I have trying to model the scattering of an acoustic pulse from a cylinder( 2d) using Linearized Euler equation.I use a 6th order compact scheme in space and a 3rd Order runga kutta time stepping.The filtering is a 10th order pade type filter.I was doing the grid convergence studies and faced this weird problem.I'm testing a structured non uniform grid.The boundary conditions on the cylinder surface are non penetration and dp/dn=0.Non reflecting boundary conditions are used at the artificial boundaries.I have validated the numerical schemes and artificial boundary conditions by comparison with benchmark and can say for sure that they might not be the reason.

My results converge to a periodic oscillation after some time intervals but the amplitude of oscillation and phase does not converge.I got a peak pressure amplitude(non dimensional) of 0.7 for a 150*150 grid which changed to 0.9 for a 200*200 grid and decreased to 0.8 for a 250*250 grid and again increased to 0.85 for a 300*300 grid.For the current study using 200*200 grid was sufficient for a polar grid to achieve convergence.

Would like comments from anyone who faced similar problems before.

amplitude 0.7 ... 0.9 ... 0.8 ... 0.85 ...

I wouldn't be so sure it's not converging based on these numbers. I'd at least try one finer grid. (it's not "monotonically" converging but it doesn't have to.)

This is an unsteady problem, right? What about temporal resolution/convergence? Are you reducing the time step as you increase the grid resolution?

Yes this is an unsteady problem.The time step is reduced automatically based on the grid spacing.

Regarding the numbers, the solution at each point becomes sinusoidal after the transient pulses have left the computational domain.So if I observe the results at any point in the domain all I would have is the sinusoidal variation in time.The problem which I'm facing is the amplitude of the sinusoidal fluctuation is not converging with grid refinement.The one particular problem I have is a coarse cell near the front and back stagnation points of the cylinder.But I'm not sure if that could be a reason.I will try refining that cell and check if it makes any difference.