High-Order Consistent Splitting Schemes for the Navier–Stokes Equations and Related Models

发布时间：2026-06-02 作者：浏览次数：

Speaker:	黄富铿	DateTime:	2026年6月8日（周一）上午9:30-10:15
Brief Introduction to Speaker: 黄富铿，宁波东方理工大学		Place:	文科楼401
Abstract:Consistent splitting schemes for the Navier–Stokes equations decouple the computations of pressure and velocity. However, to date, only the first-order version has been proven to be unconditionally stable for the time-dependent Stokes equations. In this talk, we develop a new class of consistent splitting schemes of orders two to four for the Navier–Stokes equations, derived via Taylor expansions at time $t_{n+\beta}$ with $\beta \geq 1$. By selecting appropriate values of $\beta$, we obtain, for the first time, unconditionally stable and fully decoupled schemes of orders two to four for both velocity and pressure, together with rigorous optimal error estimates. Furthermore, the proposed schemes can be readily extended to other models related to the Navier–Stokes equations, including magnetohydrodynamics (MHD), Cahn–Hilliard–Navier–Stokes (CHNS), and Navier-Stokes–Darcy systems.