We know shock tube problem will give discontinuous solution of primitive variables ($\rho$, $v$, $p$). Will it give discontinuous result in flux terms?$F =[\rho u, \rho u^2 +p, \rho e_v]^T$. I tried that on one FORTRAN code of analytical solution on shock tube problem. I have plotted  $\rho u$ in the following figureHere all the flux quantities are having discontinuity. In gas dynamics for steady 1D flow one of the governing equations is $\rho_1u_1= \rho_2u_2$, but the figure doesn't show such phenomena. Is it because shock tube problem is transient and equation $\rho_1u_1= \rho_2u_2$ is steady?If so, then how to quantify conservativeness in analytical solution?
Conservatives in shock tube
fluid dynamics;computational physics;conservation