RiemannExact(p1,rho​1,u1,p4,rho4,u4,tol​)

The code gives the exact solution of Euler's 1-D unsteady Riemann problem of the shock tube.

The code gives the exact solution of Euler's 1-D unsteady Riemann problem of the shock tube. The analytical solution is calculated by means of the Newton-Raphson's method and the characteristic equations.
After having set the inputs to the left and right gases' variables, one can easily check the waves generated from the discontinuity; the program returns in output the type of the solution, which can be for example an RCS (meaning that an expansion has generated on the first family and a shock on the second family). The user then has the chance to get the most important variables (sound speed, pressure, velocity) plotted versus the shock tube's length coordinate. NB: all interactions are neglected.
INPUTS:

p1: pressure of the gas in the left part of the shock tube
rho1: density of the gas in the left part of the shock tube
u1: velocity of the particles in the left part of the shock tube
p4: pressure of the gas in the right part of the shock tube
rho4: density of the gas in the right part of the shock tube
u4: velocity of the particles in the right part of the shock tube
tol: tolerance of solution

Virginia Notaro