Semi-Lagrangian approximations of the transfer operator in divergent form
-
Vladimir V. Shaydurov
and
Viktoriya S. Petrakova
Abstract
The paper demonstrates two approaches to constructing monotonic difference schemes for the transfer equation in divergent form from the family of semi-Lagrangian methods: Eulerian–Lagrangian and Lagrangian–Eulerian. Within each approach, a monotonic conservative difference scheme is proposed. It is shown that within the framework of the Lagrangian–Eulerian approach, based on the use of curvilinear grids formed by the characteristics of the approximated transfer operator, it is possible to construct monotonic difference schemes of second order accuracy.
Funding statement: The work was 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. 075-02-2024-1378).
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- Monte Carlo simulation of polarized lidar returns for atmospheric clouds sensing
- Stochastic simulation of exciton transport in semiconductor heterostructures
- Semi-Lagrangian approximations of the transfer operator in divergent form
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Articles in the same Issue
- Frontmatter
- Simulation algorithms for stationary sequences with distributions in the form of a mixture of Gaussian distributions
- Monte Carlo simulation of polarized lidar returns for atmospheric clouds sensing
- Stochastic simulation of exciton transport in semiconductor heterostructures
- Semi-Lagrangian approximations of the transfer operator in divergent form
- Numerical modelling of large elasto-plastic multi-material deformations on Eulerian grids
