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Physics-based preconditioners for ocean simulation. (English) Zbl 1406.86005
Summary: We develop and characterize a physics-based preconditioner for ocean simulation based on barotropic-baroclinic splitting. Physics-based preconditioning is a highly successful approach for multiple time scale problems where an accurate simulation is desired on the dynamical time scale. Our approach is the development of a preconditioning strategy for a fully implicit, fully coupled, second order accurate time integration of the momentum, continuity, temperature, and salinity transport equations and equation of state of ocean dynamics. The nonlinear system is solved via preconditioned Jacobian-free Newton-Krylov, where we reformulate traditional barotropic-baroclinic splitting as a preconditioner. This strategy effectively preconditions the fully coupled three-dimensional vector system by only inverting a scalar, horizontal, two-dimensional system. Furthermore, the desired solution is timestep converged with timesteps on the order of the dynamical time scale. We provide numerical examples to support the study and compare to explicit methods to verify second order convergence and demonstrate algorithmic scalability.
Reviewer: Reviewer (Berlin)

86-08 Computational methods for problems pertaining to geophysics
86A05 Hydrology, hydrography, oceanography
65F08 Preconditioners for iterative methods
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
65F10 Iterative numerical methods for linear systems
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