论文信息 - Two stable POD-based approximations to the Navier–Stokes equations

Two stable POD-based approximations to the Navier–Stokes equations

Abstract.The governing equations of viscous flows, the Navier–Stokes equations, are approximated by means of a low order model based on proper orthogonal decomposition (POD). Numerical evidence and analysis of simplified models show that the resulting time-wise semidiscretization is only marginally stable. Here, two methods providing additional stabilization are described: the first is based on a Lax–Wendroff type artificial diffusion term, while the second is a reinterpretation of POD in the frame of the finite element functional least square method.

Jean-Antoine Désidéri | Stéphane Lanteri | Alain Dervieux | Angelo Iollo

[1] T. Hughes,et al. A new finite element formulation for computational fluid dynamics: I. Symmetric forms of the compressible Euler and Navier—Stokes equations and the second law of thermodynamics , 1986 .

[2] L. Sirovich. Turbulence and the dynamics of coherent structures. I. Coherent structures , 1987 .

[3] Angelo Iollo. Remarks on the Approximation of the Euler Equations by a Low Order Model , 1997 .