• Journal of computational fluids engineering
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• v.3 no.2
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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.

• 한국전산유체공학회:학술대회논문집
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• 1998.11a
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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.

• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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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.

• Journal of computational fluids engineering
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• v.13 no.4
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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.

• 한국전산유체공학회:학술대회논문집
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• 2008.03a
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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.

• 한국전산유체공학회:학술대회논문집
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• 2008.10a
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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.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.29 no.9 s.240
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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.

• KIEAE Journal
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• v.16 no.1
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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.

• Journal of ILASS-Korea
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• v.5 no.1
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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.

• Journal of Ocean Engineering and Technology
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• v.11 no.4
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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.