Stable split time stepping schemes for large-scale ocean modeling
Journal of Computational Physics
High order one-step monotonicity-preserving schemes for unsteady compressible flow calculations
Journal of Computational Physics
A high-order finite volume remapping scheme for nonuniform grids: The piecewise quartic method (PQM)
Journal of Computational Physics
Hi-index | 31.45 |
A hierarchy of high-order regridding-remapping schemes for use in generalized vertical coordinate ocean models is presented. The proposed regridding-remapping framework is successfully used in a series of idealized one-dimensional numerical experiments as well as two-dimensional internal wave and overflow test cases. The model is capable of replicating z-, sigma- and isopycnal-coordinate results, among others. Particular emphasis is placed on the design of a continuous isopycnal framework, which is a more general alternative to the layered isopycnal paradigm. Continuous isopycnal coordinates use target interface densities to define layers. In contrast to traditional layered isopycnal models, in which along-layer density gradients vanish, general coordinate approaches must deal with extra terms. For example, the calculation of pressure gradient force is more complicated and must be evaluated carefully. High-order reconstructions within boundary cells are crucial for obtaining sensible results and for reducing spurious diffusion near boundaries. Vertical advection is implicitly embedded in the remapping step and directly benefits from high-order schemes. Volume and all tracers are conserved to machine precision, which is a necessary ingredient for long-term ocean climate modeling. This hybrid vertical coordinate model provides the framework to easily capture the impact of different coordinate systems on dynamics.