用于解决边界层问题的空间指数近似指数时差法

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Numerical Methods for Partial Differential Equations Pub Date : 2024-08-26 DOI:10.1002/num.23145

Liyong Zhu, Xinwei Wang, Tianzheng Lu

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引用次数: 0

摘要

本研究提出了一种高效稳定的指数时差法，用于解决边界层问题。通过将指数时差方案与基于指数边界层近似的空间直接非连续伽勒金离散化相结合，所提出的算法不仅可以容许较大的时间步长，而且即使在边界层相当粗糙的空间网格上也能提供良好的空间近似。数值方案的一些能量稳定性得到了严格推导。数值示例说明了算法的准确性、稳定性和效率。

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Exponential time difference methods with spatial exponential approximations for solving boundary layer problems

In this work, an efficient and stable exponential time difference method is presented for solving boundary layer problems. By combining exponential time difference schemes with spatial direct discontinuous Galerkin discretization based on exponential boundary layer approximations, the proposed algorithm not only may admit large time step sizes but also could provide good spatial approximations even if on rather coarse spatial grids in the boundary layer. Some energy stabilities of the numerical scheme are rigorously derived. Numerical examples illustrate the accuracy, stability and efficiency of the algorithm.

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来源期刊

Numerical Methods for Partial Differential Equations 数学-应用数学

CiteScore

7.20

自引率

2.60%

发文量

审稿时长

9 months

期刊介绍： An international journal that aims to cover research into the development and analysis of new methods for the numerical solution of partial differential equations, it is intended that it be readily readable by and directed to a broad spectrum of researchers into numerical methods for partial differential equations throughout science and engineering. The numerical methods and techniques themselves are emphasized rather than the specific applications. The Journal seeks to be interdisciplinary, while retaining the common thread of applied numerical analysis.