High-order numerical solutions to the shallow-water equations on the rotated cubed-sphere grid

Stéphane Gaudreault,Martin Charron,Valentin Dallerit,Mayya Tokman

Journal of Computational Physics（2022）

引用 5|浏览8

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摘要

•High-order numerical methods are applied to the shallow-water equations on the sphere.•A space-time tensor formalism is used to express the equations of motion covariantly on the rotated cubed-sphere grid.•The spatial discretization is done with the direct flux reconstruction method.•New multistep exponential propagation iterative methods of orders 4, 5 and 6 are introduced.•Several test cases demonstrate the correct convergence behavior and conservation properties.

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关键词

Geophysical fluid dynamics,Space-time tensors,Direct flux reconstruction,Jacobian-free methods,Exponential integrators

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