求解声子-玻色模型的改进Rusanov格式

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Kamel Mohamed, M. Abdelrahman
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引用次数: 2

摘要

摘要本文考虑固体低温下的一维热传导模型,即声子-玻色模型。非线性模型由能量密度e和热流Q守恒方程组成,其中∣Q∣< e。我们给出了一类简单而精确的有限体积格式,用于动脉热流的数值模拟。该方案由预测步和校正步组成,预测步包含一个控制方案数值扩散的参数,该参数利用极限理论和黎曼不变量进行调制,校正步恢复平衡守恒方程;该格式可以在不依赖黎曼问题求解器的情况下计算出与解的实际状态相对应的数值通量,因此可以在流量变化较大的区域将其转换为1阶,在流量规律的区域将其转换为2阶。数值测试用例证明了所提出的有限体积格式(改进的Rusanov)的高分辨率,并证实了它能够提供强激波流型下热流的精确模拟。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The modified Rusanov scheme for solving the phonon-Bose model
Abstract This paper considers the one-dimensional model of heat conduction in solids at low temperature, the so called phonon-Bose model. The nonlinear model consists of a conservation equation for the energy density e and the heat flux Q with ∣Q∣ < e. We present a simple and accurate class of finite volume schemes for numerical simulation of heat flow in arteries. This scheme consists of predictor and corrector steps, the predictor step contains a parameter of control of the numerical diffusion of the scheme, which modulate by using limiter theory and Riemann invariant, the corrector step recovers the balance conservation equation, the scheme can compute the numerical flux corresponding the real state of solution without relying on Riemann problem solvers and it can thus be turned to order 1 in the regions where the flow has a strong variation and to order 2 in the regions where the flow is regular. The numerical test cases demonstrate high resolution of the proposed finite volume scheme (modified Rusanov) and confirm its capability to provide accurate simulations for heat flow under flow regimes with strong shocks.
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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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