Abstract:
We develop the semi-Lagrangian algorithm on triangular grids for two-dimensional advection problem. The semi-Lagrangian method is established numerical technique in atmospheric modeling and other physical processes. It allows to achieve the Courant-Friedrichs-Lewy condition without restriction for time step. The method is based on the exact identity of spatial integrals on adjacent time layers. Numerical solution is constructed as a piecewise constant function on neighborhood of each grid node. The proposed method has first order of convergence for smooth solutions. Acknowledgements This work is supported by the Krasnoyarsk Mathematical Center and financed by the Ministry of Science and Higher Education of the Russian Federation in the framework of the establishment and development of regional Centers for Mathematics Research and Education (Agreement No. 075–02–2023–912).
