Difference between discrete and continuous adjoint?

Drean · March 12, 2023, 03:45

Hi all. Is there some documents I can read that can explain the difference between discrete and continuous adjoint methods use by SU2? Lower level one will be better since I am newbie.

bigfootedrockmidget · March 12, 2023, 06:59

Here is a long list of publications about SU2, discrete and continuous adjoints

https://su2code.github.io/publications.html

Perhaps this presentation about discrete adjoints:
https://su2code.github.io/documents/su2_dev_gauger.pdf
And this recent 'introduction' youtube video:

https://www.youtube.com/watch?v=k_PKjlWbH14

This one for the continuous adjoint method for compressible flows:
https://stuff.mit.edu/afs/athena/sof...-2015-1946.pdf

You need to know a bit about partial differential equations and computational fluid dynamics. Basically you need the background of at least a BSc. in a STEM field to be able to go through this. So I hope 'newbie' means you are at that level or you will have a hard time.

Drean · March 12, 2023, 07:09

Hi bigfootedrockmidget. Yes, seems like I will have a hard time fore sure but thank you so much for the help.

Sprotte · March 13, 2023, 06:35

The adjoint equations we solve in SU2 are for problems in gradient/sensitivity computation, and they are, therefore, based on a linearization of the (e.g. Navier-Stokes, Euler, ..) equations.
If we want to implement a linearization of those equations, we can either derive them on paper and then go implement the formulas just like the non-linearized flow formulas ("continuous" method, as derived in the context of function spaces); or we can linearize our implementation (i.e. linearize the discretization -> discrete method). The latter is done almost automatically in SU2 via algorithmic differentiation.

Hope this helps :-)

March 12, 2023, 03:45	Difference between discrete and continuous adjoint?	#1
Drean New Member Drean Join Date: Mar 2023 Posts: 3 Rep Power: 3	Hi all. Is there some documents I can read that can explain the difference between discrete and continuous adjoint methods use by SU2? Lower level one will be better since I am newbie.

March 12, 2023, 06:59		#2
bigfootedrockmidget Senior Member bigfoot Join Date: Dec 2011 Location: Netherlands Posts: 657 Rep Power: 19	Here is a long list of publications about SU2, discrete and continuous adjoints https://su2code.github.io/publications.html Perhaps this presentation about discrete adjoints: https://su2code.github.io/documents/su2_dev_gauger.pdf And this recent 'introduction' youtube video: https://www.youtube.com/watch?v=k_PKjlWbH14 This one for the continuous adjoint method for compressible flows: https://stuff.mit.edu/afs/athena/sof...-2015-1946.pdf You need to know a bit about partial differential equations and computational fluid dynamics. Basically you need the background of at least a BSc. in a STEM field to be able to go through this. So I hope 'newbie' means you are at that level or you will have a hard time. Drean likes this.

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March 12, 2023, 07:09		#3
Drean New Member Drean Join Date: Mar 2023 Posts: 3 Rep Power: 3	Hi bigfootedrockmidget. Yes, seems like I will have a hard time fore sure but thank you so much for the help.

March 13, 2023, 06:35		#4
Sprotte Member Ole Burghardt Join Date: Mar 2016 Location: Kiel, Germany Posts: 60 Rep Power: 10	The adjoint equations we solve in SU2 are for problems in gradient/sensitivity computation, and they are, therefore, based on a linearization of the (e.g. Navier-Stokes, Euler, ..) equations. If we want to implement a linearization of those equations, we can either derive them on paper and then go implement the formulas just like the non-linearized flow formulas ("continuous" method, as derived in the context of function spaces); or we can linearize our implementation (i.e. linearize the discretization -> discrete method). The latter is done almost automatically in SU2 via algorithmic differentiation. Hope this helps :-)