In the code with finite volume method, we want to upgrade the discretization oreder of convective term. Now the schemes in the present code are hybrid and QUICK. What is the higher order scheme than these ? If there is the reference, let me know. Thank you~

Hi,

You can use TVD schemes which are in general 2nd order but will degenerate to 1st order at a discontinuity. However, for convection problems, this is unlikely to be a problem at low speeds. Also, TVD schemes use for convection tend to give a very smooth solution instantaneously. TVD schemes include Van Leer (dissipative) and Superbee (compressive) as well as many others. ENO schemes can also be used. Look for papers by Shu and Osher. I think that these ENO schemes are usually only used for scalar convection not the momentum equations.

Thank you for your kindness.

I mean that the oder is 3rd order or higher than this.

In FVM, which scheme is higher than 3rd ?

You can define a higher order upwind biased interpolation function to increase the order of discretization. I have been reading a paper by Tamamidis and Assanis (Numerical Heat Transfer B, Vol. 24, No. 1) that describes a fifth-order upwind scheme. The face value is given by

Uf = (-6Ui-2 + 540Ui-1 + 94Ui+1 - 26Ui+2 + 4Ui+3)/120

and they use QUICK near bundaries.

Thank you very much~~ It's very useful to me. ^^

I have one more question. if the grid is non-uniform, above equation can not be applied in my thought ?? In non-unoform grid system, more complex equation is needed ???

You map to a uniform computational domain and then use the same formulae.