求解热传导问题中不可接近边界上热通量的差分法

IF 0.58 Q3 Engineering

Journal of Applied and Industrial Mathematics Pub Date : 2023-11-04 DOI:10.1134/S1990478923030183

S. B. Sorokin

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引用次数: 0

摘要

考虑了热方程的延拓问题。确定不可接近边界上的热流可以归结为一个反问题。采用隐式差分格式对反问题进行数值求解。在每个时间步长，用经济直接法计算椭圆方程差分模拟的可达边界上的热通量。所提出的算法大大扩展了正在解决的问题的范围，并可用于创建能够实时确定不可测量的非均匀结构部件上的热流的设备，例如，由各种材料制成的管道内径上的热流。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

A Difference Method for Calculating the Heat Flux on an Inaccessible Boundary in a Heat Conduction Problem

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A Difference Method for Calculating the Heat Flux on an Inaccessible Boundary in a Heat Conduction Problem

The continuation problem for the heat equation is considered. Determining the heat flux on an inaccessible boundary reduces to an inverse problem. An implicit difference scheme is used for the numerical solution of the inverse problem. At each time step, the heat flux on the inaccessible boundary is calculated for the difference analog of the elliptic equation by an economical direct method. The proposed algorithm substantially expands the range of problems being solved and can be used to create devices capable of real-time determination of the heat flux on parts of inhomogeneous structures inaccessible for measurements, for example, on the inner radius of pipes made of various materials.

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来源期刊

Journal of Applied and Industrial Mathematics Engineering-Industrial and Manufacturing Engineering

CiteScore

1.00

自引率

0.00%

发文量

期刊介绍： Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.