Question abt. the Riemann analytic solver

jinwon

I am solving numerous of 1D Riemann problem and new to such a problem.

My biggest question is the role of the Riemann solver which determines the pressure and the velocity at the contact discontinuity.

Based on the formulation, we can think that it is used to determine the variables including pressure and velocity at the contact discontinuity using the initial condition which is separated by a membrane or something else.

If so, I wonder if pressure and velocity computed by a Riemann analytic solver remain constant over the entire time integration.

The reason I am wondering is that the Eulerian code is advanced by a time scheme to get a target final time, thus the pressure and velocity is also increased or decreased with time. But the scheme based on a Riemann analytic solver only provides constant pressure and velocity based on the initial two constant conditions(left and right).

I also wonder if the pressure and velocity at the contact discontinuity needs to be computed at each instant or just needs at the first time step.

Please help me. I am stuck with this issue for a month.

Thanks in advance

Best regards