L2 norm for 1st and 2nd order upwind discretization for laminar flow
 

I am evaluating the difference between the 1st and 2nd order upwind discretization scheme for momentum by calculating the L2 norm at one location of the flow.

The flow is laminar. It runs between two parallel plates. The Reynold's number is 500 and I utilize three different mesh resolution for each order (5 x 50, 10 x100, 20 x200) to plot the trendline for each order (each line has three points. The geometry is assumed to be symmetric at the centerline with 0.5m height (the whole height is 1m) The inflow velocity is 1m/s and this is pressure driven flow. The convergence value is 1e-6.

The L2 norm equation i used is L2 = Sqrt (sum (u numerical - u analytical)^2)
u analytical = 1.5 * (1-y^2/0.5^2)



Why is this happening? is it because the inertial forces are dominating the viscous forces given the Re ratio?

if Re is decreased to 100 then both lines behave as first order accuracy!!

what is the reason that this is happening ?


Thank you