A Finite-difference Scheme for the Two-way Nested Mesh Model

A finite-difference scheme with variable mesh scale for the two-way nested mesh model is designed, to which the finite difference formulas with different order of accuracy in coarse and fine meshes are applied. The calculation repeated at the grids of the coarse and fine overlapping meshes is avoided. The analytic solutions and the results of the numerical experiments show that as compared with other difference schemes with non-uniform gird, the scheme would produce small false reflectivity for the shortwave. A nested mesh model of barotropic primitive equation is constructed by means of the scheme. A time-spliting and spatial-spliting method is used in the model, in which the two-dimensional equation is transformed into two sets of one–dimensional equation so that the numerical calculating and computer programming are simplified. A series of the results of numerical experiments using ideal fields as initial data show that the model is computational stability. Finally, by the use of the model, some results for forecasting typhoon track are given