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

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Old   December 23, 2020, 14:25
Default Second order linear upwind or 50% blending with central scheme?
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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
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Old   December 23, 2020, 16:15
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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.
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Old   December 24, 2020, 06:37
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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.
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Old   December 24, 2020, 11:39
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Quote:
Originally Posted by Moreza7 View Post
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.
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Old   December 25, 2020, 02:33
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Thank you all,

How about blending 50% between second order linear upwind and central difference scheme? Is that a better choice?
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Old   December 25, 2020, 06:03
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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
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