[mihirmakwana6]

I am trying to implement a second order MUSCL scheme discussed in the following paper
http://www.sciencedirect.com/science...07904X05000442

Here, phi at west face (phi_w) of the scalar C.V and ratio r are given by the equation show here

http://i.imgur.com/FxY0oAm.jpg

where phi_W, phi_WW and phi_P are values of phi at West(W), West of West(WW) and C.V (P) GRID POINTS

But, it is no where mentioned whether these equations are for west cell face velocity greater ( flow L to R ) or less ( flow R to L ) than zero.
I think they are for flow direction L to R. but i am not sure.
( In many papers, r is defined as the inverse of the one used here. I don't know why !! )



Is there a way to write a general equation for phi at the east as well as west face of the C.V based on flow direction ?

Thanks in advance

[mihirmakwana6]

can someone please help me with this ?

[mprinkey]

I have not implemented these lately, but you are right. There is plenty of confusion about the definition of r vs 1/r. I don't know why either. The most cogent paper I've read about TVD schemes on structured and unstructured meshes is from Marsha Berger, et. al.

https://www.nas.nasa.gov/assets/pdf/...nas-05-007.pdf

The first five pages of that paper should give you keen and consistent insight into this subject.

In reference to your question, generally speaking, the interpolation is ALWAYS assumed to be upwind. TVD schemes...well at least those starting with Flux Corrected Transport ideas...start with the first-order upwind interpolation and then add in anti-diffusion terms to some degree to cancel out the numerical diffusion implicit in FOU. It is typical to illustrate the scheme assuming a positive flux (to the right, say) and then assume that the stencil is reversed when flow is negative.

To my knowledge, there is no formula that doesn't have some directional bias. QUICK, ENO, and WENO schemes all pick stencils with additional samples in the upwind direction. So there is no "one true" formula that is independent of flow direction.

Sorry I don't have a more comprehensive answer. Like I said, it has been a long time for me.

Good luck.

[mihirmakwana6]

Originally Posted by mprinkey

I have not implemented these lately, but you are right. There is plenty of confusion about the definition of r vs 1/r. I don't know why either. The most cogent paper I've read about TVD schemes on structured and unstructured meshes is from Marsha Berger, et. al.

https://www.nas.nasa.gov/assets/pdf/...nas-05-007.pdf

The first five pages of that paper should give you keen and consistent insight into this subject.

In reference to your question, generally speaking, the interpolation is ALWAYS assumed to be upwind. TVD schemes...well at least those starting with Flux Corrected Transport ideas...start with the first-order upwind interpolation and then add in anti-diffusion terms to some degree to cancel out the numerical diffusion implicit in FOU. It is typical to illustrate the scheme assuming a positive flux (to the right, say) and then assume that the stencil is reversed when flow is negative.

To my knowledge, there is no formula that doesn't have some directional bias. QUICK, ENO, and WENO schemes all pick stencils with additional samples in the upwind direction. So there is no "one true" formula that is independent of flow direction.

Sorry I don't have a more comprehensive answer. Like I said, it has been a long time for me.

Good luck.

Ok. Thankyou for the help sir.