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学术报告:A New Hydrostatic Reconstruction Scheme For Shallow Water Equations Based on Subcell Reconstructions

发布时间:2017年06月12日 浏览次数:发布者:mathky

报告人:陈国贤副教授

  武汉大学

报告题目:A New Hydrostatic Reconstruction Scheme For Shallow Water Equations Based on Subcell Reconstructions

报告时间: 2017616日下午14:30

报告地点:海韵实验楼108

内容摘要:A key difficulty in the analysis and numerical approximation of the shallow water equations is the non-conservative product of measures due to the gravitational force acting on a sloped bottom. Solutions may be non-unique, and numerical schemes are not only consistent discretizations of the shallow water equations, but they also make a decision how to model the physics. Our derivation is based on a subcell reconstruction using infinitesimal singular layers at the cell boundaries, as inspired by [Noelle, Xing, Shu, JCP 2007]. One key step is to separate the singular measures. Another aspect is the reconstruction of the solution variables in the singular layers. We study three reconstructions. The first leads to the well-known scheme of [Audusse, Bristeau, Bouchut, Klein, Perthame, SISC 2004], which introduces the hydrostatic reconstruction. The second is a modification proposed in [Morales, Castro, Pares, AMC 2013], which analyzes if a wave has enough energy to overcome a step. The third is our new scheme, and borrows its structure from the wet-dry front. For a number of cases discussed in recent years, where water runs down a hill, Audusse’s scheme converges slowly or fails. Morales’ scheme gives a visible improvement. Both schemes are clearly outperformed by our new scheme.

报告人简介:陈国贤博士,男,武汉大学副教授。陈国贤于2008年从北京大学数学科学学院获得博士学位,同年前往香港科技大学大学从事博士后研究,于2010年转到武汉大学工作至今。期间2012年和2013年在德国亚琛工业大学得到DFG项目资助从事博士后研究,并于2013年底在武汉大学获得副教授职称。陈国贤博士的研究方向是计算流体力学,其在广义黎曼问题方法,移动网格方法有一定研究,并将这些方法在空气动力学,多分量流、水动力学方面的应用,尤其是在对于具有源项的双曲守恒律方程的数值格式设计有一定的建树。

学院联系人:吴聪敏副教授

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