hi friends could some one please explain to me what is the Riemann problem? what is so big about it? and how is it solved? or atleast provide me a link that answers me. I am new to cfd and am willing to learn a lot. I understand that it is about discontinuities. also tell me how it is used in FVM where there are discontinuities at cell interfaces? I come across problems which are named Riemann-xxx problems.. xxx is some other name. so please tell me if the classic riemann problem is called by some other names too. Also tel me is this the same riemann problem used to solve shock problems at ramps. thank u

The Riemann problem is a method of solving a special class of problems related the hyperbolic partial differential equations by use of the so-called "Riemann invariants". The classic problem of this type is the breaking of a dam in shallow water (see for example the book "Elementary fluid dynamics" by D.J. Acheson). It's application to CFD goes back to Godunov and is described in detail in the book "Finite volume methods for hyperbolic problems" by R.J. Leveque.

Also known as Shock-Tube Problem

or

Sod's problem

Book by Toro explains all, although Leveques is a lot cheaper.

[immortality]

hi
Whats the name of book of Toro?