报告题目：On L^2-dissipativity of linearized finite-difference schemes with a regularization for the gas dynamics equations

主 讲 人：Timofey A. Lomonosov副教授（俄罗斯国立高等经济大学）

报告邀请人：李树光 副教授

报 告 时间：2025年04月30日下午15:30-17:30

报告地点：数理楼 224

报告摘要：LExplicit two-level difference schemes on staggered meshes are studied for two well-known regularizations of 1D barotropic gas dynamics equations, including schemes with discretization in x with the property of total energy dissipation. The criteria for L2-dissipativity in the Cauchy problem are derived for their linearizations on a constant solution with zero background velocity. The criteria for schemes on nonstaggered and staggered meshes are compared. The case of 1D Navier-Stokes equations without an artificial viscosity coefficient is also considered. For one of their regularizations, the maximum time step is guaranteed by the choice of the regularization parameter, where and are the background sound speed and kinematic viscosity; this choice is independent of the meshes. To analyze the case of 1D Navier-Stokes-Cahn-Hilliard equations, the criteria are derived and tested for the L2-dissipativity and stability of an explicit difference scheme for a nonstationary equation of the 4th order in x with a second order term in x. The obtained criteria can be useful in calculating flows at low Mach numbers..

个人简历：Timofey A. Lomonosov是俄罗斯高等经济大学副教授，物理数学科学副博士，毕业于俄罗斯高等经济大学。历任俄罗斯高等经济大学助教、讲师、副教授、高级研究员等。Timofey A. Lomonosov副教授主要从事计算数学和偏微分方程数值解领域的研究，特别是对双曲型方程和可压缩纳维-斯托克斯方程，提出了一系列行之有效的数值计算方法。目前，已发表了40余篇高水平学术文章。