报告题目：Derivative-based finite-volume MR-HWENO scheme for steady-state problems
时 间：2024年9月26日（星期四）15:00
地 点：科研楼18号楼1102
主 办：数学与统计学院, 福建省分析数学及应用重点实验室、福建省应用数学中心（福建师范大学）、福建师范大学数学研究中心
参加对象：感兴趣的老师和研究生
报告摘要：In this presentation, we further extend the derivative-based finite-volume multi-resolution Hermite weighted essentially non-oscillatory (MR-HWENO) scheme proposed in our previous article (Li, Shu and Qiu, J. Comput. Phys., 446:110653, 2021) to simulate the steady-state problem. When dealing with the steady-state problem, the process of updating and reconstructing the function values is similar to the previous scheme, but the treatment of the derivative values is changed. To be more specific, instead of evolving in time, in the sense of cell averages, the scheme uses the derivative at the current time step and the function at the next time step to reconstruct the derivative at the next time step by direct linear interpolation. There are two advantages for this approach: the first is its high efficiency, when handling the derivative, neither the update on time nor the calculation of nonlinear weights is required; in the meantime, the CFL number can still be taken up to 0.6 as in the original scheme; the second is its strong convergence, the corresponding average residual can quickly converge to machine accuracy, thus obtaining the desired steady-state solution. One- and two-dimensional numerical experiments are given to verify the high efficiency and strong convergence of the proposed MR-HWENO scheme for the steady-state problems.
报告人简介：邱建贤，厦门大学数学科学学院闽江学者、特聘教授。主要从事计算流体力学及微分方程数值解法的研究工作，在间断Galerkin（DG）、加权本质无振荡（WENO）数值方法的研究及其应用方面取得了一些重要成果，已发表论文一百多篇。主持国家自然科学基金重点项目和联合基金重点支持项目各一项, 参与欧盟第六框架特别研究项目, 是项目组中唯一非欧盟的成员，多次应邀在国际会议上作大会报告。获2020年度高等学校科学研究优秀成果奖（科学技术）--自然科学奖二等奖。