Тип публикации: доклад, тезисы доклада, статья из сборника материалов конференций
Конференция: 13th International Hybrid Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2021
Год издания: 2022
Идентификатор DOI: 10.1063/5.0100835
Аннотация: We present the semi-Lagrangian approximation of transfer operator for three-dimensional convection-diffusion problem with corresponding initial and boundary conditions. This problem describes, for instance, a transfer of a substance with diffusion. To construct numerical method, we decompose operator of this equation into two partsПоказать полностью. The first one is the transfer operator. The second part is the elliptic diffusion terms. To approximate the first part, we use conservative semi-Lagrangian approximation connecting two integrals of solution at neighboring time levels. To compute integral at the previous time level, we approximate integral domain by 48 tetrahedrons and interpolate solution by trilinear functions. The second part is approximated by conventional finite differences. Finally, we combine approximations of two parts to get a system of linear equations at each time level. Matrix of this system at each time level is the symmetric M-matrix. The proposed approximation has the first-order convergence that is confirmed by computational experiments. © 2022 Author(s).
Журнал: AIP Conference Proceedings
Выпуск журнала: Vol. 2522
Номера страниц: 110010
ISSN журнала: 0094243X
Издатель: American Institute of Physics Inc.