Im working on a CFD project for school here and I am expected to do some analysis of my results. When I plot the log of the l2 norm of the change in solution vs timestep, the plot is not constantly decreasing. There are some oscillations. The code is correct as it does converge to the exact solution, and overall the norms decrease, but does anybody know what causes these oscilations. Why would the norm decrease, increase a little bit, then keep decreasing? This is a 2d navier stokes solver on a square uniform mesh for simple channel flow. I am just solving for pressure,x and y velocities and plotting those norms. Thank you very much

A guess:

I'm assuming you're going to the steady state (no transient terms) and you're solving by (under) relaxation.

This sort of oscillation is fairly common if your relaxation factors are near the maximum values that will converge. In my experience, reducing them will remove the oscillations. Also, in my experience, this will often result in more iterations being required to reach convergence!

Good luck.

Thank you for your reply. I havent fiddled with relaxation yet, so thats at 1. My main concern is what causes these oscillations in the norms. They arent a problem for me, but i am looking for an explanation. Thanks

I really don't know.

The effect is just something that I've observed (and read about). If I were studying the effect, I'd probably try to find some analogy with overdamned or underdamped oscillatory systems.

Good luck!

There could be some waves which keep moving between the inner and outer boundary until they die down. I observe these in subsonic calculations. Or it could also be due to local time-stepping where the solution at different points is at different times. Try to see how it converges with global time-stepping. Limiters are also notorious for causing such oscillatory convergence, and they even hamper convergence especially the min-max limiter.

The precise explanation of the oscillations of the L2 norm depends on the details of your computational method. Another possibility for certain types of iterative procedures, such as Newton-Raphson, is that the surface defined as the L2 norm as a function of solution vector is not sufficiently smooth to insure monotonic decay of L2 from one iteration to the next. For nonlinear systems of algebraic equations, this surface can have local extrema, saddle points, and other unhelpful features that hinder convergence. To figure out why this particular study found the oscillations, we would need more details about exactly how the calculation is being done.