[FMDenaro]

Originally Posted by vesp

Why would multi D Riemann solvers be important? all the FV codes I have seen in use at big conpanies just use 1D RP solvers normal to the faces...

Yes but that is a low order accurate reconstruction. Consider that some propagation directions are privileged, that is the directions orthogonal to the faces of the volumes. This may lead to large numerical errors, especially if the mesh is not a classical Cartesian one.
There exist several papers in literature showing the improvement in using multidimensional Rieman solver. For example I remember some tests showing the carbuncle phenomenon disappearing.

[sbaffini]

Originally Posted by FMDenaro

What book do you think is better for that

Let me say that, in my opinion, for different reasons, they are both awful for beginners. Still, of course, they both have merits.

[FMDenaro]

Originally Posted by Eifoehn4

Yes that's maybe true, but i think it is also hard to skip this topic when someone starts to learn the finite volume theory and you have to explain him afterwards e.g. things asked by TurbJet.

In my opinion it is really helpful to introduced common finite volume
approximations along with the Riemann problem theory.

The books of Leveque and Toro are good references, but i would also suggest to use second literature, where the focus is more on numerical methods, especially for the incompressible Navier Stokes equations.

Regards

Skipping this topic no, but there is a theoretical issue for adopting the Riemann problem as general basis for a FVM, in a general viscous flow there is no longer the existence of Riemann invariants as well as of a discontinuity. So approaching the problem this way is only a first order accurate factorization between convection and diffusion of momentum.

[FMDenaro]

Originally Posted by sbaffini

Let me say that, in my opinion, for different reasons, they are both awful for beginners. Still, of course, they both have merits.

Paolo, as you know is impossibile to have a single textbook as a standard for teaching CFD. Better to have a couple of reference for each level of CFD courses.