Тип публикации: доклад, тезисы доклада, статья из сборника материалов конференций
Конференция: 13th International Conference on Mesh Methods for Boundary-Value Problems and Applications, 2020
Год издания: 2022
Идентификатор DOI: 10.1007/978-3-030-87809-2_41
Ключевые слова: advection equation, approximation, convergence, finite volume method, gauss-ostrogradsky theorem
Аннотация: Two finite volume schemes for two-dimensional advection equation are compared. First one is based on Gauss-Ostrogradsky theorem for volume bounded by a small rectangle at upper time level, four sides formed by characteristic trajectories issued out backward in time from boundary of this rectangle, and curvilinear quadrangle carved Показать полностьюby these trajectories at the previous time level. The curvilinear quadrangle at the previous time level is approximated by straight-sided quadrangle. The solution is sought in the class of piecewise constant functions on a rectangular grid. The substantiation of the first order of approximation and the convergence for the obtained grid problem is carried out. In the second scheme, two-dimensional advection operator is decomposed in two one-dimensional operators. The justifying the approximation and the convergence for this scheme is obtained by a simple generalization of these properties for one-dimensional discrete operators. Comparison of algorithmic realization of these schemes demonstrates the different properties. The first one is more complicated for assembling but is more appropriate for implementation to the problems with high velocities. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Журнал: Lecture Notes in Computational Science and Engineering
Выпуск журнала: Vol. 141
Номера страниц: 545-561
ISSN журнала: 14397358
Издатель: Springer Science and Business Media Deutschland GmbH