On the \(2\)-D Riemann problem for the compressible Euler equations. II: Interaction of contact discontinuities
The authors study the interaction of nonliner waves for the two-dimensional compressible Euler equations for gas dynamics: \[ \begin{cases} \rho_t+(\rho u)_x+(\rho v)_y=0\\ (\rho u)+(\rho u^2+p)_x+(\rho uv)_y=0\\ (\rho v)_t+(\rho uv)_x +(\rho v^2+p)=0\\ \left(\rho\left (e+{u^2+v^2\over 2}\right) \right)_t+ \left(\rho u\left(h +{u^2+v^2\over 2}\right)\right)_x+\left(\rho v\left(h+ {u^2 +v^2 \over 2}\right) \right)_y=0,\end{cases} \] where \(\rho,p\), and \((u,v)\) represent the density, the pressure, and the velocity, respectively; the internal energy \(e\) and the enthalpy \(h\) are determined by \(e={p\over(\gamma-1) \rho}\) with \(1<\gamma\leq 3\) and \(h=e+ {P\over\rho}\), respectively. In this paper, the authors focus mainly on the interation of contact discontinuities, which consists of two different cases. For each case the authors analyze the structure of Riemann solution. For Part I, cf. ibid. 1, 555-584 (1995; Zbl 0874.76031).
scientific article; zbMATH DE number 1492641