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Second- and fourth-order accurate finite-difference approximations of the equations governing a free surface autobarotropic fluid are compared with each other and with a second-order approximation on a one-half mesh. It is concluded that once the mesh size has been reduced sufficiently to adequately resolve the scales of interest then further reduction in mesh size would be inefficient in comparison with the use of more accurate finite-difference approximations.
Second- and fourth-order accurate finite-difference approximations of the equations governing a free surface autobarotropic fluid are compared with each other and with a second-order approximation on a one-half mesh. It is concluded that once the mesh size has been reduced sufficiently to adequately resolve the scales of interest then further reduction in mesh size would be inefficient in comparison with the use of more accurate finite-difference approximations.
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