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• W2971048986 abstract "Abstract A parallel and fully implicit method is developed for numerical simulations of the thermal convection of an incompressible fluid in a rotating spherical shell. The method is based on a pseudo-compressibility approach with dual time stepping in order to tackle with the numerical difficulty of the solenoidal condition in the incompressible Navier-Stokes equations. The numerical solution of the nonlinear governing equations is based on the method of lines, whereby the partial differential equations are transformed into ordinary differential equations by a suitable spatial discretization. A second-order cell-centered finite volume discretization based on a collocated cubed-sphere grid is used here. In order to relax the time step limit and accurately integrate the semi-discrete nonlinear ordinary differential equations in time, we employ a second-order explicit-first-step, single-diagonal-coefficient, diagonally implicit Runge–Kutta (ESDIRK) method with adaptive time stepping. The nonlinear algebraic system arising at each pseudo-time step is solved by a Newton–Krylov–Schwarz algorithm to achieve good load balance on modern supercomputers. The numerical results are in good agreement with the benchmark solutions and more accurate than those obtained with a fractional step approach in our previous research. Large-scale tests on the Tianhe-2 supercomputer indicate that the fully implicit solver can achieve good parallel scalabilities in both strong and weak senses." @default.
• W2971048986 created "2019-09-05" @default.
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• W2971048986 date "2019-10-01" @default.
• W2971048986 modified "2023-09-26" @default.
• W2971048986 title "Parallel and fully implicit simulations of the thermal convection in the Earth’s outer core" @default.
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• W2971048986 doi "https://doi.org/10.1016/j.compfluid.2019.104278" @default.
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