Nonstaggered Grid under High-Order Finite-Difference Scheme—Analysis Based on a Shallow Water Equation

Although the nonstaggered grid has better physical consistency than the staggered grid, it is still not widely used, mainly because of its poor accuracy for simulating the geostrophic adjustment process under the second-order accuracy difference scheme. However, for higher-order finite-difference schemes, the validity of the above conclusion is still unknown. In this paper, we present a theoretical analysis and a numerical test for shallow water equation under high-order difference schemes. The analysis and test results are as follows. (1) For a low wavenumber, the dispersion of a staggered grid does not change with the accuracy of the difference scheme, while the dispersion of nonstaggered grid is significantly improved, and the dispersion of both grids become very close under the fourth-order scheme. (2) The maximum frequency of nonstaggered grid still exists under high-order difference schemes, and it moves toward a higher wavenumber as the accuracy of the difference scheme increases. The frequency of the staggered grid monotonically increases with the wavenumber and gets closer to the real solution under high-order difference schemes. (3) When the high-frequency noise is removed by explicitly adding a diffusion term, the pros and cops to grid staggering choices diminish with high-order schemes. In general, the nonstaggered grid is an attractive choice for the discretization of the dynamical frame in numerical models under high-order difference scheme.