1-D Flow Computation Using the Unified Coordinates

Abstract

The gas dynamics equations in Eulerian coordinates (t, x) are written in conservation PDE form as

$$ \frac{\partial } {{\partial t}}\left( \begin{gathered} \rho \hfill \\ \rho u \hfill \\ \rho e \hfill \\ \end{gathered} \right) + \frac{\partial } {{\partial x}}\left( \begin{gathered} \rho u \hfill \\ \rho u^2 + p \hfill \\ u\left( {\rho e + p} \right) \hfill \\ \end{gathered} \right) = 0, $$

((4.1))

where

$$ e = \frac{1} {2}u^2 + \frac{1} {{\gamma - 1\rho }}\frac{p} {\rho }. $$