Semi-Lagrangian semi-implicit space splitting regional baroclinic atmospheric model

Abstract

A finite difference semi-Lagrangian semi-implicit scheme applied to a adiabatic baroclinic regional model of atmosphere is developed. The full scheme consists of the explicit semi-Lagrangian scheme used to calculate the provisional tendencies of the model variables and the subsequent correction scheme for finding the full tendencies. The former is sufficiently simple but requires using too small time steps and the latter permits increasing the time step up to 1 hour under a horizontal resolution of 75 km but requires solving one 3D elliptic problem. This problem is transformed by vertical decoupling to a set of 2D elliptic problems solved by efficient multigrid methods. To achieve a computationally economic scheme space splitting techniques are applied. First, the Burridge approach is used to correct only the fastest vertical modes, which produce the more rigid restrictions on time step. Then, the Turkel–Zwas horizontal space splitting is applied to the slowest vertical modes to achieve a desired time step without loss of accuracy. The criteria of stability of multilevel fully discretized scheme is derived to demonstrate the possibility of using the increased time steps. The efficiency of proposed variant of semi-Lagrangian semi-implicit scheme is evaluated.