Shock-shock, shock-vortex interactions

ROHAN · May 3, 2015, 16:26

Hi, I have made some changes in the HLL multidimensional solver and now I am trying to test its accuracy.
Probs:
1. Ran it for shock vortex test case, the results looks good but I need exact soln to be able to calculate norm and claim its accuracy increase or decrease. But the exact soln is no where to be found... any suggestions??

2. i wish to run the code for shock-shock interaction problem for inviscid flow, but am not able to find a std test case for inviscid case... can i create my own test case and compare the results with the exact soln which i can calculate analytically??

Rami · May 7, 2015, 03:43

The common approach is to compare a series of runs of increasing resolution and verify the solution converges to the finest grid solution, assuming this finest grid solution is close to the exact. This is usually done when no exact or reference solution is available, as is often the case.

An alternative is to use the manufactured solution method. Here you assume a solution, plug it into the equations and "swallow" all the imbalances a source and boundary condition terms (which become usually quite complicated). If the algebra is carefully done, you thus generate an exact solution, to which you may apply your solver (if it can cope with the extra terms).

I have found this approach useful in the verification and validation of codes and assessing the rate of convergence.

I hope this answers your questions. Good luck!

May 3, 2015, 16:26	Shock-shock, shock-vortex interactions	#1
ROHAN New Member ROHAN Join Date: Oct 2013 Posts: 4 Rep Power: 12	Hi, I have made some changes in the HLL multidimensional solver and now I am trying to test its accuracy. Probs: 1. Ran it for shock vortex test case, the results looks good but I need exact soln to be able to calculate norm and claim its accuracy increase or decrease. But the exact soln is no where to be found... any suggestions?? 2. i wish to run the code for shock-shock interaction problem for inviscid flow, but am not able to find a std test case for inviscid case... can i create my own test case and compare the results with the exact soln which i can calculate analytically??

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May 7, 2015, 03:43		#2
Rami Senior Member Rami Ben-Zvi Join Date: Mar 2009 Posts: 155 Rep Power: 17	The common approach is to compare a series of runs of increasing resolution and verify the solution converges to the finest grid solution, assuming this finest grid solution is close to the exact. This is usually done when no exact or reference solution is available, as is often the case. An alternative is to use the manufactured solution method. Here you assume a solution, plug it into the equations and "swallow" all the imbalances a source and boundary condition terms (which become usually quite complicated). If the algebra is carefully done, you thus generate an exact solution, to which you may apply your solver (if it can cope with the extra terms). I have found this approach useful in the verification and validation of codes and assessing the rate of convergence. I hope this answers your questions. Good luck!