Abstract
This paper proposes the combination of matrix exponential method with the semi-Lagrangian approach for the time integration of shallow water equations on the sphere. The second order accuracy of the developed scheme is shown. Exponential semi-Lagrangian scheme in the combination with spatial approximation on the cubed-sphere grid is verified using the standard test problems for shallow water models. The developed scheme is as good as the conventional semi-implicit semi-Lagrangian scheme in accuracy of slowly varying flow component reproduction and significantly better in the reproduction of the fast inertia-gravity waves. The accuracy of inertia-gravity waves reproduction is close to that of the explicit time-integration scheme. The computational efficiency of the proposed exponential semi-Lagrangian scheme is somewhat lower than the efficiency of semi-implicit semi-Lagrangian scheme, but significantly higher than the efficiency of explicit, semi-implicit, and exponential Eulerian schemes.
Funding statement: The work was carried out at Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences with support of the Russian Science Foundation grant No. 19-71-00160
Acknowledgment
The authors are grateful to Mikhail Tolstykh and Rostyslav Fadeev (INM RAS) for inspiring collaboration, Andrey Glazunov (INM RAS) for the comments on the paper draft. Authors thank Prof. Janusz Pudykiewicz (Environment Canada) for productive discussions.
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