Finite volume and finite volume element methods for nonsymmetric problems /
Mathematical models of many physical processes are described with elliptic boundary value problems. An interesting and still not well understood is th metric problems. Important examples are steady-state convection-do Navier-Stokes flows with small viscosity. Our goal in this dissertate and study...
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| Format: | Thesis Book |
| Language: | English |
| Published: |
[Place of publication not identified] :
[publisher not identified] ;
1996.
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| Subjects: | |
| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=743273571&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | Mathematical models of many physical processes are described with elliptic boundary value problems. An interesting and still not well understood is th metric problems. Important examples are steady-state convection-do Navier-Stokes flows with small viscosity. Our goal in this dissertate and study stable numerical approximations of some nonsymmetric bo lems that preserve the important characteristics of the continuous pro mass conservation and monotonicity. The standard finite element and finite difference methods for con problems are stable only for sufficiently small mesh sizes. On Vor scribed cell-centered finite volume meshes we develop three upwin schemes: upwind, modified upwind and Il'in's. All of the considered s mass conservative, unconditionally stable, and satisfy the discrete m We show that the upwind scheme has first order of accuracy. All are second order accurate in the discrete H'-norm. We also provide utilizing a discrete variant of the Aubin-Nitsche trick. The finite volume element method is another conservative discretization technique for elliptic partial differential equations. We develop a theory for both diffusion dominated and convection dominated problems on 3-D tetrahedral meshes. Upwind approximations are applied for the discretization of the saturation equation in the total velocity model of two-phase flow in porous media. The linearization strategy is proposed and tested for some model problems. |
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| Item Description: | Vita. "Major Subject: Mathematics". |
| Physical Description: | xii, 186 leaves : illustrations ; 28 cm. Issued also on microfiche from University Microfilms Inc. |
| Bibliography: | Includes bibliographical references. |