I'm working on a problem of acoustic scattering of a periodic pressure pulse from a cylinder using Linearized Euler equation.The spatial discretization is a higher order central difference and Runga-Kutta is used for time marching.I have a numerical filter to add stability and a buffer zone at domain outlet to absorb the outgoing waves.Since the problem is symmetric I use just half the cylinder with a symmetry condition.

I ran my code on different grid sizes and the results do not converge.Once the results become periodic the acoustic pressure is just a sine wave of the initial time period T.My results,for different grid sizes attain periodicity with different peak amplitudes.On a 500*500 grid the peak amplitude was 3e-5,4.5e-5 on a 600*600 grid and 3.4e-5 on a 700*700 grid.There is no dispersion error.

I need some advice on what could be the reason for the observed oscillations.

What makes you think convergence has to be monotonous? Try 800x800. If you get an amplitude around 4e-5, you're closing in...