• 제목/요약/키워드: Unstructured grid, matrix solver

검색결과 12건 처리시간 0.02초

비정렬 혼합 격자에서 내재적 방법을 이용한 비압축성 유동해석 (Implicit Incompressible flow solver on Unstructured Hybrid grids)

  • 김종태;김용모;맹주성
    • 한국전산유체공학회지
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    • 제3권2호
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    • pp.17-26
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    • 1998
  • The three-dimensional incompressible Navier-Stokes equations have been solved by a node-centered finite volume method with unstructured hybrid grids. The pressure-velocity coupling is handled by the artificial compressibility algorithm and convective fluxes are obtained by Roe's flux difference splitting scheme with linear reconstruction of the solutions. Euler implicit method with Jacobi matrix solver is used for the time-integration. The viscous terms are discretised in a manner to handle any kind of grids such as tetragedra, prisms, pyramids, hexahedra, or mixed-element grid. Inviscid bump flow is solved to check the accuracy of high order convective flux discretisation. And viscous flows around a circular cylinder and a sphere are studied to show the efficiency and accuracy of the solver.

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Newton-Krylov Method for Compressible Euler Equations on Unstructured Grids

  • Kim Sungho;Kwon Jang Hyuk
    • 한국전산유체공학회:학술대회논문집
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    • 한국전산유체공학회 1998년도 추계 학술대회논문집
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    • pp.153-159
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    • 1998
  • The Newton-Krylov method on the unstructured grid flow solver using the cell-centered spatial discretization oi compressible Euler equations is presented. This flow solver uses the reconstructed primitive variables to get the higher order solutions. To get the quadratic convergence of Newton method with this solver, the careful linearization of face flux is performed with the reconstructed flow variables. The GMRES method is used to solve large sparse matrix and to improve the performance ILU preconditioner is adopted and vectorized with level scheduling algorithm. To get the quadratic convergence with the higher order schemes and to reduce the memory storage. the matrix-free implementation and Barth's matrix-vector method are implemented and compared with the traditional matrix-vector method. The convergence and computing times are compared with each other.

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On the artificially-upstream flux splitting method

  • Sun M.;Takayama K.
    • 한국전산유체공학회:학술대회논문집
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    • 한국전산유체공학회 2003년도 The Fifth Asian Computational Fluid Dynamics Conference
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    • pp.156-157
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    • 2003
  • A simple method is proposed to split the flux vector of the Euler equations by introducing two artificial wave speeds. The direction of wave propagation can be adjusted by these two wave speeds. This idea greatly simplifies the upwinding, and leads to a new family of upwind schemes. Numerical flux function for multi-dimensional Euler equations is formulated for any grid system, structured or unstructured. A remarkable simplicity of the scheme is that it successfully achieves one-sided approximation for all waves without recourse to any matrix operation. Moreover, its accuracy is comparable with the exact Riemann solver. For 1-D Euler equations, the scheme actually surpasses the exact solver in avoiding expansion shocks without any additional entropy fix. The scheme can exactly resolve stationary contact discontinuities, and it is also freed of the carbuncle problem in multi­dimensional computations.

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비정렬격자 SIMPLE 알고리즘기반 이상유동 수치해석 기법 (NUMERICAL METHOD FOR TWO-PHASE FLOW ANALYSIS USING SIMPLE-ALGORITHM ON AN UNSTRUCTURED MESH)

  • 김종태;박익규;조형규;김경두;정재준
    • 한국전산유체공학회지
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    • 제13권4호
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    • pp.86-95
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    • 2008
  • For analyses of multi-phase flows in a water-cooled nuclear power plant, a three-dimensional SIMPLE-algorithm based hydrodynamic solver CUPID-S has been developed. As governing equations, it adopts a two-fluid three-field model for the two-phase flows. The three fields represent a continuous liquid, a dispersed droplets, and a vapour field. The governing equations are discretized by a finite volume method on an unstructured grid to handle the geometrical complexity of the nuclear reactors. The phasic momentum equations are coupled and solved with a sparse block Gauss-Seidel matrix solver to increase a numerical stability. The pressure correction equation derived by summing the phasic volume fraction equations is applied on the unstructured mesh in the context of a cell-centered co-located scheme. This paper presents the numerical method and the preliminary results of the calculations.

비정렬격자 SIMPLE 알고리즘기반 이상유동 수치해석 기법 (NUMERICAL METHOD FOR TWO-PHASE FLOW ANALYSIS USING SIMPLE-ALGORITHM ON AN UNSTRUCTURED MESH)

  • 김종태;박익규;조형규;김경두;정재준
    • 한국전산유체공학회:학술대회논문집
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    • 한국전산유체공학회 2008년도 학술대회
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    • pp.71-78
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    • 2008
  • For analyses of multi-phase flows in a water-cooled nuclear power plant, a three-dimensional SIMPLE-algorithm based hydrodynamic solver CUPID-S has been developed. As governing equations, it adopts a two-fluid three-field model for the two-phase flows. The three fields represent a continuous liquid, a dispersed droplets, and a vapour field. The governing equations are discretized by a finite volume method on an unstructured grid to handle the geometrical complexity of the nuclear reactors. The phasic momentum equations are coupled and solved with a sparse block Gauss-Seidel matrix solver to increase a numerical stability. The pressure correction equation derived by summing the phasic volume fraction equations is applied on the unstructured mesh in the context of a cell-centered co-located scheme. This paper presents the numerical method and the preliminary results of the calculations.

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비정렬격자 SIMPLE 알고리즘기반 이상유동 수치해석 기법 (NUMERICAL METHOD FOR TWO-PHASE FLOW ANALYSIS USING SIMPLE-ALGORITHM ON AN UNSTRUCTURED MESH)

  • 김종태;박익규;조형규;김경두;정재준
    • 한국전산유체공학회:학술대회논문집
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    • 한국전산유체공학회 2008년 추계학술대회논문집
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    • pp.71-78
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    • 2008
  • For analyses of multi-phase flows in a water-cooled nuclear power plant, a three-dimensional SIMPLE-algorithm based hydrodynamic solver CUPID-S has been developed. As governing equations, it adopts a two-fluid three-field model for the two-phase flows. The three fields represent a continuous liquid, a dispersed droplets, and a vapour field. The governing equations are discretized by a finite volume method on an unstructured grid to handle the geometrical complexity of the nuclear reactors. The phasic momentum equations are coupled and solved with a sparse block Gauss-Seidel matrix solver to increase a numerical stability. The pressure correction equation derived by summing the phasic volume fraction equations is applied on the unstructured mesh in the context of a cell-centered co-located scheme. This paper presents the numerical method and the preliminary results of the calculations.

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비정렬격자계를 사용하는 3차원 유동해석코드 개발 (I) - 수치해석방법 - (Development of 3-D Flow Analysis Code Using Unstructured Grid System (I) - Numerical Method -)

  • 김종태;명현국
    • 대한기계학회논문집B
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    • 제29권9호
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    • pp.1049-1056
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    • 2005
  • A conservative pressure-based finite-volume numerical method has been developed for computing flow and heat transfer by using an unstructured grid system. The method admits arbitrary convex polyhedra. Care is taken in the discretization and solution procedures to avoid formulations that are cell-shape-specific. A collocated variable arrangement formulation is developed, i.e. all dependent variables such as pressure and velocity are stored at cell centers. Gradients required for the evaluation of diffusion fluxes and for second-order-accurate convective operators are found by a novel second-order accurate spatial discretization. Momentum interpolation is used to prevent pressure checkerboarding and the SIMPLE algorithm is used for pressure-velocity coupling. The resulting set of coupled nonlinear algebraic equations is solved by employing a segregated approach, leading to a decoupled set of linear algebraic equations fer each dependent variable, with a sparse diagonally dominant coefficient matrix. These equations are solved by an iterative preconditioned conjugate gradient solver which retains the sparsity of the coefficient matrix, thus achieving a very efficient use of computer resources.

건물의 3차원 구조체에 대한 전열해석 프로그램 개발 중 서로 다른 열전도율을 갖는 복합재질 3차원 구조의 비정렬 격자에 대한 전산해석 방법 (Numerical heat transfer analysis methodology for multiple materials with different heat transfer coefficient in unstructured grid for development of heat transfer analysis program for 3 dimensional structure of building)

  • 이주희;장진우;이현균;이용준;이규성
    • KIEAE Journal
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    • 제16권1호
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    • pp.81-87
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    • 2016
  • Purpose: Heat transfers phenomena are described by the second order partial differential equation and its boundary conditions. In a three-dimensional structure of a building, the heat transfer phenomena generally include more than one material, and thus, become complicate. The analytic solutions are useful to understand heat transfer phenomena, but they can hardly be applied in engineering or design problems. Engineers and designers have generally been forced to use numerical methods providing reliable results. Finite volume methods with the unstructured grid system is only the suitable means of the analysis for the complex and arbitrary domains. Method: To obtain an numerical solution, a discretization method, which approximates the differential equations, and the interpolation methods for temperature and heat flux between two or more materials are required. The discretization methods are applied to small domains in space and time, and these numerical solutions form the descretized equations provide approximated solutions in both space and time. The accuracy of numerical solutions is dependent on the quality of discretizations and size of cells used. The higher accuracy, the higher numerical resources are required. The balance between the accuracy and difficulty of the numerical methods is critical for the success of the numerical analysis. A simple and easy interpolation methods among multiple materials are developed. The linear equations are solved with the BiCGSTAB being a effective matrix solver. Result: This study provides an overview of discretization methods, boundary interface, and matrix solver for the 3-dimensional numerical heat transfer including two materials.

비정렬 유한체적법을 이용한 유동장 내의 연료액적 증발 특성 해석 (Unstructured Finite-Volume Analysis of Vaporization Characteristics of Fuel Droplets in Laminar Flow Field)

  • 김태준;김용모;손정락
    • 한국분무공학회지
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    • 제5권1호
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    • pp.13-22
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    • 2000
  • The present study has numerically analyzed the vaporization characteristics of fuel droplets in the high temperature convective flow field. The axisymmetric governing equations for mass, momentum, energy, and species are solved by an iterative and implicite unstructured finite-volume method. The moving boundary due to vaporization is handled by the deformable unstructured grid technique. The pressure-velocity coupling in the density-variable flows is treated by the SIMPLEC algorithm. In terms of the matrix solver, Bi-CGSTAB is employed for the numerically efficient and stable convergence. The n-decane is used as a liquid fuel and the initial droplet temperature is 300K. Computations are performed for the nonevaporating and evaporating droplets with the relative interphase velocity(25m/s). The unsteady vaporization process has been simulated up to the nondimensional time, 25. Numerical results indicate that the mathematical model developed in this study succesfully simulates the main features of the droplet vaporization process in the convective environment.

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부유체 주위의 2차원 회절 문제를 위한 내율적 비정렬 격자 유한요소해법 (An Implicit Unstructured Finite Element Method for Diffraction of Water Waves by Two-Dimensional Floating Breakwaters)

  • 정구창
    • 한국해양공학회지
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    • 제11권4호
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    • pp.90-101
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    • 1997
  • A hybrid element method is presented for two-dimensional diffraction problem of water waves. In this method, only a limited fluid domain close to irregular bodies is discretized into conventional finite elements, while the remaining infinite domain is treated as one element with analytical representations of high accuracy. A finite element grid is automatically generated by using Dealunay triangulation based on the Bowyer's algorithm and a linear system of equations is approximately solved with the ILU-CGS algorithm. To validate the present scheme, Computational results are compared with the existing experimental data and other numerical solutions.

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