Dissipation and entropy production of high-order numerical methods for hyperbolic conservation laws

双曲守恒定律高阶数值方法的耗散和熵产生

• 批准号: 391673438
• 负责人: Professor Dr. Thomas Sonar
• 金额: --
• 依托单位: Institut für Partielle Differentialgleichungen
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2017
• 资助国家: 德国
• 起止时间: 2016-12-31 至 2020-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/391673438?language=en
• 关键词: Dissipation; entropy; production; order; numerical

This project is targeted at the investigation of stability and dissipation of high-order numerical methods for hyperbolic balance laws using the concept of nonlinear entropy stability. The entropy rate criterion of Dafermos will be used as a basis for the development and investigation of numerical methods and specially constructed numerical entropy fluxes will be studied regarding their significance in getting information about the properties of numerical solutions.Firstly, Godunov's flux for systems will be investigated. This numerical flux satisfies for scalar conservation laws a variational principle regarding the entropy dissipation. Afterwards, nonoscillatory recovery schemes based on variational entropy principles will be constructed and compared with their classical counterparts. Such variational ideas will be used for known entropy stable schemes and the resulting methods will be investigated regarding their stability properties.Moreover, information gained from specially constructed numerical entropy fluxes will be used to enhance the quality and stability of numerical methods, e.g. to apply and control additional dissipation via artificial viscosity or filtering. Finally, variational ideas will be applied to time discretisations.

本计画的目的是利用非线性熵稳定性的概念，研究双曲型平衡律高阶数值方法的稳定性与耗散性。Dafermos的熵率准则将被用作数值方法的发展和研究的基础，并且专门构造的数值熵通量将被研究它们在获得关于数值解的性质的信息方面的意义。这个数值通量满足标量守恒律的熵耗散的变分原理。之后，基于变分熵原理的非振荡恢复方案将被构造，并与它们的经典对应方案进行比较。这种变分思想将被用于已知的熵稳定的计划和由此产生的方法将调查其稳定性properties.此外，从特别构造的数值熵通量获得的信息将被用来提高数值方法的质量和稳定性，例如，通过人工粘性或过滤应用和控制额外的耗散。最后，变分思想将应用于时间离散化。

项目成果

Error Boundedness of Discontinuous Galerkin Methods with Variable Coefficients

变系数间断伽辽金法的误差有界性

• DOI: 10.1007/s10915-018-00902-1
• 发表时间: 2019
• 期刊: Journal of Scientific Computing
• 影响因子: 2.5
• 作者: P. Öffner;H. Ranocha
• 通讯作者: H. Ranocha

On strong stability of explicit Runge–Kutta methods for nonlinear semibounded operators

非线性半有界算子显式RungeâKutta方法的强稳定性

• DOI: 10.1093/imanum/drz070
• 发表时间: 2020
• 期刊: IMA Journal of Numerical Analysis
• 影响因子: 2.1
• 作者: H. Ranocha

Mimetic properties of difference operators: product and chain rules as for functions of bounded variation and entropy stability of second derivatives

差分算子的拟态性质：二阶导数的有界变分函数和熵稳定性的乘积规则和链规则

• DOI: 10.1007/s10543-018-0736-7
• 发表时间: 2018
• 期刊: BIT Numerical Mathematics
• 影响因子: 1.5
• 作者: H. Ranocha

Using the Dafermos entropy rate criterion in numerical schemes

• DOI: 10.1007/s10543-022-00927-x
• 发表时间: 2022-02
• 期刊: BIT Numerical Mathematics
• 影响因子: 1.5
• 作者: S. Klein