[farah.elias]

Hi,

I am running a 2D test case for the Taylor-Green vortex in OF. I have a structured uniform mesh (hence deltaX = deltaY, and no non-orthogonality is present).

For the PISO algorithm, the pressure loop is set to 3 while the non-orthogonality corrector is 0.

The numerical schemes chosen are as follows:

• Unsteady Term --> backward (2nd order)
• Gradient Terms --> Gauss linear (2nd order)
• Divergence Terms --> Gauss linear (2nd order)
• Laplacian Terms --> Gauss linear orthogonal (2nd order)
• Interpolation --> linear (2nd order)

Theoretically, the discretization should be second-order accurate in space and time. Am I right?

If I try to compute L1, L2, and Linf norms to test the temporal accuracy for different values of deltaT (which I compared to a reference refined solution with very small deltaT), I obtain a log-log plot with a slope ~= 2 for every norm.

While as, if I try and do the same for the spatial accuracy for different values of deltaX (=deltaY), and compare it with the analytical solution, I obtain a slope ~= 1 for every norm.

The procedure for calculating the error norms is the following:

1. I am running my simulations for different grid sizes (40x40, 80x80, 160x160, and 320x320).
2. Then I calculated 4 different analytical solutions to get values of p & U on the x and y coordinates that coincide with the x and y coordinates of the CV centers for every grid size where I computed the numerical solution.
3. Afterward, I calculate the L1, L2, and Linf norms for the velocity error in x and y separately.
4. Then after obtaining different values of the L1, L2, and Linf errors for every grid spacing I computed the slope, which was equal to 1 for every norm.

What could be the problem here? Why I am not obtaining a second-order accurate solution in space?

Any help is highly appreciated.