完全非内插半拉格朗日格式在一维Burgers方程及二维浅水波方程上的应用

An Application of Noninterpolating Semi-Lagrangian Scheme to One-Dimensional Burgers Equation and Two-Dimensional Shallow Water Equations

在作者过去提出的完全非内插半拉格朗日格式的基础上 ,针对半拉格朗日格式由于内插带来预报场人为的光滑性问题 ,进一步发展了这种计算格式 ,证明了此格式的计算稳定性。为检验这种新的计算格式的性能 ,在一维和二维问题上进行了应用。在一维问题中采用了一维无粘Burgers方程 (方程中有突变点 ) ;二维问题采用了浅水波方程 ,同时将这些计算结果与Ritchie方案及欧拉方案或一般半拉格朗日内插方案的计算结果进行了比较 ,发现新格式消除了内插和预报场的人为光滑 ,并且计算精度有一定程度的提高 ,这为以后将此格式推广到全球谱模式打下了基础。

A new noninterpolating semi-Lagrangian scheme is further developed here based on the authors' previous noninterpolating semi-Lagrangian scheme. It eliminates any interpolation, so it eradicates the numerical smoothing caused by interpolation. Its stability in computation is proved. The new scheme is applied to one- and two-dimensional models respectively in order to test its property. The one-dimensional model uses Burgers equation with large variable gradient; and the two-dimensional one, the shallow water equation. The performances of the scheme are asessed by comparing their computational results with those obtained by Ritchie's noninterpolating semi-Lagrangian scheme, Eulerian scheme or the usual interpolating semi-Lagrangian scheme. It is shown that the new scheme eliminates the interpolation and so it gets rid of the smoothing caused by it. The computational accuracy is improved to some degree. The work makes a preparation for applying the scheme to global spectral models.