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数学学院、所2023年系列学术活动(第140场):楚少帅 南方科技大学深圳国际数学中心

发表于: 2023-12-15   点击: 

报告题目:Fifth-order A-WENO schemes based on the path-conservative central-upwind method

报 告 人:楚少帅,南方科技大学深圳国际数学中心 研究学者

报告时间:2023年12月26日09:00---10:00

报告地点:数学楼323

校内联系人:马世琪 mashiqi@jlu.edu.cn


报告摘要: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.


报告人简介:楚少帅,南方科技大学深圳国际数学中心研究学者。2023年博士毕业于南方科技大学数学系,研究方向为双曲方程与守恒律。目前在JCP, JSC, CICP等计算数学杂志发表论文10余篇。