme, shouldn't the whole system become linearised based on their neighbouring cells? Are there some equations that will always remain nonlinear?

FMDenaro · August 14, 2020, 04:30

Quote:

Originally Posted by Baum

Hi Filippo, thanks for the reply. Of course the NSE are non-linear, but if I choose a simple first order discretisation scheme, shouldn't the whole system become linearised based on their neighbouring cells? Are there some equations that will always remain nonlinear?

Wouldn't be a first order upwind still non-linear for an implicit method? Think about that for the simple 1D Burgers equation, you will see that the first order scheme is still non-linear.

Baum · August 14, 2020, 05:05

Well, here it shows that I definitely need to read up again on these things. Do you mean that due to the u² staying in the equation even after first-order discretisation, the equation stays non-linear? If that's it, it makes sense to me. I think I mixed up the linear interpolation of the face values with the linearity of the equations themselves.

FMDenaro · August 14, 2020, 05:16

Quote:

Originally Posted by Baum

Well, here it shows that I definitely need to read up again on these things. Do you mean that due to the u² staying in the equation even after first-order discretisation, the equation stays non-linear? If that's it, it makes sense to me. I think I mixed up the linear interpolation of the face values with the linearity of the equations themselves.

Yes you got that

August 13, 2020, 12:35	Is the resulting set of discretised equations for a general CFD problem nonlinear?	#1
Baum New Member Join Date: Dec 2019 Posts: 29 Rep Power: 8	Hi, I was just wondering this while reading up about it: As far as I understand, the PDEs/Navier-Stokes equations in each cell are discretised via different schemes and then solved iteratively in a huge system of equations (matrix). From this, you get the mass, momentum, temperature, pressure etc. in each cell, and you use those to calculate new source terms, densities etc. for the next iteration. Now, my question is the following: Is the resulting equation system that Fluent/OF/whatever solver solves linear, due to the discretisation schemes being used? In other words, are nonlinear equation system solvers necessary for the solution of a CFD problem? Cheers, Baum

Thread Tools	Search this Thread
Show Printable Version Email this Page	Search this Thread: Advanced Search
Display Modes
Linear Mode Switch to Hybrid Mode Switch to Threaded Mode

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Remeshing for Rotation in CFX via ICEMCFD	gera	CFX	3	September 23, 2017 13:29
CFD Salary	CFD	Main CFD Forum	17	January 3, 2017 18:09
How to assign the inlet B.C using a bunch of data set for an unsteady problem?	ali8500	CFX	3	March 28, 2012 19:41
Which is better to develop in-house CFD code or to buy a available CFD package.	Tareq Al-shaalan	Main CFD Forum	10	June 13, 1999 00:27
CFD - Trends and Perspectives	Jonas Larsson	Main CFD Forum	16	August 7, 1998 17:27

August 14, 2020, 04:08		#3
Baum New Member Join Date: Dec 2019 Posts: 29 Rep Power: 8	Hi Filippo, thanks for the reply. Of course the NSE are non-linear, but if I choose a simple first order discretisation scheme, shouldn't the whole system become linearised based on their neighbouring cells? Are there some equations that will always remain nonlinear?

August 14, 2020, 05:05		#5
Baum New Member Join Date: Dec 2019 Posts: 29 Rep Power: 8	Well, here it shows that I definitely need to read up again on these things. Do you mean that due to the u² staying in the equation even after first-order discretisation, the equation stays non-linear? If that's it, it makes sense to me. I think I mixed up the linear interpolation of the face values with the linearity of the equations themselves.