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Title: Quadratic finite elements and incompressible viscous flows.

Abstract

Pressure stabilization methods are applied to higher-order velocity finite elements for application to viscous incompressible flows. Both a standard pressure stabilizing Petrov-Galerkin (PSPG) method and a new polynomial pressure projection stabilization (PPPS) method have been implemented and tested for various quadratic elements in two dimensions. A preconditioner based on relaxing the incompressibility constraint is also tested for the iterative solution of saddle point problems arising from mixed Galerkin finite element approximations to the Navier-Stokes equations. The preconditioner is demonstrated for BB stable elements with discontinuous pressure approximations in two and three dimensions.

Authors:
;
Publication Date:
Research Org.:
Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
990988
Report Number(s):
SAND2005-0252J
Journal ID: ISSN 0045-7825; CMMECC; TRN: US201020%%657
DOE Contract Number:  
AC04-94AL85000
Resource Type:
Journal Article
Journal Name:
Proposed for publication in Computer Methods in Applied Mechanics and Engineering.
Additional Journal Information:
Journal Volume: 195; Journal Issue: 13-16; Journal ID: ISSN 0045-7825
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; 97 MATHEMATICAL METHODS AND COMPUTING; APPROXIMATIONS; INCOMPRESSIBLE FLOW; VISCOUS FLOW; FINITE ELEMENT METHOD; ITERATIVE METHODS; NAVIER-STOKES EQUATIONS

Citation Formats

Dohrmann, Clark R, and Gartling, David K. Quadratic finite elements and incompressible viscous flows.. United States: N. p., 2005. Web.
Dohrmann, Clark R, & Gartling, David K. Quadratic finite elements and incompressible viscous flows.. United States.
Dohrmann, Clark R, and Gartling, David K. 2005. "Quadratic finite elements and incompressible viscous flows.". United States.
@article{osti_990988,
title = {Quadratic finite elements and incompressible viscous flows.},
author = {Dohrmann, Clark R and Gartling, David K},
abstractNote = {Pressure stabilization methods are applied to higher-order velocity finite elements for application to viscous incompressible flows. Both a standard pressure stabilizing Petrov-Galerkin (PSPG) method and a new polynomial pressure projection stabilization (PPPS) method have been implemented and tested for various quadratic elements in two dimensions. A preconditioner based on relaxing the incompressibility constraint is also tested for the iterative solution of saddle point problems arising from mixed Galerkin finite element approximations to the Navier-Stokes equations. The preconditioner is demonstrated for BB stable elements with discontinuous pressure approximations in two and three dimensions.},
doi = {},
url = {https://www.osti.gov/biblio/990988}, journal = {Proposed for publication in Computer Methods in Applied Mechanics and Engineering.},
issn = {0045-7825},
number = 13-16,
volume = 195,
place = {United States},
year = {Sat Jan 01 00:00:00 EST 2005},
month = {Sat Jan 01 00:00:00 EST 2005}
}