What is special about QUICK scheme? Is it because it is a third order upwind scheme? Why not use combined compact difference scheme, which is noted for extreme accuracy for this flow?

QUICK and QUICKEST schemes are well detailed by Leonard in this chapter

P. Leonard, Elliptic Systems: Finite-Difference Method IV, in W. J. Minkowycz, E. M. Sparrow, G. E. Schneider, R. H. Pletcher (eds.), Handbook of Numerical Heat Transfer, chap. 9, pp. 347-378, John Wiley,,New York, 1988

Have you some specific problem?

What is special about QUICK scheme? Is it because it is a third order upwind scheme? Why not use combined compact difference scheme, which is noted for extreme accuracy for this flow?

Dear Professors Filippo Maria Denaro and Tapan K. Sengupta ,

What would be a good scheme if you have highly nonlinear source terms causing dispersive oscillations?

By "good", I mean a scheme that doesn't "smear" the solution and at the same time is computationally-efficient.

Assume a transient convection-diffusion problem (not necessarily the same lid-driven cavity problem addressed here) solved using FDM.

First of all, do not use FD but use FV to preserve some fundamental properties both in conservation and wave propagation.

Then, do not focus only on spatial discretization but focus on the global properties of the time and space discretization.

For example, QUICK is not suitable for wave propagation while the QUICKEST scheme has better properties

If it's the first time you're writing and testing a CFD code, I would recommend going with Finite volume method + staggered grid + SIMPLE + First order upwind scheme. Higher order schemes like CDS and QUICK have issues with convergence. Once your First order scheme is converging and you've sorted out any other errors in the code, you can write and test the higher order schemes. Also preferably use FORTRAN or C++ instead of python.

I've recently written a code for this problem and learnt these through a lot of mistakes.

An introduction to CFD by Versteeg and Malalasekera is an excellent reference.

Thanks all for the contribution

Filippo Maria Denaro I saw the reference it is very useful, but a bit expensive to buy.

Tapan K. Sengupta I have solved the problem using first order upwind scheme, it is easier for me to convert it to QUICK scheme than to apply a new scheme.

Navin Mahto Yes this is the first problem I am coding I am using

Finite volume method + staggered grid + SIMPLE + First order upwind scheme through deferred correction technique from following reference.

Martínez, J., et al. "Influence of momentum interpolation methods on the accuracy and convergence of pressure–velocity coupling algorithms in OpenFOAM®." Journal of Computational and Applied Mathematics 309 (2017): 654-673.

Now I am looking for the same kind of reference to apply the QUICK scheme.

Muhammad Usman: you can use other third order upwind scheme as well. While it is written in flux vector form in my book (chapter 12 of High Accuracy Computing Methods, CUP, 2013), you can find many other sources, including journal papers. Once upon a time, we have used third order variants of Kuwahara's scheme. Honestly, I would advice you to use higher accuracy methods.

Best wishes for your research.

Muhammad Usman

Maybe you can buy on internet only the Leonard's chapter of the book at a cheaper cost. However, be aware of the fact the the QUICK scheme can be used mainly for the steady formulation, therefore for Re

Muhammad Usman

I do not want to scare you. But you can see our recent ultra-high accuracy results for 2D LDC problem in:

Article Grid sensitivity and role of error in computing a lid-driven...

There are still so many aspects to explore.....

Best wishes.

Navin Mahto while using First order upwind scheme I am facing difficulty for writing the equations for the boundary nodes, do you have any valuable reference in this regard?

Same reference: versteeg and malalsekara. There's an entire chapter on boundary conditions and it addresses BC specification for staggered grids. I'm also attaching a document which might be useful.

Navin Mahto The method described here the fictitious cell across the physical boundary is applied on StaggeredGrid, but I am considering the non-staggered mesh,

What excatly do you need?

Do you need the code or you have some specific doubt?

If you've already coded 1st order upwind, assuming you coded in C++, replace void Upwind() with void Quick().

Just remember to use 1st order upwind at boundary faces, and 2nd order in the interior.

I coded this inmy MTech, for intro to CFD course.

Where are you stuck?

Vatsalya Sharma Can I have the code so I case if I would need I could ask question. My code is giving divergence.