Approximation of non linear hyperbolic problems by globally continuous representation on polygons via virtual finite element techniques

：Remi Abgrall（瑞士苏黎世大学）
：2024-07-16 16:00
：海韵园实验楼105报告厅

报告人：Remi Abgrall（瑞士苏黎世大学）

时  间：2024年7月16日16:00

地  点：海韵园实验楼105报告厅

内容摘要:

In a series of unpublished papers, P.L. Roe and his students have started to develop a new third order method able to work on triangular unstructured meshes, using a continuous representation of data and no Riemann solvers. The degrees of freedom are the vertices of the elements and the mid points of the edges, as well as the average value of the conserved variables. The integration in time is done by a variant of the method of characteristics that allow to evaluate the flux at several sub-time steps. This explains the name ”Active Flux”. This idea has then been developed by Roe and others, a very un-complete list of references can be found at [1, 2, 3, 4, 5]. In this talk, I will make a personal review of this method using the material of [6, 7], show how to develop higher than third order schemes on triangles following [8]. Then I will explain the connection with the approximation tools provided by the Virtual Finite elements spaces and show several numerical results that confirms the stability and the accuracy of the methods. Some perspective will be drawn. This is a joint work with Yongle Liu (U. Zurich), Jianfang Lin (U. Zurich), W. Boscheri (U. Chambery, France) and W. Barsukow (U. Bordeaux, France).

References

[1] T.A. Eyman and P.L. Roe. 20 th AIAA Computationa Fluid Dynamics Conference, 2011.

[2] C. Helzel, D. Kerkmann, and L. Scandurra. J. Sci. Comput., 80(3):35–61, 2019.

[3] W. Barsukow. J. Sci. Comput., 86(1):Paper No. 3, 34, 2021.

[4] E. Chudzik, C. Helzel, M. Lukacova-Medvidova. J. Sci. Comput., 99(1):39, 2024.

[5] W. Barsukow, J. Hohm, C. Klingenberg, P. L. Roe. J. Sci. Comput., 81(1):594-622, 2019.

[6] R. Abgrall. Commun. Appl. Math. Comput., 5(1):370–402, 2023.

[7] R. Abgrall and W. Barsukow. ESAIM, Math. Model. Numer. Anal., 57(2):991–1027, 2023.

[8] R. Abgrall, J. Lin, and Y. Liu. Arxiv 2312.11.

个人简介：

Remi Abgrall，瑞士苏黎世大学（University of Zurich）教授。Remi Abgrall长期从事计算流体力学、守恒定律的数值分析、多相流和Hamilton-Jacobi方程等方面的研究以及它们在气体动力学和材料科学等领域的应用。是《Journal of Computational Physics》的现任主编，2014年国际数学大会45分钟报告人，工业与应用数学学会会士（SIAM fellow），法国大学研究所的名誉会员。曾获法国科学院颁发的布莱兹·帕斯卡奖和欧洲研究理事会的高级CORDIS资助。

 

联系人：赵状