A new scheme for two-way, nesting, quadrilateral grid in an estuarine model

Grid-Nesting is a common method of local refinement when using structured quadrilateral grid in estuarine models. Nevertheless, various issues need to be improved, such as the Courant-Friedrichs-Lewy (CFL) limitations of external gravity wave and information exchange between two-way nesting grids. Based on the material conservation law, a novel scheme with Implicit, Grid-Nesting Elevation Solution (IGNES) and matched Nesting Boundary Flux Conservation Interpolation (NBFCI) was developed in this paper. The unstructured quadrilateral grid, finite-differencing, estuarine and coastal ocean model (UFDECOM) was update to UFDECOM-i. The gravity wave propagation experiment shows that the IGNES can relax the CFL limitations. Compared to traditional i-j two-direction strip refinement, the new scheme has higher computational efficiency. When the root-mean-square-error of elevation and current velocity increases by less than 0.05% and 0.2%, the calculation time is reduced by 40%. When simulating vortex motion, it overcomes the problem of simulation collapse caused by errors in nested boundaries. When simulating material transport, NBFCI scheme has smaller errors at the nesting boundary compared to quadratic interpolation, the high-order spatial interpolation at the middle temporal level (HSMIT) parabolic interpolation, upwind Advection-Equivalent interpolation, and HSIMT Advection-Equivalent interpolation scheme. The simulation results of the severe saltwater intrusion in the Changjiang Estuary in the late summer and early autumn of 2022 demonstrate that the UFDECOM-i with NBFCI and IGNES has higher computational efficiency and accuracy.