報告題目：Fifth-order A-WENO schemes based on the path-conservative central-upwind method
報 告 人：楚少帥，南方科技大學深圳國際數學中心 研究學者
報告時間：2023年12月26日09:00---10:00
報告地點：數學樓323
校内聯系人：馬世琪 mashiqi@jlu.edu.cn
報告摘要：We develop fifth-order A-WENO finite-difference schemes based on the path-conservative central-upwind method for nonconservative one- and two-dimensional hyperbolic systems of nonlinear PDEs. The main challenges in development of accurate and robust numerical methods for the studied systems come from the presence of nonconservative products. Semi-discrete second-order finite-volume path-conservative central-upwind (PCCU) schemes recently proposed in Castro Díaz et al. (2019) provide one with a reliable Riemann-problem-solver-free numerical method for nonconservative hyperbolic system. In this paper, we extend the PCCU schemes to the fifth-order of accuracy in the framework of A-WENO finite-difference schemes. We apply the developed schemes to the two-layer shallow water equations. We ensure that the developed schemes are well-balanced in the sense that they are capable of exactly preserving “lake-at-rest” steady states. We illustrate the performance of the new fifth-order schemes on a number of one- and two-dimensional examples, where one can clearly see that the proposed fifth-order schemes clearly outperform their second-order counterparts.
報告人簡介：楚少帥，南方科技大學深圳國際數學中心研究學者。2023年博士畢業于南方科技大學數學系，研究方向為雙曲方程與守恒律。目前在JCP, JSC, CICP等計算數學雜志發表論文10餘篇。
