求解偏微分方程的时间滤波器方法

张亚兰; 黄鹏展

doi:10.13568/j.cnki.651094.651316.2024.01.14.0002

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求解偏微分方程的时间滤波器方法

更新时间：2026-01-21

- 求解偏微分方程的时间滤波器方法
- Journal of Xinjiang University (Natural Science Edition in Chinese and English) Vol. 42, Issue 1, Pages: 36-47(2025)
- 作者机构：
  
  新疆大学数学与系统科学学院
- 作者简介：
- 基金信息：
- DOI：10.13568/j.cnki.651094.651316.2024.01.14.0002
  CLC： O241.82
- Published：2025
- 稿件说明：
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[1]张亚兰,黄鹏展.求解偏微分方程的时间滤波器方法[J].新疆大学学报(自然科学版中英文),2025,42(01):36-47.
[1]张亚兰,黄鹏展.求解偏微分方程的时间滤波器方法[J].新疆大学学报(自然科学版中英文),2025,42(01):36-47. DOI： 10.13568/j.cnki.651094.651316.2024.01.14.0002.

DOI：10.13568/j.cnki.651094.651316.2024.01.14.0002.

摘要

偏微分方程在计算流体力学领域有着广泛的应用

但大多数的偏微分方程无法直接解得显式解

所以建立一种能高效求解的数值方法是至关重要的.对于数值计算方法来说

精度和有效性是一个算法的核心.时间滤波算法是一种基于复杂系统原始计算代码的数值后处理算法.该方法是在原始数值格式的基础上添加一个简单的时间滤波器来提高时间精度

而不额外增加计算复杂度

因而该方法在流体问题数值求解中得到了广泛运用.梳理了一些基于时间滤波器的数值方法以及时间滤波器在几种方程中的应用.最后

基于时间滤波器

针对Navier-Stokes方程

提出变时间滤波器.

Abstract

Partial differential equations have a wide range of applications in many areas of computational fluid dynamics. However

most of these equations cannot be solved directly. Hence it is crucial to establish numerical methods that can solve them efficiently. For numerical methods

accuracy and effectiveness are the core of an algorithm. The filtering algorithm is a numerical post-processing algorithm based on the original computational code of a complex system. The method is based on adding a simple time filter to the original numerical scheme to improve the time accuracy without additional computational complexity

and is widely used in fluid problems. In this paper

we describe the time filters

some numerical methods based on time filter

and the application of time filters to several equations. Moreover

we design the time variable filter to the Navier-Stokes equations.

关键词

Keywords

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