发散形式转移算子的半拉格朗日近似值

Pub Date : 2024-06-01 DOI:10.1515/rnam-2024-0015
V. Shaydurov, Viktoriya S. Petrakova
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引用次数: 0

摘要

本文展示了从半拉格朗日方法系列中为发散形式的传递方程构建单调差分方案的两种方法:欧拉-拉格朗日法和拉格朗日-欧拉法。每种方法都提出了一种单调保守差分方案。研究表明,在拉格朗日-欧拉方法的框架内,基于使用由近似转移算子的特征形成的曲线网格,可以构建二阶精度的单调差分方案。
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Semi-Lagrangian approximations of the transfer operator in divergent form
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.
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