报告题目 (Title)：High-order alternative finite difference WENO (A-WENO) schemes and their applications (高阶交替有限差分WENO (A-WENO)格式及其应用)
报告人 (Speaker)：Chi-Wang Shu 教授（美国布朗大学）
报告时间 (Time)：2025年6月20日(周五) 9:30-11:30
报告地点 (Place)：校本部GJ303
邀请人(Inviter)：李常品、蔡敏
报告摘要：The weighted essentially non-oscillatory (WENO) finite difference schemes are popular high order numerical methods for solving hyperbolic conservation laws, balance laws and related equations. Comparing with finite volume WENO schemes, finite difference schemes have a dimension by dimension feature and are much cheaper in computational cost for multi-dimensional problems. Most finite difference WENO solvers are based on the Shu-Osher lemma, converting the design of numerical flux in a conservative finite difference scheme to that of the one-dimensional finite volume reconstruction. This approach has the advantage of simplicity and easiness in coding, as the same finite volume reconstruction routine can be used in the finite difference code. For this reason, the original approach in the Shu-Osher 1988 JCP paper, which is based on WENO interpolation rather than on WENO reconstruction, had largely been forgotten until 2013, when Jiang, Shu and Zhang revived this "alternative formulation" and used it to obtain more effective WENO schemes with Lax-Wendroff time discretization and for free-stream preserving. Later referred to as alternative WENO, or A-WENO, this approach has recently been explored to yield several interesting results, including effective finite difference A-WENO schemes for compressible two-medium flows, local characteristic decomposition free high order finite difference A-WENO schemes for hyperbolic systems endowed with a coordinate system of Riemann invariants, and a high-order well-balanced A-WENO method with the exact conservation property for certain systems of hyperbolic balance laws. In this talk we will survey the A-WENO schemes and their recent applications.