Hermite WENO schemes for hyperbolic conservation laws
科研大讨论系列报告
报告题目(Title)：Hermite WENO schemes for hyperbolic conservation laws
报告人(Speaker)：邱建贤（厦门大学）
地点(Place)：后主楼1124
时间(Time)：2024年3月29日（周五）下午4:00-5:00
邀请人(Inviter)：潘亮
报告摘要
In this presentation, we would give a brief review on a class of high-order weighted essentially non-oscillatory (WENO) schemes which are based on Hermite polynomials and termed HWENO (Hermite WENO) schemes, for solving nonlinear hyperbolic conservation law systems. The con- struction of HWENO schemes is based on a finite volume formulation, Hermite interpolation, and nonlinearly stable Runge-Kutta methods. The idea of the reconstruction in the HWENO schemes comes from the original WENO schemes, however both the function and its first deriva- tive values are evolved in time and used in the reconstruction, while only the function values are evolved and used in the original WENO schemes. Comparing with the original WENO schemes of Liu et al. [J. Comput. Phys. 115 (1994) 200] and Jiang and Shu [J. Comput. Phys. 126 (1996) 202], one major advantage of HWENO schemes is its compactness in the reconstruction. For example, five points are needed in the stencil for a fifth-order WENO (WENO5) reconstruction, while only three points are needed for a fifth-order HWENO (HWENO5) reconstruction in one dimensional case. Numerical results are presented for both one and two dimensional cases to show the efficiency of the schemes.
