Speaker：Remi Abgrall (University of Zurich)

Time：2024-7-16, 16:00

Location：Conference Room 105 at Experiment Building at Haiyun Campus

Abstract:

In a series of unpublished papers, P.L. Roe and his students have started to develop a new third order method able to work on triangular unstructured meshes, using a continuous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.