数苑经纬讲坛（104）：Efficient numerical methods for stationary statistical behavior of some geophysical fluid models
来源：
发布时间：2026-07-03
报告时间：- 2026年6月29日 （周一）上午10:00-11:30
- 报告地点：
- 国交二号楼315会议室
- 报告人：
- 韩道志
- 报告人单位：
- 美国纽约州立大学水牛城分校
- 邀请人：
- 杨欢欢
- 摘要：
- We introduce a highly efficient, second-order time-marching scheme for nonlinear geophysical fluid models, designed to accurately approximate invariant measures—that is, the stationary statistical properties (or “climate”) of the underlying dynamical system. Beyond second-order accuracy in time, the scheme is particularly well suited for long-time simulations due to two key features: (i) it requires solving only a fixed symmetric positive-definite linear system with constant coefficients at each step, and (ii) it guarantees long-time stability, producing uniformly bounded solutions in time for any bounded external forcing, regardless of initial data. We rigorously prove convergence of both global attractors and invariant measures of the discrete system to those of the continuous model in the vanishing time-step limit. Applications to the Lorentz 96 model, the 2D Navier-Stokes and the continuously stratified QG model will be discussed.
韩道志（美国纽约州立大学水牛城分校）
韩道志是美国纽约州立大学水牛城分校数学系副教授。主要研究方向为流体力学中的非线性偏微分方程，以及相关的数值计算和分析。他的研究工作获得美国国家科学基金会和Simons基金会的资助。在Journal of Differential Equations, Journal of Computational Physics, Numerische Mathematik，SIAM 系列等刊物发表论文多篇。
