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이산화된 Navier-Stokes 방정식의 영역분할법을 위한 병렬 예조건화
최형권,유정열,강성우,Choi, Hyoung-Gwon,Yoo, Jung-Yul,Kang, Sung-Woo 대한기계학회 2003 大韓機械學會論文集B Vol.27 No.6
A finite element code for the numerical solution of the Navier-Stokes equation is parallelized by vertex-oriented domain decomposition. To accelerate the convergence of iterative solvers like conjugate gradient method, parallel block ILU, iterative block ILU, and distributed ILU methods are tested as parallel preconditioners. The effectiveness of the algorithms has been investigated when P1P1 finite element discretization is used for the parallel solution of the Navier-Stokes equation. Two-dimensional and three-dimensional Laplace equations are calculated to estimate the speedup of the preconditioners. Calculation domain is partitioned by one- and multi-dimensional partitioning methods in structured grid and by METIS library in unstructured grid. For the domain-decomposed parallel computation of the Navier-Stokes equation, we have solved three-dimensional lid-driven cavity and natural convection problems in a cube as benchmark problems using a parallelized fractional 4-step finite element method. The speedup for each parallel preconditioning method is to be compared using upto 64 processors.
최소자승법과 Level-set 방법을 이용한 3차원 슬로싱 유동의 수치해석
최형권(Hyoung-gwon Choi) 대한기계학회 2008 대한기계학회 춘추학술대회 Vol.2008 No.11
In the present study, a three-dimensional least square/level set based two-phase flow code was developed for the simulation of three-dimensional sloshing problems using finite element discretization. The present method can be utilized for the analysis of a free surface flow problem in a complex geometry due to the feature of FEM. Since the finite element method is employed for the spatial discretization of governing equations, an unstructured mesh can be naturally adopted for the level set simulation of a free surface flow without an additional load for the code development except that solution methods of the hyperbolic type redistancing and advection equations of the level set function should be devised in order to give a bounded solution on the unstructured mesh. From the numerical experiments of the present study, it is shown that the proposed method is both robust and accurate for the simulation three-dimensional sloshing problems.
Level Set Finite Element Analysis of Flow Fields with Free Surfaces
Hyoung gwon Choi(최형권),Hee won Lee(이희원) 한국유체기계학회 2006 유체기계 연구개발 발표회 논문집 Vol.- No.-
As far as the author knows, few papers have been reported for the level set simulation of a two phase flow based on unstructured background mesh. Almost all existing studies are based on structured mesh using finite difference or finite volume method as spatial discretization. Therefore, the application of the existing level set methods based on structured mesh to a free surface flow problem in a complex geometry is not straightforward. In the present study, a level set based free surface flow code has been developed using finite element discretization, which can be utilized for the analysis of a free surface flow in a complex geometry. Since the finite element method has been employed for the spatial discretization of governing equations, an unstructured mesh can be naturally adopted for the level set simulation of a free surface flow. A solution method of the hyperbolic type redistancing and advection equations of the level set function has been devised in order to give a bounded solution on an unstructured mesh. In this study, some results of the level set simulation based on finite element method for free surface flow problems are discussed and compared with the existing results. It has been shown that the present simulation method based on FEM gives a satisfactory solution with the level set method alone while the other researches based on finite difference/volume method use a combined level-set/volume-of-fluid method(CLSVOF) or solve another equation of the volume conservation constraint in order to circumvent a volume loss/gain problem in a level set simulation.
유체-구조물 상호작용을 위한 유한요소 결합공식화의 예조건화에 대한 연구
최형권(Hyoung-gwon Choi) 대한기계학회 2009 大韓機械學會論文集B Vol.33 No.4
AILU type preconditioners for a two-dimensional combined P2P1 finite element formulation of the interaction of rigid cylinder with incompressible fluid flow have been devised and tested by solving fluidstructure interaction (FSI) problems. The FSI code simulating the interaction of a rigid cylinder with an unsteady flow is based on P2P1 mixed finite element formulation coupled with combined formulation. Four different preconditioners were devised for the two-dimensional combined P2P1 finite element formulation extending the idea of Nam et al., which was proposed for the preconditioning of a P2P1 mixed finite element formulation of the incompressible Navier-Stokes equations. It was found that PC-Ⅲ or PC-Ⅳ among them perform well with respect to computational memory and convergence rate for some bench-mark problems.
Level Set 유한요소해석의 Redistance 방정식의 Dirichlet 경계조건에 대한 연구
최형권(Hyoung-gwon Choi) 대한기계학회 2008 대한기계학회 춘추학술대회 Vol.2008 No.5
The proper imposition of the Dirichlet boundary condition of the redistance equation of level set method is a very important factor for an accurate simulation of multiphase flows, especially for the matter of mass conservation. In this paper, a new method which improves the conventional procedure of the imposition of the Dirichlet boundary condition of the redistance equation of level set method is proposed. The key idea of the proposed method is to correct the level set values of finite elements which an interface line/surface intersects using a direct method. For the numerical solution of the incompressible Navier-Stokes equation PIPI four-step fractional method is employed and least-square method is used for the solution of the advection and redistance equation. Some benchmark problems are solved using the proposed method and compared with the results of the conventional method.
채널 유동에서 점성이 단일 입자 혼합 유동의 suspension 에 미치는 영향
최형권(Hyoung-gwon Choi) 대한기계학회 2009 大韓機械學會論文集B Vol.33 No.3
Suspension of a single solid particle in a channel flow with a constant pressure gradient is studied numerically. The interaction of a circular particle with a surrounding Newtonian fluid is formulated using a combined formulation. Numerical results are presented using two dimensionless variables: the sedimentation Reynolds number and the generalized Froude number. From the present results, it has been shown that a solid particle is suspended at a smaller generalized Froude number as the viscosity of the surrounding fluid increases. The time taken for equilibrium position is found to be smaller as fluid viscosity increases when both : the sedimentation Reynolds number and the generalized Froude number are the same while, at the same situation, the dimensionless time taken for equilibrium position is to be nearly the same regardless of fluid viscosity when a dimensionless time variable is introduced
판으로 나뉘어진 2차원 충류 채널유동에서 동적 유체-구조물 상호작용 수치해석
남궁각,최형권,유정열,Namkoong, Kak,Choi, Hyoung-Gwon,Yoo, Jung-Yul 대한기계학회 2002 大韓機械學會論文集B Vol.26 No.12
In the FSI (Fluid-Structure Interaction) problems, two different governing equations are to be solved together. One is fur the fluid and the other for the structure. Furthermore, a kinematic constraint should be imposed along the boundary between the fluid and the structure. We use the combined formulation, which incorporates both the fluid and structure equations of motion into a single coupled variational equation so that it is not necessary to calculate the fluid force on the surface of structure explicitly when solving the equations of motion of the structure. A two-dimensional channel flow divided by a Bernoulli-Euler beam is considered and the dynamic response of the beam under the influence of channel flow is studied. The Navier-Stokes equations are solved using a P2P1 Galerkin finite element method with ALE (Arbitrary Lagrangian-Eulerian) algorithm. The internal structural damping effect is not considered in this study and numerical results are compared with a previous work fer steady case. In addition to the Reynolds number, two non-dimensional parameters, which govern this fluid-structure system, are proposed. It is found that the larger the dynamic viscosity and density of the fluid are, the larger the damping of the beam is. Also, the added mass is found to be linearly proportional to the density of the fluid.