Enforcing energy, helicity and strong mass conservation in finite element computations for incompressible Navier–Stokes simulations

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摘要

We study a finite element scheme for the 3D Navier–Stokes equations (NSE) that globally conserves energy and helicity and, through the use of Scott–Vogelius elements, enforces pointwise the solenoidal constraints for velocity and vorticity. A complete numerical analysis is given, including proofs for conservation laws, unconditional stability and optimal convergence. We also show the method can be efficiently computed by exploiting a connection between this method, its associated penalty method, and the method arising from using grad-div stabilized Taylor–Hood elements. Finally, we give numerical examples which verify the theory and demonstrate the effectiveness of the scheme.

论文关键词:Navier–Stokes equations,Helicity conservation,Strong mass conservation,Scott–Vogelius elements

论文评审过程:Available online 30 June 2011.

论文官网地址:https://doi.org/10.1016/j.amc.2011.05.111