First order upwind scheme can produce better results?

Achilleas · January 1, 2018, 06:37

Happy new year to all of you,

I want to study the behaviour of the airflow around a 2d airfoil in steady state conditions. More specifically, my investigation concerns the performance of different RANS models.

Speaking for the implementation of Spalart-Allmaras turbulence model, I get worst results when I use a second order upwind scheme for the discretisation of flow compared to a first order upwind scheme. I compare my results with those in the literature. Could anyone guide me around this subject?

Thank you in advance for your help

Achilleas

LuckyTran · January 2, 2018, 18:50

The order of convergence of a particular scheme is not the same as absolute accuracy and both of these depend on the flow in question and the grid quality (also on the phase of the moon, whether the planets are aligned and so on). It should not at all be surprising that you get "better results" with a 1st order XXXX scheme compared to 2nd YYYY scheme for some scenarios.You hardly find this fact in textbooks, few practical details are ever in academic texts. But in my opinion, it is a well-observed practical occurrence (just as you've seen).

Unless you have a specific question, a general answer is complicated and will send you down a rabbit hole.

If you want the same results from "literature" then I would suggest to contact those authors, ask for their grid, all their settings, their custom code if applicable and try to replicate it.

ram_call · January 2, 2018, 19:01

I have similar XP in one case where 1st order produce more stable results. Generally depends on problem and the flow field. It can be considered that 2nd order impose more diffusion in solution.

Achilleas · January 2, 2018, 19:30

Thank you for your response

LuckyTran: The validation is conducted with experimental results.

I can accept that second order scheme is not suitable for certain cases but I can't understand why.

I refined the mesh with a good analysis of the boundary layer. I played with the relaxation factors and I think that I can accept the level of the achieved convergence (my residuals for the lift coefficient were fluctuating around +- 0.01% while the residuals of momentum, energy and continuity were remaining in a low level); first order scheme provided more stable residuals indeed. What happened with the accuracy of the results?

ram_call: you mean that second order scheme can overestimate the things?

ram_call · January 2, 2018, 20:57

Quote:

Originally Posted by Achilleas

Thank you for your response

LuckyTran: The validation is conducted with experimental results.

I can accept that second order scheme is not suitable for certain cases but I can't understand why.

I refined the mesh with a good analysis of the boundary layer. I played with the relaxation factors and I think that I can accept the level of the achieved convergence (my residuals for the lift coefficient were fluctuating around +- 0.01% while the residuals of momentum, energy and continuity were remaining in a low level); first order scheme provided more stable residuals indeed. What happened with the accuracy of the results?

ram_call: you mean that second order scheme can overestimate the things?

lets not call it overestimate, just slightly more diffusion in solution. well, in cases that are sensitive to slight diffusion, can impose and expand unstablity in domain especially in transient simulation. totally depends on the problem. if governing Eqs are all send order or no, if high gradiant field is present or no. for eg: boundary layer mesh in high gradiant boundaries can subside this effect of 2nd order scheme

LuckyTran · January 3, 2018, 19:33

Classical 2nd order upwind (and higher order schemes in general) can introduce non-physical oscillations (overshoots and undershoots). These oscillations are clearly inaccurate since they yield solutions which are impossible whereas a 1st order scheme which does not produce these oscillations will produce much more accurate solutions (even though their order of convergence is lower). Lots of limiters are used to prevent these oscillations and prevent them from becoming non-physical; hence the importance of developing TVD schemes.

In either case (oscillations or none), all this assumes you even have the correct gradient in the first place in order to extrapolate cell values to face fluxes. Getting gradients on an unstructed mesh is simply tricky. And then how do you find the face fluxes? Also, you never actually solve for gradients but calculate them based on the solution values, i.e. you need to discretize the gradient also.

In an ideal scenario the 2nd order upwind scheme by itself should have certain desired properties (and there's nothing wrong with this theory). But many other issues are encountered before you can actually solve a real CFD problem. That is, how the heck can you even use a 2nd order upwind scheme for fluxes if you don't even know what the gradient is?

January 1, 2018, 06:37	First order upwind scheme can produce better results?	#1
Achilleas New Member Join Date: Sep 2015 Posts: 15 Rep Power: 10	Happy new year to all of you, I want to study the behaviour of the airflow around a 2d airfoil in steady state conditions. More specifically, my investigation concerns the performance of different RANS models. Speaking for the implementation of Spalart-Allmaras turbulence model, I get worst results when I use a second order upwind scheme for the discretisation of flow compared to a first order upwind scheme. I compare my results with those in the literature. Could anyone guide me around this subject? Thank you in advance for your help Achilleas Last edited by Achilleas; January 2, 2018 at 09:09.

January 2, 2018, 18:50		#2
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,735 Rep Power: 66	The order of convergence of a particular scheme is not the same as absolute accuracy and both of these depend on the flow in question and the grid quality (also on the phase of the moon, whether the planets are aligned and so on). It should not at all be surprising that you get "better results" with a 1st order XXXX scheme compared to 2nd YYYY scheme for some scenarios.You hardly find this fact in textbooks, few practical details are ever in academic texts. But in my opinion, it is a well-observed practical occurrence (just as you've seen). Unless you have a specific question, a general answer is complicated and will send you down a rabbit hole. If you want the same results from "literature" then I would suggest to contact those authors, ask for their grid, all their settings, their custom code if applicable and try to replicate it. PENGGEGE777 and khannakartik like this.

January 2, 2018, 19:01		#3
ram_call Member ram Join Date: Apr 2013 Posts: 37 Rep Power: 13	I have similar XP in one case where 1st order produce more stable results. Generally depends on problem and the flow field. It can be considered that 2nd order impose more diffusion in solution. PENGGEGE777 likes this.

January 3, 2018, 19:33		#6
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,735 Rep Power: 66	Classical 2nd order upwind (and higher order schemes in general) can introduce non-physical oscillations (overshoots and undershoots). These oscillations are clearly inaccurate since they yield solutions which are impossible whereas a 1st order scheme which does not produce these oscillations will produce much more accurate solutions (even though their order of convergence is lower). Lots of limiters are used to prevent these oscillations and prevent them from becoming non-physical; hence the importance of developing TVD schemes. In either case (oscillations or none), all this assumes you even have the correct gradient in the first place in order to extrapolate cell values to face fluxes. Getting gradients on an unstructed mesh is simply tricky. And then how do you find the face fluxes? Also, you never actually solve for gradients but calculate them based on the solution values, i.e. you need to discretize the gradient also. In an ideal scenario the 2nd order upwind scheme by itself should have certain desired properties (and there's nothing wrong with this theory). But many other issues are encountered before you can actually solve a real CFD problem. That is, how the heck can you even use a 2nd order upwind scheme for fluxes if you don't even know what the gradient is? phPatras, wc34071209 and PENGGEGE777 like this.

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January 2, 2018, 19:30		#4
Achilleas New Member Join Date: Sep 2015 Posts: 15 Rep Power: 10	Thank you for your response LuckyTran: The validation is conducted with experimental results. I can accept that second order scheme is not suitable for certain cases but I can't understand why. I refined the mesh with a good analysis of the boundary layer. I played with the relaxation factors and I think that I can accept the level of the achieved convergence (my residuals for the lift coefficient were fluctuating around +- 0.01% while the residuals of momentum, energy and continuity were remaining in a low level); first order scheme provided more stable residuals indeed. What happened with the accuracy of the results? ram_call: you mean that second order scheme can overestimate the things?