A semi-implicit barotropic mode solver for the MPAS-Ocean

Monday, December 9, 2019 - 08:45
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A semi-implicit barotropic mode solver for an oceanic model branch of the Model for Prediction Across Scales (MPAS) has been implemented as a competitor to the existing explicit subcycling scheme to allow faster simulation while not sacrificing accuracy. Combinations of a semi-implicit formulation using the Crank-Nicolson method for the barotropic mode and a finite volume horizontal discretization reveal that this nonlinear system is positive definite and symmetric. To solve the nonlinear system as a linear system, sea surface height inside the divergence operator is replaced by a lagged value from the previous iteration. We implement the s-step conjugate gradient method, which has only one global synchronization per iteration to solve the system. To accelerate convergence, a block-Jacobi preconditioner constructed from the linear system of the barotropic mode, which has the smallest condition number when reordering of the global matrix among the several options for preconditioners, is applied to the system. Evaluated with several numerical test cases that have a range of horizontal resolutions, the system is solved within 15-20 iterations using a 10-10 tolerance. Compared to the existing scheme, the semi-implicit scheme shows better parallel scalability and computational efficiency. Using 14,440 cores for 1.4 million cells, parallel scalability and the wall-clock time for the semi-implicit scheme are 53% higher and 27% faster than those of the explicit subcycling scheme, respectively. This study is still underway so some numerical features may be further improved in the areas of load balancing and preconditioning.

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