Two versions of the semi-implicit scheme using alternating directions implicit (ADI) method and Robert's approach with a multigrid (MG) method are presented. Experiments with a regional baroclinic model using 11 levels for the vertical discretization and 75 km step on horizontal grids with 97x97 and 93x101 points are carried out. The 24-hours forecasts quality does not depend on the model version. The MG method permits to reduce the computational time cost about 14% in comparison with Robert's method using successive over-relaxations. Under a choice of equal time steps Robert's MG method is less efficient than the ADI method. But usage of the maximum time steps allowed by the numerical stability condition of each version reveals an advantage of the MG version. Absence of the splitting permits to use the multigrid methods in frame of semi-implicit semi-lagrangian schemes with increased time step without loss of accuracy.
Atmospheric baroclinic model; Numerical weather prediction; Semi-implicit schemes; Multigrid methods; Alternating directions implicit methods
