(A) conservative covolume method for the navier-stokes equations = 나비어 스톡스 방정식의 보존적인 유한영역법

We introduce a new covolume method for approximating the stationary Navier-Stokes equations and analyze its convergence. There are two ways to introduce the covolume approximation to the Navier-Stokes equations. One uses the divergence (or conservative) form of Navier-Stokes equations which we call the conservative covolume method, the another uses its original form. Primal and dual grids are used in the covolume method. Test functions are piecewise constant on the dual grid. In the covolume method the momentum equation is integrated over the dual element and the continuity equation over the primal element. The finite element space for the velocity is the Crouzeix-Raviart space for triangles or nonconforming $P_1$ element consisting of piecewise linear functions and the finite element space for the pressure is the space of piecewise constant functions on the primal elements, whereas the test function space for the velocity consists of certain piecewise constant functions on the dual elements. An abstract theory based on the results of approximation for branches of nonsingular solutions of nonlinear problems gives us an opportunity to study of the convergence of the covolume method for the Navier-Stokes equations. Efficiency of the proposed method has been tested on a number of test problems. Numerical results using a simple Picard type of iteration for solving the discrete Navier-Stokes equations are provided.
Advisors
Kwak, Do-Youngresearcher곽도영researcher
Publisher
한국과학기술원
Issue Date
2009
Identifier
327744/325007  / 020054504
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수리과학과, 2009. 8., [ iii, 42 p. ]

Keywords

Covolume method; Navier-Stokes equations; 유한 체적법; 나비어 스톡스 방정식; Covolume method; Navier-Stokes equations; 유한 체적법; 나비어 스톡스 방정식

URI
http://hdl.handle.net/10203/41924
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=327744&flag=t
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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