不连续系数守恒方程的一种预测-校正格式

IF 0.5 Q4 MULTIDISCIPLINARY SCIENCES

Journal of Mathematical and Fundamental Sciences Pub Date : 2020-12-31 DOI:10.5614/J.MATH.FUND.SCI.2020.52.3.6

Nasrin Okhovati, M. Izadi

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引用次数: 4

摘要

本文提出了一种明确的预测-校正有限差分格式，用于数值求解各种物理模型问题(如交通流和多孔介质中的两相流)中具有不连续通量函数的一维守恒律。该方法基于二阶MacCormack有限差分格式，通过对一阶格式的修正得到求解。结果表明，当应用于不连续问题时，均匀网格在网格间距上的收敛阶是二次的。为了说明所提出的格式的一些性质，给出了应用于线性和非线性问题的数值结果。

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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A Predictor-Corrector Scheme for Conservation Equations with Discontinuous Coefficients

In this paper we propose an explicit predictor-corrector finite difference scheme to numerically solve one-dimensional conservation laws with discontinuous flux function appearing in various physical model problems, such as traffic flow and two-phase flow in porous media. The proposed method is based on the second-order MacCormack finite difference scheme and the solution is obtained by correcting first-order schemes. It is shown that the order of convergence is quadratic in the grid spacing for uniform grids when applied to problems with discontinuity. To illustrate some properties of the proposed scheme, numerical results applied to linear as well as non-linear problems are presented.

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来源期刊

Journal of Mathematical and Fundamental Sciences MULTIDISCIPLINARY SCIENCES-

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

24 weeks

期刊介绍： Journal of Mathematical and Fundamental Sciences welcomes full research articles in the area of Mathematics and Natural Sciences from the following subject areas: Astronomy, Chemistry, Earth Sciences (Geodesy, Geology, Geophysics, Oceanography, Meteorology), Life Sciences (Agriculture, Biochemistry, Biology, Health Sciences, Medical Sciences, Pharmacy), Mathematics, Physics, and Statistics. New submissions of mathematics articles starting in January 2020 are required to focus on applied mathematics with real relevance to the field of natural sciences. Authors are invited to submit articles that have not been published previously and are not under consideration elsewhere.