Riemann-Problem

As Riemann problem ( after Bernhard Riemann ) a special initial value problem in calculus called, in which the initial data is defined as constant, up to a point where they are discontinuous.

Riemann problems are very helpful for the understanding of hyperbolic partial differential equations, because in them show up all phenomena such as shocks, shock waves or rarefaction waves. Also, like the Euler equations exact solutions constructible, which is not possible for arbitrary initial data for complex nonlinear equations.

In numerical mathematics dive Riemann problems occurring naturally in finite-volume method to the solution of conservation laws. There, the Riemann problems are addressed by so-called approximate Riemann solver.