What is the bottom cross-section dimension of the second order of accuracy?

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Multiple Choice

What is the bottom cross-section dimension of the second order of accuracy?

Second-order accuracy means the numerical error decreases roughly with the square of the grid spacing (h^2) as you refine the mesh. To observe and achieve that level of accuracy on the bottom cross-section, you need a mesh fine enough that the h^2 terms dominate the error behavior. Among the options, the configuration with the most grid points per dimension provides the smallest spacing, giving the best chance to realize second-order accuracy. The coarser grids produce larger spacing and larger truncation errors, which typically do not demonstrate the second-order behavior. Therefore, the bottom cross-section dimension that supports second-order accuracy is the finer 40 x 40 configuration.

Second-order accuracy means the numerical error decreases roughly with the square of the grid spacing (h^2) as you refine the mesh. To observe and achieve that level of accuracy on the bottom cross-section, you need a mesh fine enough that the h^2 terms dominate the error behavior. Among the options, the configuration with the most grid points per dimension provides the smallest spacing, giving the best chance to realize second-order accuracy. The coarser grids produce larger spacing and larger truncation errors, which typically do not demonstrate the second-order behavior. Therefore, the bottom cross-section dimension that supports second-order accuracy is the finer 40 x 40 configuration.

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