Name
Title | ||
|---|---|---|
Unconditional long-time stability of a velocity-vorticity method for the 2D Navier-Stokes equations. |
Abstract | ||
|---|---|---|
We prove unconditional long-time stability for a particular velocity---vorticity discretization of the 2D Navier---Stokes equations. The scheme begins with a formulation that uses the Lamb vector to couple the usual velocity---pressure system to the vorticity dynamics equation, and then discretizes with the finite element method in space and implicit---explicit BDF2 in time, with the vorticity equation decoupling at each time step. We prove the method's vorticity and velocity are both long-time stable in the $$L^2$$L2 and $$H^1$$H1 norms, without any timestep restriction. Moreover, our analysis avoids the use of Gronwall-type estimates, which leads us to stability bounds with only polynomial (instead of exponential) dependence on the Reynolds number. Numerical experiments are given that demonstrate the effectiveness of the method. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1007/s00211-016-0794-1 | Numerische Mathematik |
Keywords | Field | DocType |
65M12, 65M60, 76D05 | Discretization,Vorticity,Reynolds number,Exponential function,Polynomial,Mathematical analysis,Vorticity equation,Finite element method,Mathematics,Navier–Stokes equations | Journal |
Volume | Issue | ISSN |
135 | 1 | 0945-3245 |
Citations | PageRank | References |
1 | 0.36 | 6 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Timo Heister | 1 | 111 | 11.73 |
| Maxim A. Olshanskii | 2 | 326 | 42.23 |
| Leo G. Rebholz | 3 | 141 | 24.08 |