## Riemann Problem

Given a set of hyperbolic conservation laws in one space dimension plus time, the Riemann problem is to find the solution to the special initial value problem in which two different constant states each occupy one half of the initial line

Philip L. Roe

2015

#### Scholarcy highlights

• Given a set of hyperbolic conservation laws in one space dimension plus time, the Riemann problem is to find the solution to the special initial value problem in which two different constant states each occupy one half of the initial line
• It is helpful to consider a specific example of a Riemann problem, namely, the shock tube problem
• The diaphragm is ruptured, and the high-pressure gas rushes toward the low-pressure gas, pushing it ahead at high speed
• In the case of a general Riemann problem, the left and right states are entirely arbitrary

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