Riemann invariants

Summary

A Riemann invariant of a hyperbolic system is a function of the state that is constant along certain waves. For a system of two equations, such as one-dimensional isentropic gas dynamics, each Riemann invariant is constant along one family of characteristic curves. Changing to Riemann invariants as unknowns decouples the system into two transport equations. Riemann introduced them in 1860 to study sound waves of finite amplitude, and they underlie the method of characteristics in gas dynamics. See the definition.