A Computational Scheme for the Nesting Fine Mesh in the Primitive Equation Model

Abstract

A finite difference scheme is proposed in performing the numerical time integration over the domain which consists of two different grid systems. The scheme employs the flux method in space and Euler backward method in time.
In order to examine the proposed scheme, numerical experiments are conducted by applying the primitive equation model to an incompressible, homogeneous atmosphere contained in a channel with the free surface. As the coarse mesh size 600km is taken up and as the fine mesh a half of the coarse grid interval (300km) is adopted. The present scheme combines both grid systems, minimizing the occurrence of noise motions at the boundary between different grid systems.
Results of the numerical experiment show smooth patterns throughout 96 hours for an initial field consisting of two wave patterns. The main conservative quantities such as mass, total energy, etc. well keep its initial value during the whole computation.
As far as the present simple experiment is concerned, the combined grid system results in a calculated pattern just like as a composite of the results obtained by using uniformly the coarse grid net alone and the fine grid net alone. Although the present experiment is limited, we may expect the results as a first step towards the nesting of the fine grid subdomain in the coarse grid net.