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분리/통합 유한요소법을 이용한 비압축성 Navier-Stokes 방정식의 해법에 대한 연구
조명환(Myung H. Cho),최형권(Hyoung G. Choi),유정열(Jung Y. Yoo) 대한기계학회 2005 대한기계학회 춘추학술대회 Vol.2005 No.5
Numerical algorithms of the incompressible Navier-Stokes equations using P1P1 splitting and P2P1 integrated finite element methods are presented. P1P1 allocates velocity and pressure at the same node, while P2P1 interpolates both variables by linear basis function with velocity allocated at two times finer grid than pressure. For comparison of the elapsed time and accuracy of the two methods, they have been applied to the well-known benchmark problems. The three cases chosen are the two-dimensional steady and unsteady flow around a fixed cylinder, decaying vortex problem to check spatial accuracy and impinging slot jet problem.
비압축성 2 상 유동 해석을 위한 CLSVOF 방법에 관한 수치적 연구
조명환(Myung H. Cho),최형권(Hyoung G. Choi),유정열(Jung Y. Yoo) 대한기계학회 2007 대한기계학회 춘추학술대회 Vol.2007 No.10
We present a coupled level set and volume-of-fluid (CLSVOF) method for incompressible two-phase flows. This method combines some of the advantages of the volume-of-fluid method with the level set method. The CLSVOF method can not only calculate an interfacial curvature accurately but also can meet mass conservation well. The CLSVOF method is applied to numerical simulation of broken dam problem and cavity filling problem. The results are in good agreement with the experimental results of Martin and Moyce.
P2P1 유한요소 공식을 이용한 비압축성 Navier-Stokes 방정식의 반-분리 해법에 관한 연구
조명환(Myung H. Cho),최형권(Hyoung G. Choi),유정열(Jung Y. Yoo),박재인(Jae I. Park) 한국유체기계학회 2006 유체기계 연구개발 발표회 논문집 Vol.- No.-
The conventional segregated finite element formulation produces a small and simple matrix at each step than in an integrated formulation. And the memory and cost requirements of computations are significantly reduced because the pressure equation for the mass conservation of the Navier-Stokes equations is constructed only once if the mesh is fixed. However, segregated finite element formulation solves Poisson equation of elliptic type so that it always needs a pressure boundary condition along a boundary even when physical information on pressure is not provided. On the other hand, the conventional integrated finite element formulation in which the governing equations are simultaneously treated has an advantage over a segregated formulation in the sense that it can give a more robust convergence behavior because all variables are implicitly combined. Further it needs a very small number of iterations to achieve convergence. However, the saddle-point-type matrix (SPTM) in the integrated formulation is assembled and preconditioned every time step, so that it needs a large memory and computing time. Therefore, we newly proposed the P2P1 semi-segregation formulation. In order to utilize the fact that the pressure equation is assembled and preconditioned only once in the segregated finite element formulation, a fixed symmetric SPTM has been obtained for the continuity constraint of the present semi-segregation finite element formulation. The momentum equation in the semi-segregation finite element formulation will be separated from the continuity equation so that the saddle-point-type matrix is assembled and preconditioned only once during the whole computation as long as the mesh does not change. For a comparison of the CPU time, accuracy and condition number between the two methods, they have been applied to the well-known benchmark problem. It is shown that the newly proposed semi-segregation finite element formulation performs better than the conventional integrated finite element formulation in terms of the computation time.
P2P1 유한요소를 이용한 비압축성 Navier-Stokes 방정식 해법들의 행렬 특성
조명환(Myung H. Cho),최형권(Hyoung G. Choi),유정열(Jung Y. Yoo) 한국전산유체공학회 2009 한국전산유체공학회 학술대회논문집 Vol.2009 No.4
Numerical algorithms for solving the incompressible Navier-Stokes equations using P2P1 finite element are compared regarding the eigenvalues of matrices. P2P 1 element allocates pressure at vertex nodes and velocity at both vertex and mid nodes. Therefore, compared to the P1P1 element, the number of pressure variables in the P2P1 element decreases to 1/4 in the case of two-dimensional problems and to 1/8 in the three-dimensional problems. Fully-implicit-integrated, semi-implicit- integrated and semi-segregated finite element formulations using P2P1 element are compared in terms of elapsed time, accuracy and eigenvlue distribution (condition number). For the comparison, they have been applied to the well-known benchmark problems. That is, the two-dimensional unsteady flows around a fixed circular cylinder and decaying vortex flow are adopted to check spatial accuracy.