A new class of higher-order stiffly stable schemes with application to the Navier-Stokes equations
홍영준
129동 406호
0
643
04.19 22:53
| 구분 | 응용수학 |
|---|---|
| 일정 | 2026-04-28(화) 15:30~17:00 |
| 세미나실 | 129동 406호 |
| 강연자 | Jie Shen (Eastern Institute of Technology) |
| 담당교수 | 홍영준 |
| 기타 |
How to construct stable second- and higher-order fully decoupled schemes for the incompressible Navier-Stokes equations has been a long standing open problem. A main issue is that stability regions of usual multistep time discretization decrease as their order of accuracy increase, so they do not possess enough stability to control the higher-order explicit treatment of the pressure in a fully decoupled scheme.
We shall construct a new class of IMEX schemes, by using Taylor expansion at $t_{n+\beta}$ (with $\beta\ge 1$ as a parameter) for updating the solution at $t_{n+1}$, whose stability region increases with $\beta$, thus allowing us to choose $\beta$ according to the stability and accuracy requirement. In particular, by choosing suitable $\beta$, we are able to construct higher-order unconditionally stable (in $H^1$ norm), fully decoupled consistent splitting schemes for the Navier-Stokes equations, and derive uniform optimal error estimates. We shall also present ample numerical results to show the computational advantages of these schemes for some nonlinear parabolic systems, including in particular Navier-Stokes equations.
