非笛卡尔网格上粗糙速度场平流方程的离散化

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Quarterly of Applied Mathematics Pub Date : 2023-03-30 DOI:10.1090/qam/1649

Pierre-Emmanuel Jabin, Datong Zhou

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引用次数: 0

摘要

研究了一般非笛卡尔网格和图上平流方程离散化的性质。在非笛卡尔网格上离散的平流方程一直是一个长期的挑战，因为网格的结构可能导致解中的强振荡，即使在其他恒定速度场中也是如此。本文介绍了一种跟踪任意图上粗糙速度场解的振荡的新方法。该方法特别强调了网格在解上传播正则性的一些固有结构条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Discretizing advection equations with rough velocity fields on non-Cartesian grids

We investigate the properties of discretizations of advection equations on non-Cartesian grids and graphs in general. Advection equations discretized on non-Cartesian grids have remained a long-standing challenge as the structure of the grid can lead to strong oscillations in the solution, even for otherwise constant velocity fields. We introduce a new method to track oscillations of the solution for rough velocity fields on any graph. The method in particular highlights some inherent structural conditions on the mesh for propagating regularity on solutions.

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来源期刊

Quarterly of Applied Mathematics 数学-应用数学

CiteScore

1.90

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： The Quarterly of Applied Mathematics contains original papers in applied mathematics which have a close connection with applications. An author index appears in the last issue of each volume. This journal, published quarterly by Brown University with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.