Conservative Semi-Lagrangian Numerical Algorithm with Decomposition of Integration Domain into Tetrahedrons for Three-Dimensional Advection Problem
A conservative semi-Lagrangian method is developed in order to solve three-dimensional linear advection equation. It based on balance equation in integral form. Main feature of proposed method consists in way of computation of integral at lower time level. To compute integral, we decompose a domain of integration into several tetrahedrons and approximate integrand by trilinear function.
KeywordsSemi-Lagrangian method Advection equation Decomposition of integration domain Local conservation low
The reported study was funded by Russian Foundation for Basic Research, Government of Krasnoyarsk Territory, Krasnoyarsk Regional Fund of Science to research project No. 18-41-243006.
- 1.Wiin-Nielson, A.: On the application of trajectory methods in numerical forecasting. Tellus 11, 180–186 (1959)Google Scholar
- 5.Andreeva, E., Vyatkin, A., Shaidurov, V.: The semi-Lagrangian approximation in the finite element method for Navier-Stokes equations for a viscous incompressible fluid. In: AIP Conference Proceedings, vol. 1611 (2014). https://doi.org/10.1063/1.4893794
- 13.Vyatkin, A.: A semi-Lagrangian algorithm based on the integral transformation for the three-dimensional advection problem. In: AIP Conference Proceedings, vol. 1684, p. 090012 (2015). https://doi.org/10.1063/1.4934337