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Conclusions and Future Simulations
To build a well-conditioned model that converges to accurate numerical solution, the mesh density in all 3 dimensions must be in the same order of magnitude, and refined enough to resolve the region where fluid flows vary violently; "uniform" in z direction is not equivalent to no components in z direction, thus 3D model with periodic boundary condition may not be equivalent to 2D model, which also put more doubts in the validity of 2D models.