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Numerical simulation of cavity flow by using conforming and nonconforming finite elements : 순응 및 비순응 유한요소를 이용한 공동 구조에서의 유체 유동 수치 해석
DC Field | Value | Language |
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dc.contributor.advisor | 신동우 | - |
dc.contributor.author | 임록택 | - |
dc.date.accessioned | 2017-07-14T06:06:07Z | - |
dc.date.available | 2017-07-14T06:06:07Z | - |
dc.date.issued | 2014-08 | - |
dc.identifier.other | 000000021294 | - |
dc.identifier.uri | https://hdl.handle.net/10371/125439 | - |
dc.description | 학위논문 (박사)-- 서울대학교 대학원 : 협동과정 계산과학전공, 2014. 8. 신동우. | - |
dc.description.abstract | This thesis presents a numerical method for solving the incompressible flow in a square cavity without smoothing the corner singularities. Since nonconforming finite element method can avoid vertex degree of freedom, the values at the upper corners of the cavity are not required to solve the problem. By taking this advantage it is possible to compute accurate numerical solution of the cavity flow without any modification of the problem. The stable nonconforming P1-P0 pair used to solve the incompressible flow problem. DSSY finite elements are added to elements which are on the top corners in the cavity to obtain a more accurate approximation of the boundary condition. Numerical solutions by using conforming finite element are computed for the purposes of comparison. The numerical results are compared with those in the literature and show good agreement. Numerical results computed by using the stable nonconforming P1-P0 pair show excellent accuracy. | - |
dc.description.tableofcontents | Contents
Abstract i Chapter 1 Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Model equations . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Chapter 2 Preliminaries 8 2.1 Finite element discretization . . . . . . . . . . . . . . . . . . . . 8 2.2 The stable nonconforming P1-P0 element pair . . . . . . . . . . 10 2.2.1 The P1-nonconforming quadrilateral element . . . . . . 10 2.2.2 The piecewise constant element . . . . . . . . . . . . . . 12 2.2.3 The stable cheapest finite element pair . . . . . . . . . . 13 Chapter 3 Numerical methods for the discretized Navier-Stokes problems 14 3.1 Iterative solvers . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.1.1 Krylov subspace methods . . . . . . . . . . . . . . . . . 19 3.1.2 Uzawa method . . . . . . . . . . . . . . . . . . . . . . . 22 3.2 Preconditiong . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.2.1 Algebraic multigrid preconditioner . . . . . . . . . . . . 25 3.2.2 Block preconditioners for saddle point problems . . . . . 30 3.3 Test problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.3.1 Algebraic multigrid preconditioner . . . . . . . . . . . . 35 3.3.2 The stationary Stokes problem . . . . . . . . . . . . . . 37 Chapter 4 Numerical simulation of lid driven cavity flow 39 4.1 Lid driven square cavity flow problem . . . . . . . . . . . . . . 39 4.2 Indicators for accuracy . . . . . . . . . . . . . . . . . . . . . . . 41 4.3 Implementation of the stable P1 NC-P0 element . . . . . . . . . . 43 4.4 Numerical simulation . . . . . . . . . . . . . . . . . . . . . . . . 46 Chapter 5 Conclusion 85 국문초록 93 감사의 글 94 | - |
dc.format | application/pdf | - |
dc.format.extent | 3580978 bytes | - |
dc.format.medium | application/pdf | - |
dc.language.iso | en | - |
dc.publisher | 서울대학교 대학원 | - |
dc.subject | conforming finite element method | - |
dc.subject | nonconforming finite element method | - |
dc.subject | stable nonconforming P1-P0 pair | - |
dc.subject | DSSY finite element | - |
dc.subject | the incompressible Navier-Stokes equations | - |
dc.subject | lid driven cavity problem | - |
dc.subject.ddc | 004 | - |
dc.title | Numerical simulation of cavity flow by using conforming and nonconforming finite elements | - |
dc.title.alternative | 순응 및 비순응 유한요소를 이용한 공동 구조에서의 유체 유동 수치 해석 | - |
dc.type | Thesis | - |
dc.description.degree | Doctor | - |
dc.citation.pages | x,94 | - |
dc.contributor.affiliation | 자연과학대학 협동과정 계산과학전공 | - |
dc.date.awarded | 2014-08 | - |
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