Non-hydrostatic Adiabatic Kernel for HIRLAM

Part III

Semi-implicit Eulerian scheme

Rein Rõõm, Aarne Männik

Abstract

The adiabatic kernel of the nonhydrostatic HIRLAM with the semi-implicit Eulerian integration scheme is presented. The new development supplements the nonhydrostatic Eulerian scheme with a semi-implicit integration option. In this respect, the new model represents a nonhydrostatic extension of the hydrostatic semi-implicit Eulerian HIRLAM. In the anelastic approximation used in the explicit version of the nonhydrostatic HIRLAM, the sound waves are filtered prior to the discretization, and the time-step is limited by the fastest internal buoyancy waves with the phase speeds of 100 m/s approximately. Due to this, the time-step of the explicit model is relatively large (approximately 1 minute at 10 km resolution), and the further time-step enhancement by a semi-implicit scheme is not so dramatic as in an elastic model or in the hydrostatic HIRLAM (where the time-step increase due to transition from the explicit Eulerian to the semi-implicit Eulerian scheme is of the order of two magnitudes). However, approximately a doubling of the time-step is achieved at 10 to 5 km resolutions. It is essential to note that the time-step increase is achieved at no extra computational cost, as the semi-implicit extension uses, in essence, the same basic integration algorithm as the explicit nonhydrostatic scheme. Therefore, the semi-implicit scheme will give rise to the numerical efficiency in comparison with the explicit model, even when the anelastic approximation is used, and consequently, this scheme is worth developing.

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