[Amir]

Hi,

Can anyone suggest a reliable high order scheme for convective term of a tensor equation in which convective term is much more dominated? I examine upwind, limitedLinear, Gamma, SFCD, QUICK and Minmod but the results change with increasing grid resolution and it becomes unreasonable for my simple 2D geometry.

Thanks in advance,

[pbohorquez]

Hilary and Henry Weller implemented new polynomial-fit higher-order schemes (quadraticLinearFit, quadraticLinearPureUpwindFit, among others) in OF versions >= 1.6. For further details on the discretisation schemes see their papers:

http://www.met.reading.ac.uk/~sws02hs/publications/
http://www.met.reading.ac.uk/~sws02hs/AtmosFOAM/

However, spatial discretisation in OF is formally based on Taylor series including only the first two terms of the expansion. So I think that we are limited to 2nd order accuray in space. Recall that higher order schemes are difficult to be implemented in arbitrary polyhedral meshes.

Regards,
patricio.

[Amir]

Originally Posted by pbohorquez

Hilary and Henry Weller implemented new polynomial-fit higher-order schemes (quadraticLinearFit, quadraticLinearPureUpwindFit, among others) in OF versions >= 1.6. For further details on the discretisation schemes see their papers:

http://www.met.reading.ac.uk/~sws02hs/publications/
http://www.met.reading.ac.uk/~sws02hs/AtmosFOAM/

However, spatial discretisation in OF is formally based on Taylor series including only the first two terms of the expansion. So I think that we are limited to 2nd order accuray in space. Recall that higher order schemes are difficult to be implemented in arbitrary polyhedral meshes.

Regards,
patricio.

Dear Patricio,

Thanks for your reply; certainly I'll check these schemes but before I take a look over these paper, do you know about their order or stability?
BTW, we have also SFCD as a second order scheme with good stability but it is said that it's very diffusive; do you have any experience with? because my convective term is very large so I prefer more diffusive schemes.

Bests,

[pbohorquez]

Hi Amir, the schemes are high order with exponent very close to 2.00. Curious, for convective dominated problem on simple geometries I usually prefer low diffusive WENO schemes (order >=5). Best wishes, patricio

[Amir]

Originally Posted by pbohorquez

Hi Amir, the schemes are high order with exponent very close to 2.00. Curious, for convective dominated problem on simple geometries I usually prefer low diffusive WENO schemes (order >=5). Best wishes, patricio

Really!? I thought such high order schemes may lead to instability in convection dominated cases! Is there any WENO schemes in OpenFOAM?

[pbohorquez]

Originally Posted by Amir

Really!? I thought such high order schemes may lead to instability in convection dominated cases! Is there any WENO schemes in OpenFOAM?

Hi Amir, WENO works with success without introducing stability difficulties (Shu, 2009). Unfortunately, OF does not implement this family of numerical schemes that will improve the result of many solvers (e.g. interFoam)

C.-W. Shu, High order weighted essentially non-oscillatory schemes for convection dominated problems , SIAM Review, v51 (2009), pp.82-126.

[Amir]

Originally Posted by pbohorquez

Hi Amir, WENO works with success without introducing stability difficulties (Shu, 2009). Unfortunately, OF does not implement this family of numerical schemes that will improve the result of many solvers (e.g. interFoam)

C.-W. Shu, High order weighted essentially non-oscillatory schemes for convection dominated problems , SIAM Review, v51 (2009), pp.82-126.

Thanks for your time,

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Hi, what's your experience, among these higher order schemes, quadraticLinearFit, quadraticLinearPureUpwindFit, MUSCL, etc. which works better if I want to use higher order schemes for better accuracy? Say my flow is convection dominated.

Thanks a lot!

[idefix]

Hello,

I hope it´s correct to ask this question here.
In Jasak´s PhD thesis I found the following sentences:

For good accuracy, it is necessary for the order of the discretisation to
be equal to or higher than the order of the equation that is being discretised

(page 77)

Can anyone explain me why it is so?

Thanks
Idefix