Method of characteristics in gas dynamics

Summary

The method of characteristics in gas dynamics solves the equations of smooth compressible flow by following the curves along which sound waves travel. In one-dimensional isentropic flow these curves move with speeds $u + c$ and $u - c$, where $u$ is the flow velocity and $c$ the speed of sound. Along each family a Riemann invariant stays constant, so the partial differential equations reduce to bookkeeping along curves. It is the classical tool for nozzle design, simple waves and the formation of shock waves. It is a special case of the general method of characteristics. See the definition.