Applications to Gas Dynamics

Abstract

In earlier sections, we have written the equations of gas dynamics in several different forms (see equations (18.3) and (18.3)′ of this chapter, and Examples 1 and 2 in Chapter 15). In many standard texts, it is shown that they are all equivalent for classical solutions ; i.e., they determine the same classical solutions. What we shall do here first is to prove that the computation of eigenvalues, Riemann invariants, and the genuine nonlinearity or linear degeneracy of the characteristic fields, are all independent of our choice of equations. That is, they are invariant under coordinate changes.