Acoustic Pulse

pankos · August 1, 2011, 11:47

I want to validate a Euler equations solver using the acoustic pulse as test case.
However, the exact solution of it, is complex to derived due to the appearence of integral which involves a bessel function.

What can i do for derive the exact solution? Any suggestions?

cfdnewbie · August 2, 2011, 03:23

would it have to be an acoustic pulse? you may start with sth simpler and build up from there to validate the code...e.g. the standard test case: pulse in rho..

panou · August 2, 2011, 05:30

Could you tell me more information for this case? Some papers which setup the test?

The convection of isentropic vortex is not good problem for validation?

andy_ · August 2, 2011, 07:46

Quote:

Originally Posted by pankos

I want to validate a Euler equations solver using the acoustic pulse as test case.
However, the exact solution of it, is complex to derived due to the appearence of integral which involves a bessel function.

What can i do for derive the exact solution? Any suggestions?

Integrate the Bessel function using one of the many tricks you learnt at school and university? If your recall is a bit wonky then googling "integrate Bessel function" is likely to provide a whole bunch of options.

cfdnewbie · August 2, 2011, 12:23

Start by using a density pulse with a velocity field (should be convected along the streamlines).
If that works, use the method of the manufactured solution to create sth like a sinewave solution and test convergence with that - if you actually have access to the code and can add a source term, that is....

piljilaki · August 5, 2011, 14:19

just ask wolframalpha.com to integrate it for you.

August 1, 2011, 11:47	Acoustic Pulse	#1
pankos Member kostas Join Date: Jun 2010 Posts: 43 Rep Power: 15	I want to validate a Euler equations solver using the acoustic pulse as test case. However, the exact solution of it, is complex to derived due to the appearence of integral which involves a bessel function. What can i do for derive the exact solution? Any suggestions?

August 5, 2011, 14:19	wolfram alpha	#6
piljilaki New Member phillip Join Date: Aug 2011 Posts: 7 Rep Power: 14	just ask wolframalpha.com to integrate it for you.

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August 2, 2011, 03:23		#2
cfdnewbie Senior Member cfdnewbie Join Date: Mar 2010 Posts: 557 Rep Power: 20	would it have to be an acoustic pulse? you may start with sth simpler and build up from there to validate the code...e.g. the standard test case: pulse in rho..

August 2, 2011, 05:30		#3
panou New Member aaaaaaaaaaaaaa Join Date: Apr 2011 Posts: 23 Rep Power: 15	Could you tell me more information for this case? Some papers which setup the test? The convection of isentropic vortex is not good problem for validation?

August 2, 2011, 12:23		#5
cfdnewbie Senior Member cfdnewbie Join Date: Mar 2010 Posts: 557 Rep Power: 20	Start by using a density pulse with a velocity field (should be convected along the streamlines). If that works, use the method of the manufactured solution to create sth like a sinewave solution and test convergence with that - if you actually have access to the code and can add a source term, that is....