shock tube exact solution

Ardalan · February 5, 2016, 09:21

I need the exact solution of 1d shock tube problem after the waves are reflected from the walls. Existing codes and solutions are about the case that region are infinite (for example sod shock tube).

naffrancois · February 5, 2016, 14:17

Hello,

What you can do if you have an exact riemann solver in hand is to split the problem in two parts. You first get your solution before waves reach the wall then you take your star states and reinject them into a second exact riemann solver run. For example in the Sod shock tube you have a shock traveling to the right. Take the right star state (e.g. the state between the contact and the shock) then build new initial states for the second run.

Your second run will have as initial left state the above right star state, and initial right state the same right star state with inverse velocity (this is your wall). This second configuration will give you a double shock problem where the solution you are looking for will be located between the left traveling shock and the contact. This gives you the solution for your reflected shock.

Good luck !

February 5, 2016, 09:21	shock tube exact solution	#1
Ardalan Member Ardalan Join Date: Feb 2010 Location: Baku Posts: 50 Rep Power: 16	I need the exact solution of 1d shock tube problem after the waves are reflected from the walls. Existing codes and solutions are about the case that region are infinite (for example sod shock tube).

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February 5, 2016, 14:17		#2
naffrancois Senior Member Join Date: Oct 2011 Posts: 239 Rep Power: 16	Hello, What you can do if you have an exact riemann solver in hand is to split the problem in two parts. You first get your solution before waves reach the wall then you take your star states and reinject them into a second exact riemann solver run. For example in the Sod shock tube you have a shock traveling to the right. Take the right star state (e.g. the state between the contact and the shock) then build new initial states for the second run. Your second run will have as initial left state the above right star state, and initial right state the same right star state with inverse velocity (this is your wall). This second configuration will give you a double shock problem where the solution you are looking for will be located between the left traveling shock and the contact. This gives you the solution for your reflected shock. Good luck !