Second order linear upwind or 50% blending with central scheme?

Moreza7 · December 23, 2020, 15:25

Hello,
I want to choose between Second order linear upwind scheme or 50% blending between central and first order scheme.

I want to know which one is more accurate and less dissipative?

Thank you

aerosayan · December 23, 2020, 17:15

Wouldn't that be based on the characteristic waves of the equations you're trying to solve?

In some cases the central scheme doesn't represent the physics well, so we need the upwind schemes. Your blending scheme seems interesting. Waiting to see what the experts say.

sbaffini · December 24, 2020, 07:37

Well, for a pure, straight 50% blending, I think it is the second order upwind the more accurate one, just in terms of order of magnitude of truncation errors, as the blended scheme will inevitably carry the first order error. Of course, the specific weighting might imply that the grid spacing required to see the 1st order error dominant might be quite fine.

Note that, more accurate and less dissipative are not synonyms but, again, I'm pretty sure that the blended scheme will also be more dissipative.

However, both these questions are easily answered by putting down the scheme and making the usual Neumann analysis and/or comparing the relative truncation errors.

FMDenaro · December 24, 2020, 12:39

Quote:

Originally Posted by Moreza7

Hello,
I want to choose between Second order linear upwind scheme or 50% blending between central and first order scheme.

I want to know which one is more accurate and less dissipative?

Thank you

Blended scheme is more suitable for capturing shock waves but can be highly dissipative near the discontinuity. Second order upwind produces a strong dispersive error.
Finally, you have to consider the combined effect of the time integration.

Moreza7 · December 25, 2020, 03:33

Thank you all,

How about blending 50% between second order linear upwind and central difference scheme? Is that a better choice?

FMDenaro · December 25, 2020, 07:03

Quote:

Originally Posted by Moreza7

Thank you all,

How about blending 50% between second order linear upwind and central difference scheme? Is that a better choice?

Have a look here and try to discover the answer.
https://www.researchgate.net/publica..._wave_equation

December 23, 2020, 15:25	Second order linear upwind or 50% blending with central scheme?	#1
Moreza7 Senior Member Join Date: Jan 2018 Posts: 121 Rep Power: 8	Hello, I want to choose between Second order linear upwind scheme or 50% blending between central and first order scheme. I want to know which one is more accurate and less dissipative? Thank you aerosayan likes this.

December 24, 2020, 07:37		#3
sbaffini Senior Member Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 2,192 Blog Entries: 29 Rep Power: 39	Well, for a pure, straight 50% blending, I think it is the second order upwind the more accurate one, just in terms of order of magnitude of truncation errors, as the blended scheme will inevitably carry the first order error. Of course, the specific weighting might imply that the grid spacing required to see the 1st order error dominant might be quite fine. Note that, more accurate and less dissipative are not synonyms but, again, I'm pretty sure that the blended scheme will also be more dissipative. However, both these questions are easily answered by putting down the scheme and making the usual Neumann analysis and/or comparing the relative truncation errors. Moreza7, aerosayan and aero_head like this.

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December 23, 2020, 17:15		#2
aerosayan Senior Member Sayan Bhattacharjee Join Date: Mar 2020 Posts: 495 Rep Power: 8	Wouldn't that be based on the characteristic waves of the equations you're trying to solve? In some cases the central scheme doesn't represent the physics well, so we need the upwind schemes. Your blending scheme seems interesting. Waiting to see what the experts say.

December 25, 2020, 03:33		#5
Moreza7 Senior Member Join Date: Jan 2018 Posts: 121 Rep Power: 8	Thank you all, How about blending 50% between second order linear upwind and central difference scheme? Is that a better choice?