Vorticity Stream Function on Airfoil
I am writing a code to solve the laminar flow over an airfoil for ( Re < 100000 ) in Generalized Coord using Stream function vorticity formulation
my code follows this algorithm
1 - Solve the StreamFunction using GS-SOR to tolerance 1e-8
2 - Calculate the Contravariant velocity
3 - Calculate the Vorticity Value at the Airfoil Surface
4- Advance the Vorticity Transport Equation one time step using ( Explicit Euler or ADI )
5- Check Vorticity Convergence else return to step 1
I use a C-grid of 257 x 129 with 129 points on the airfoil surface and min normal spacing of 1e-3 , the grid is Orthogonal on the airfoil surface points are clustered on near the LE ( to capture Circulation ) and TE to Capture seperation.
The values of SF and Vort. are updated on the Cut ( Wake ) by simple average up & down the Cut.
The Problem is that Convergence keeps stalling at points near the LE and I don't know what to do >
by Stalling , I mean that the Convergence of max residual doesn't go down beyond some value .this value changes with Re and time step.
I tried using finer grid but the solver becomes unstable and won't run and I tried using smaller time-step I solve still stalls at the LE
as you see in the second picture the max. Error in Vorticity is stuck at around 0.0035~0.0042 , near the LE ( x = 0.0 , y = 0.0 )
first, what do you physically expect from this simulation?
setting Re=O(10^5) while specifyng that the flow is laminar can be misleading... first, is your grid really able to take into account for the low molecular diffusion close to the wall? second, laminar flow can exhibit slowly time-dependent solution. Could you be sure your 2D solution must be really steady? third, check all the tolerances you are using to avoid errors cumulate during time integration
what is your BC for the vorticity at the LE. I know that that BC gets a little tricky at the corner of a backwards facing step.
I found the problem with my my code it turns that it doesn't like first order upwind scheme for convection ( very much ) , I tried second order upwind but I get a converged but in-accurate solution so I tried central differencing and it worked like magic I got an accurate converged solution. But I still want to use an upwind scheme so I am looking for suggestion >
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