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Discretizations and solvers for coup...

Vassilev, Danail.

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Discretizations and solvers for coupling Stokes-Darcy flows with transport.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Discretizations and solvers for coupling Stokes-Darcy flows with transport./
Author:	Vassilev, Danail.
Description:	128 p.
Notes:	Source: Dissertation Abstracts International, Volume: 72-01, Section: B, page: .
Contained By:	Dissertation Abstracts International72-01B.
Subject:	Applied Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3435543
ISBN:	9781124342719

Discretizations and solvers for coupling Stokes-Darcy flows with transport.
Vassilev, Danail.

Discretizations and solvers for coupling Stokes-Darcy flows with transport. - 128 p.

Source: Dissertation Abstracts International, Volume: 72-01, Section: B, page: .

Thesis (Ph.D.)--University of Pittsburgh, 2010.

This thesis studies a mathematical model, in which Stokes-Darcy flow system is coupled with a transport equation. The objective is to develop stable and convergent numerical schemes that could be used in environmental applications. Special attention is given to discretization methods that conserve mass locally.

ISBN: 9781124342719Subjects--Topical Terms:

1669109
Applied Mathematics.

Discretizations and solvers for coupling Stokes-Darcy flows with transport.
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020 $a 9781124342719
035 $a (UMI)AAI3435543
035 $a AAI3435543
040 $a UMI $c UMI
100 1 $a Vassilev, Danail. $3 1674963
245 1 0 $a Discretizations and solvers for coupling Stokes-Darcy flows with transport.
300 $a 128 p.
500 $a Source: Dissertation Abstracts International, Volume: 72-01, Section: B, page: .
500 $a Adviser: Ivan Yotov.
502 $a Thesis (Ph.D.)--University of Pittsburgh, 2010.
520 $a This thesis studies a mathematical model, in which Stokes-Darcy flow system is coupled with a transport equation. The objective is to develop stable and convergent numerical schemes that could be used in environmental applications. Special attention is given to discretization methods that conserve mass locally.
520 $a First, we present a global saddle point problem approach, which employs the discontinuous Galerkin method to discretize the Stokes equations and the mimetic finite difference method to discretize the Darcy equation. We show how the numerical scheme can be formulated on general polygonal (polyhedral in three dimensions) meshes if suitable operators mapping from degrees of freedom to functional spaces are constructed. The scheme is analyzed and error estimates are derived. A hybridization technique is used to solve the system effectively. We ran several numerical experiments to verify the theoretical convergence rates and depending on the mesh type we observed superconvergence of the computed solution in the Darcy region.
520 $a Another approach that we use to deal with the flow equations is based on non-overlapping domain decomposition. Domain decomposition enables us to solve the coupled Stokes-Darcy flow problem in parallel by partitioning the computational domain into subdomains, upon which families of coupled local problems of lower complexity are formulated. The coupling of the subdomain problems is removed through an iterative procedure. We investigate the properties of this method and derive estimates for the condition number of the associated algebraic system. Results from computer tests supporting the convergence analysis of the method are provided.
520 $a To discretize the transport equation we use the local discontinuous Galerkin (LDG) method, which can be thought as a discontinuous mixed finite element method, since it approximates both the concentration and the diffusive flux. We develop stability and convergence analysis for the concentration and the diffusive flux in the transport equation. The numerical error is a combination of the LDG discretization error and the error from the discretization of the Stokes-Darcy velocity. Several examples verifying the theory and illustrating the capabilities of the method are presented.
590 $a School code: 0178.
650 4 $a Applied Mathematics. $3 1669109
650 4 $a Mathematics. $3 515831
690 $a 0364
690 $a 0405
710 2 $a University of Pittsburgh. $3 958527
773 0 $t Dissertation Abstracts International $g 72-01B.
790 1 0 $a Yotov, Ivan, $e advisor
790 $a 0178
791 $a Ph.D.
792 $a 2010
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3435543