【计算与应用讨论班】:An energy- and helicity-conserving enriched Galerkin method for the incompressible Navier-Stokes equations

Speaker：张倩（吉林大学，教授）

Time：5月29日14：00-15：00

Place：海纳苑2幢312

Abstract：In the ideal limit and in the absence of external forces, the incompressible Navier–Stokes equations preserve fundamental invariants, including kinetic energy and helicity. From a numerical perspective, failure to respect these invariants may reduce the physical reliability of long-time simulations of three-dimensional flows. However, numerical methods that simultaneously preserve kinetic energy and helicity remain relatively limited; many existing approaches are computationally expensive, require nonlinear solvers, or are applicable only under restrictive boundary conditions.

In this talk, I will present an efficient enriched Galerkin method that preserves both invariants. The method enriches a first-order continuous Galerkin velocity space with the lowest-order Raviart–Thomas space and uses a piecewise-constant pressure approximation. The enrichment corrects the normal component of the continuous Galerkin velocity field, yields an inf-sup stable velocity–pressure discretization, and retains the same number of global degrees of freedom as the classical Bernardi–Raugel element. Together with a carefully designed rotational-form discretization of the convective term, this formulation leads to a fully nonlinear Crank–Nicolson scheme and two linearized variants. All three schemes exactly preserve discrete kinetic energy and helicity in the inviscid limit, and each Picard iteration step of the nonlinear scheme preserves the invariants. I will also present numerical examples demonstrating the accuracy and structure-preserving performance of the proposed method.

Speaker Introduction：张倩，吉林大学数学学院教授、博士生导师，国家级青年人才入选者。2015年本科毕业于吉林大学数学学院，2018年于中国工程物理研究院获得硕士学位，2021年在美国韦恩州立大学获得博士学位。2021年至2025年在美国密歇根理工大学担任终身教职轨道助理教授。2025年全职回国加入吉林大学数学学院，任教授、博士生导师。

张倩的研究方向为偏微分方程数值解，主要从事有限元方法的设计与分析，重点关注不可压流动、线弹性及电磁场等模型的结构保持数值离散。相关成果发表于SIAM J. Numer. Anal.、SIAM J. Sci. Comput.、Comput. Methods Appl. Mech. Eng.、Numer. Math.、Math. Comp、IMA J. Numer. Anal. 等计算数学领域的重要国际期刊。

Contact Person：李雨文（liyuwen@zju.edu.cn）