Acoustic Pulse
 

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?

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..

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?

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.

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....

wolfram alpha
 

just ask wolframalpha.com to integrate it for you.