Abstract

SKIBA, Yuri N  and  FILATOV, Denis M. CONSERVATIVE SPLITTING-BASED SCHEMES FOR NUMERICAL SIMULATION OF VORTICES IN THE ATMOSPHERE. INCI [online]. 2006, vol.31, n.1, pp.16-21. ISSN 0378-1844.

A new method for the construction of finite difference schemes for the shallow water equations studied in periodic plane and spherical channels is proposed. The main advantage of the schemes is that they conserve exactly the mass and the total energy of the system. The approach is based on the method of splitting the original operator by coordinates and by physical processes. Thereby, the solution to the original complex problem is reduced to the solution of simple one-dimensional problems. A set of such schemes is proposed, which are either linear or nonlinear, depending on the choice of parameters of the scheme. Unlike existing methods in the field, this approach allows deriving conservative finite difference schemes when the equations are considered to be discrete both in time and in space. Furthermore, the numeric algorithms used to compute the solution are computationally economic, because each scheme is easily implemented by using fast direct methods of linear algebra.

Keywords : Ecuaciones de Aguas Someras ; Esquemas en Diferencias Finitas Conservativos; Método de Separación del Operador ; Simulación de Vórtices .