Application to a System of Equations

Abstract

The quasi-one-dimensional Euler equations, or gas dynamics equations, are of great practical use to represent phenomena taking place in slowly varying channels and ducts. For large Reynolds numbers, the viscous effects can be neglected, and the result will be useful for understanding steady flow in a converging-diverging nozzle, or unsteady flow in a shock tube. As a time-dependent system, we will see that it is hyperbolic and that the solution can be marched in time. As a steady system, it is a challenging coupled set of nonlinear ODEs of first-order, with singular points. For that reason, it will always be preferable to use the unsteady approach and solve for the steady flows in the limit of very large times.