Dear all

Can anyone tell me / give references of alternative methods to Gauss/Green to compute gradients of for example a scalar over a control volume.

Gauss (grad Phi)~1/V Sigma_faces (Phi_face x areavector_face)

I'll not try to dig out multiple references.

My point (helpful or not) is that there are a great many ways to calculate Phi_face.

What you choose depends on your experience, your problem, your overall algorithm, economics, the physics you're trying to simulate.

Not the answer to the question you asked.

Dear Jim

Say I have phi_face. I'm just looking for alternatives to Gauss for the gradient calculation.

Regards

The least squares method can be an alternative to the green-gauss theorem for calculating a gradient of a scalar over irregular control volumes. Both are useful and cannot say which is better; because it depends on the situation.

In my experience, two methods show similar results. The method of least squares is sometimes used in special scheme such as least-squares ENO, but it can take the place of green-gauss.

Dear Kang

Could you maybe provide references of where the least squares method is explained? Thank you

One example of calculating a gradient of a dependent variables over a control volume is presented here. Hope this will help you.

N. BALAKRISHNAN AND G. FERNANDEZ, WALL BOUNDARY CONDITIONS FOR INVISCID COMPRESSIBLE FLOWS ON UNSTRUCTURED MESHES, Int. J. Numer. Meth. Fluids 28: 1481-1501 (1998)

Tim Barth, "Recent Developments in High Order K-Exact Reconstruction on Unstructured Meshes", AIAA Paper 93-0668, 1993.

This paper describes a least-squares procedure for calculating gradients and Hessians. Gradients only are a simplification of this procedure.

Thank you for the references

Least squares reconstruction is also used by Carl F. Ollivier-Gooch. See his papers on his website. You can download some of them.

http://tetra.mech.ubc.ca/~cfog/publications/index.html