Local variation based ENO type polynomial reconstruction for high order finite volume methods

：徐正富（美国密歇根理工大学）
：2023-12-17 10:00
：海韵园数理大楼661

报告人：徐正富（美国密歇根理工大学）

时  间：2023年12月17日10:00

地  点：海韵园数理大楼661

内容摘要:

In this talk, we will discuss an ENO type polynomial reconstruction for high order finite volume methods solving hyperbolic conservation laws. Adaptive stencil choosing process was adopted in the traditional ENO method based on calculation and comparison of local divided differences of cell average values for high order finite volume methods. The computed divided differences measure the relative smoothness of each candidate stencil. One can then decide which is the smoothest stencil to choose for polynomial reconstruction. The new stencil selection strategy proposed here will rely on an approximate measurement of local variation computed from the local cell average values and the corresponding reconstructed polynomial values at interfaces. The main motivation is that the reliance on the divided difference of traditional ENO methods makes it very difficult to generalize to multidimensional problems on unstructured meshes. We also show that when the selection is biased toward a central stencil, the loss of accuracy around extrema by the traditional ENO method can be avoided.

个人简介：

Prof. Zhengfu Xu is now a Professor at the Department of Mathematics in Michigan Technological University. He received his B.Sc. and M. Sc in Mathematics from the Department of Mathematics at Peking University. Then he went on to the division of applied mathematics at Brown University for his graduate studies. He got an M.Sc (minor in computer science) and PhD of applied mathematics from Brown University. After his graduation, he worked as the S Chowla research assistant professor in the department of mathematics at Penn State University. Before he moved to the Michigan Technological University, he worked as research assistant professor in the department of mathematics at Michigan State University. His research focuses on high order numerical methods for solving partial differential equation. His interest of research also includes extensive study and application of high order finite difference and finite volume ENO/WENO methods, nonlinear optics, mathematical image processing, computational polymer chemistry.  He has published more than 40 articles in top-ranked international journals, including Math. Comput., SIAM J. Numer. Anal., SIAM J. Sci. Comput., J. Comput. Phys., etc.

 

联系人：邱建贤