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Better convergence with Upwind than High-Resolution advection scheme

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Old   September 14, 2012, 10:22
Default Better convergence with Upwind than High-Resolution advection scheme
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siw
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Hi,

Just done a fluid-porous-fluid steady-state RANS simulation (hybrid fluid mesh structured porous mesh) and ran the first 100 iterations using the Upwind advection scheme just to get the simulation going since it is more robust. I then ran the next 100 iterations using the High-Resolution scheme to improve the accuracy.

The image shows that convergence was better with the Upwind scheme, see the image. Why would that be? I'd conclude to use Upwind in all similar cases going on what this has shown.

The monitor point (mass flow rate at the outlet) was constant from about iteration 10 to the end.
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Old   September 14, 2012, 12:26
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Quote:
Originally Posted by siw View Post
Hi,

The image shows that convergence was better with the Upwind scheme, see the image. Why would that be? I'd conclude to use Upwind in all similar cases going on what this has shown.
Hello siw,

If I understood correctly you are solving a fluid flow inside a porous medium, is that so?

If that's the case, the Upwind scheme is suppose to make the convergence better. This numerical scheme is based on the upstream flow conditions (just like the flow in a river - the upstream condition push the flow). If you take a look in the theory behind the advection schemes used in CFX you will probably understand.

If your problem is a fluid flow inside a porous medium then the UDS scheme is a good estimation of the physical phenomenon.

The High-Resolution scheme is not always better than the Upwind, it depends on the conditions of the problem. Each one has its limitations and applications. To know which one to use it is necessary to understand what they do mathematically.

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Old   September 14, 2012, 12:30
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Originally Posted by Possa View Post

If you take a look in the theory behind the advection schemes used in CFX you will probably understand.
A little more about the advection schemes can be found here http://www.cfd-online.com/Wiki/Appro...onvective_term

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Old   September 14, 2012, 12:42
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My simulation could be thought of like the CFX catalytic converter tutorial but without the heating features. There is fluid domain followed by a porous domain and then another final fluid domain.
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Old   September 14, 2012, 13:47
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Hi,

Then I stand for my previous post. Your problem is a upstream problem. The Upwind scheme is physically consistent. Using HR scheme doesn't necessarily mean it will provide better results.
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Old   September 14, 2012, 14:22
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As I see it the High-Resolution scheme is an upwind scheme as well and it just includes a blending term to vary between 1st order (i.e. the same at the Upwind scheme) and 2nd order. Trying to keep it as close to 2nd order as possible to avoid wiggles.
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Old   September 14, 2012, 14:33
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Yes, you are correct, but the 1st order scheme (what CFX calls Upwind) is more robust than the High Resolution because of the order.

What I'm trying to say is that for some problems higher order schemes doesn't bring a better result, but it will probably show worse convergence. You have to analyse what scheme is better for the problem.

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Old   September 15, 2012, 07:31
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Upwinding is a first order scheme and contains lots of numerical diffusion. This means the flow is damped artifically more than it should be which results in easy and tight convergence, but inaccurate results.

High Res uses a second order scheme when possible and blends to a first order scheme to maintain boundedness. It contains far less numerical diffusion. This means the flow has less artificial damping and therefore closer to the correct amount of damping. This results in slower and less tight convergence (as more little perturbations are present) but higher accuracy.

I do not agree with Talita's comment - there is no such thing as a simulation where first order is more suited than second, any time you choose a first order scheme you are sacficising accuracy for easy convergence.

THe CFX advection schemes "Upwinding" and "High res" are both upwinding schemes, just "upwinding" is first order and "High res" is second order, and blending to first order where the flux limiter cuts in.

And finally, do not be confused into thinking that simulation error is proportional to the residual. The residual is simply how tightly the linear solver has achieved, and the link of this to accuracy is complex. The original post's second order simulation is probably more accurate than the first order bit, even though the residuals are not as tight.
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