Hi, everyone: Such algorithms as SIMPLE and PISO also has the ability to solve unsteady problems. But why they are not widely used in DNS/LES? Is it only because of their large computational expense?

thanks, Linfeng

Because they have dissipative character at small scales close to the smallest scales resolved and therefore modify the spectrum of those scales. A scheme is called dissipative when it amplifies or reduces some modes amplitudes. A centered scheme is purely dispersive, does not modify the amplitude of any scale but only its phase. As soon as you use a not purely centered scheme in a purely regular mesh, one introduces small numerical dissipation that can artificially stabilize or unstabilize the computation.

In DNS and specially LES one has to be able to solve accurately the amplitude of the modes up to the smallest scales

I guess SIMPLE type algorithms can do DNS and LES on staggered grids where seemly pure central differences can be used for any spatial derivatives. But it seems there is few such work. I do not know why.

Oh yeah you're right...sorry I had a terrible memory lapsus...

Yes I think SIMPLE algorithm would require too many sub-steps for each time step for unsteady calculations. It is best suited for steady calculations (or calculations in which you seek converged steady solution) and DNS-LES are inherently unsteady...or something like that, hope my memory is not failing again

Then it should be the case of computational expense? By the way, I am not sure whether central difference is more difficult to converge than upwind.

Sometimes time accuracy is more important than any other parameters. In DNS/LES more than second order time differencing scheme is recommended. And in spacial differencing, upwind families schmes are too dissipative so that cannot resolve small scale chacteres.