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Title: On Raviart-Thomas and VMS formulations for flow in heterogeneous materials.

Abstract

It is well known that the continuous Galerkin method (in its standard form) is not locally conservative, yet many stabilized methods are constructed by augmenting the standard Galerkin weak form. In particular, the Variational Multiscale (VMS) method has achieved popularity for combating numerical instabilities that arise for mixed formulations that do not otherwise satisfy the LBB condition. Among alternative methods that satisfy local and global conservation, many employ Raviart-Thomas function spaces. The lowest order Raviart-Thomas finite element formulation (RT0) consists of evaluating fluxes over the midpoint of element edges and constant pressures within the element. Although the RT0 element poses many advantages, it has only been shown viable for triangular or tetrahedral elements (quadrilateral variants of this method do not pass the patch test). In the context of heterogenous materials, both of these methods have been used to model the mixed form of the Darcy equation. This work aims, in a comparative fashion, to evaluate the strengths and weaknesses of either approach for modeling Darcy flow for problems with highly varying material permeabilities and predominantly open flow boundary conditions. Such problems include carbon sequestration and enhanced oil recovery simulations for which the far-field boundary is typically described with some typemore » of pressure boundary condition. We intend to show the degree to which the VMS formulation violates local mass conservation for these types of problems and compare the performance of the VMS and RT0 methods at boundaries between disparate permeabilities.« less

Authors:
Publication Date:
Research Org.:
Sandia National Laboratories
Sponsoring Org.:
USDOE
OSTI Identifier:
1030379
Report Number(s):
SAND2010-7910C
TRN: US201124%%164
DOE Contract Number:  
AC04-94AL85000
Resource Type:
Conference
Resource Relation:
Conference: Proposed for presentation at the ASME 2010 International Mechanical Engineering Congress and Exhibition held November 15-18, 2010 in Vancouver, Canada.
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; 42 ENGINEERING; BOUNDARY CONDITIONS; CARBON SEQUESTRATION; MECHANICAL ENGINEERING; PERFORMANCE; SIMULATION

Citation Formats

Turner, Daniel Zack. On Raviart-Thomas and VMS formulations for flow in heterogeneous materials.. United States: N. p., 2010. Web.
Turner, Daniel Zack. On Raviart-Thomas and VMS formulations for flow in heterogeneous materials.. United States.
Turner, Daniel Zack. Mon . "On Raviart-Thomas and VMS formulations for flow in heterogeneous materials.". United States.
@article{osti_1030379,
title = {On Raviart-Thomas and VMS formulations for flow in heterogeneous materials.},
author = {Turner, Daniel Zack},
abstractNote = {It is well known that the continuous Galerkin method (in its standard form) is not locally conservative, yet many stabilized methods are constructed by augmenting the standard Galerkin weak form. In particular, the Variational Multiscale (VMS) method has achieved popularity for combating numerical instabilities that arise for mixed formulations that do not otherwise satisfy the LBB condition. Among alternative methods that satisfy local and global conservation, many employ Raviart-Thomas function spaces. The lowest order Raviart-Thomas finite element formulation (RT0) consists of evaluating fluxes over the midpoint of element edges and constant pressures within the element. Although the RT0 element poses many advantages, it has only been shown viable for triangular or tetrahedral elements (quadrilateral variants of this method do not pass the patch test). In the context of heterogenous materials, both of these methods have been used to model the mixed form of the Darcy equation. This work aims, in a comparative fashion, to evaluate the strengths and weaknesses of either approach for modeling Darcy flow for problems with highly varying material permeabilities and predominantly open flow boundary conditions. Such problems include carbon sequestration and enhanced oil recovery simulations for which the far-field boundary is typically described with some type of pressure boundary condition. We intend to show the degree to which the VMS formulation violates local mass conservation for these types of problems and compare the performance of the VMS and RT0 methods at boundaries between disparate permeabilities.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2010},
month = {11}
}

Conference:
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