Riemann problem

A Riemann problem is a type of "subproblem" that occurs when solving equations including discontinuities, which can prevent some numerical methods from working, thus can require some special handling. Many numerical methods assume some form of continuity of the functions, often including that of derivatives up to some order. Handling the Riemann problem may require methods involving more computation, which may be mitigated by using approximations that handle the problem reasonably.

For example, using the finite volume method to carry out fluid dynamic calculations that include shock can present the problem.