期刊名称：Journal of Advances in Modeling Earth Systems
电子版ISSN：1942-2466
出版年度：2021
卷号：13
期号：4
页码：e2020MS002238
DOI：10.1029/2020MS002238
出版社：John Wiley & Sons, Ltd.
摘要：A scalable semi‐implicit barotropic mode solver for the ocean component of the model for prediction across scales has been implemented as a competitor to an existing explicit‐subcycling scheme to allow faster and more stable simulations while not sacrificing accuracy. The semi‐implicit solver adopts the pipelined preconditioned bi‐conjugate gradient stabilization algorithm as an iterative solver in conjunction with the restricted additive Schwarz preconditioner that accelerates the convergence rate of the iterative solver. The preconditioner is constructed from a linearized barotropic system that also reorders the system for optimal performance, while the semi‐implicit solver deals with the fully nonlinear barotropic system that requires reassembly of the coefficient matrix for every time step. Several numerical experiments, from simple one‐dimensional tests to three‐dimensional real‐world tests, demonstrate that the semi‐implicit solver has almost the same accuracy and better parallel scalability compared with the existing scheme while allowing faster and more stable simulations. The semi‐implicit solver accelerates the barotropic mode up to 2.9 times faster than the existing scheme on 16,320 processors, leading to an overall runtime speedup of 1.9. Plain Language Abstract The fastest gravity‐induced oceanic waves, known as the barotropic mode, travel with a vertically uniform motion. Simulating these fast two‐dimensional waves while also capturing the slower three‐dimensional waves is a major challenge in ocean modeling. In the Model for Prediction Across Scales‐Ocean, this is currently addressed with an explicit‐subcycling method that resolves the fast‐timescale waves by taking many small time steps, which requires additional work to match up to a longer time step for the longer‐timescale waves. In this paper, we implemented an alternative method that solves the barotropic system implicitly with the same time step as for the longer timescale waves. This implicit method solves a self‐consistent matrix equation for the future state by continuously improving estimates of that future state and converging to this consistent solution iteratively. To increase computational performance, we constructed a particular form of a preconditioner, which is a simplification of the full problem, and this significantly decreases the number of iterations. Numerical experiments demonstrate that this newly implemented method has maintained almost the same accuracy while providing better computational performance and more stable simulations compared with the current method.
