A semi-implicit time-splitting scheme for a regional nonhydrostatic atmospheric model

In this study a semi-implicit finite difference scheme is proposed for the nonhydrostatic atmospheric model based on the Euler equations for compressible ideal gas. Fast acoustic and gravity waves are approximated implicitly, while slow inertial processes are treated explicitly. Such time approximation requires the solution of 3D elliptic equations at each time step. An efficient elliptic solver is based on decoupling in the vertical direction and splitting in the horizontal directions. Stability analysis of the scheme shows that the time step is restricted only by the maximum wind speed and does not depend on the propagation velocity of the fast waves. A specific approximation of the advection terms keeping the second order of accuracy and possessing extended stability is employed to achieve larger time steps. The performed numerical experiments show the computational efficiency of the designed scheme and accuracy of the predicted atmospheric fields.