# Taylor-Green Vortex Spatial Error

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 February 2, 2024, 12:08 Taylor-Green Vortex Spatial Error #1 New Member   Join Date: Apr 2020 Posts: 2 Rep Power: 0 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:I am running my simulations for different grid sizes (40x40, 80x80, 160x160, and 320x320). 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. Afterward, I calculate the L1, L2, and Linf norms for the velocity error in x and y separately. 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.

 Tags accuracy, openfoam, taylor-green vortex