A multiscale V–P discretization for flow problems

Abstract

This paper gives a comprehensive numerical analysis of a multiscale method for equilibrium Navier Stokes equations. The method includes pressure regularization and eddy viscosity stabilizations both acting only on the finest scales. This method allows for equal order velocity-pressure spaces as well as the linear constant pair and the usual (P k , P k−1 ) pair. We show the method is optimal in a natural energy norm for all of these pairs of spaces, and provide guidance in choosing the regularization parameters.keywords : Navier Stokes, multiscale, subgrid eddy viscosity, pressure regularization, equal order interpolations AMS subject classifications: 65N12 76D05 65N15 2

A subgrid stabilization finite element method for incompressible magnetohydrodynamics

“…Remark 3.1 Note that the unconditional stabilities of G n H and n H are guaranteed through Equations (27) and (28) and the result of Lemma 3.2.…”

“…The technique has been used successfully for the NSE [8,18,21,27], natural convection problems [5], and the transport equations [10]. The purpose of this work is to extend these ideas for use with MHD simulations, which are more complex systems than the above listed problems, but share the problem of inability to resolve fine scales on practical meshes.…”