Paper Info
Title
Energy Stable and Momentum Conserving Hybrid Finite Element Method for the Incompressible Navier-Stokes Equations
Abstract
A hybrid method for the incompressible Navier-Stokes equations is presented. The method inherits the attractive stabilizing mechanism of upwinded discontinuous Galerkin methods when momentum advection becomes significant, equal-order interpolations can be used for the velocity and pressure fields, and mass can be conserved locally. Using continuous Lagrange multiplier spaces to enforce flux continuity across cell facets, the number of global degrees of freedom is the same as for a continuous Galerkin method on the same mesh. Different from our earlier investigations on the approach for the Navier-Stokes equations, the pressure field in this work is discontinuous across cell boundaries. It is shown that this leads to very good local mass conservation and, for an appropriate choice of finite element spaces, momentum conservation. Also, a new form of the momentum transport terms for the method is constructed such that global energy stability is guaranteed, even in the absence of a pointwise solenoidal velocity field. Mass conservation, momentum conservation, and global energy stability are proved for the time-continuous case and for a fully discrete scheme. The presented analysis results are supported by a range of numerical simulations.
Year
DOI
Venue
2012
10.1137/100818583
SIAM Journal on Scientific Computing
Keywords
DocType
Volume
momentum transport term,incompressible navier-stokes equations,global energy stability,momentum conservation,momentum advection,continuous galerkin method,momentum conserving hybrid finite,upwinded discontinuous galerkin method,hybrid method,energy stable,mass conservation,element method,pressure field,good local mass conservation,finite element,velocity field,finite element method,numerical simulation,discontinuous galerkin method,degree of freedom,galerkin method,lagrange multiplier
Journal
34
Issue
ISSN
Citations 
2
SIAM J. Sci. Comput., 34(2), 2012, A889-A913
10
PageRank 
References 
Authors
0.90
11
2
Name
Order
Citations
PageRank
Robert Jan Labeur1101.24
Garth N. Wells220220.08