On the Selection of Grids for Semi-Implicit Schemes

J. L. McGregor Australian Numerical Meteorology Research Centre, Melbourne, Australia 3001

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L. M. Leslie Australian Numerical Meteorology Research Centre, Melbourne, Australia 3001

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Abstract

It is shown that semi-implicit time differencing on a nonstaggered grid using centered time and space derivatives leads to a decoupling into four separate solutions on different subgrids. This deficiency may be successfully overcome by combining weighted averages of Laplacian operators on the subgrids. However, a far more satisfactory approach is shown to be the use of a staggered grid which appears to be a natural choice for the semi-implicit scheme.

Abstract

It is shown that semi-implicit time differencing on a nonstaggered grid using centered time and space derivatives leads to a decoupling into four separate solutions on different subgrids. This deficiency may be successfully overcome by combining weighted averages of Laplacian operators on the subgrids. However, a far more satisfactory approach is shown to be the use of a staggered grid which appears to be a natural choice for the semi-implicit scheme.

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