• Proceedings of the Korea Water Resources Association Conference
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• 2008.05a
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• pp.1624-1629
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• 2008

The governing equations in generalized curvilinear coordinates for a 3D pulsatile flow are the Incompressible Navier-Stokes (INS) equations with the artificial dissipative terms and continuity equation discretized using a second-order accurate, finite volume method on the nonstaggered computational grid. This method adopts a dual or pseudo time-stepping Artificial Compressibility (AC) method integrated in pseudo-time. The computational technique implements the implicit approximate factorization method of the Beam and Warming method (1978), which is the extension of the Alternate Direction Implicit (ADI) method. The algorithm yields practically identical velocity profiles and secondary flows that are in excellent overall agreement with an experimental measurement (Rindt & Steenhoven, 1991).

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.10
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• pp.1335-1342
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• 2000

Three-dimensional flow analysis and numerical optimization methods are presented for the design of an axial-flow fan. Steady, incompressible, three-dimensional Reynolds-averaged Navier-Stokes equations are used as governing equations, and standard k- ${\varepsilon}$ turbulence model is chosen as a turbulence model. Governing equations are discretized using finite volume method. Steepest descent method, conjugate gradient method and BFGS method are compared to determine the searching directions. Golden section method and quadratic fit-sectioning method are tested for one dimensional search. Objective function is defined as a ratio of generation rate of the turbulent kinetic energy to pressure head. Two variables concerning sweep angle distribution are selected as the design variables. Performance of the final fan designed by the optimization was tested experimentally.

• Journal of the Korean Mathematical Society
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• v.57 no.4
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• pp.915-933
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• 2020

A two-level finite element method based on the Newton iterative method is proposed for solving the Navier-Stokes/Darcy model. The algorithm solves a nonlinear system on a coarse mesh H and two linearized problems of different loads on a fine mesh h = O(H^4-𝜖). Compared with the common two-grid finite element methods for the considered problem, the presented two-level method allows for larger scaling between the coarse and fine meshes. Moreover, we prove the stability and convergence of the considered two-level method. Finally, we provide numerical experiment to exhibit the effectiveness of the presented method.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.33 no.9
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• pp.34-40
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• 2005

In present study, a two dimensional unsteady Navier-Stokes solver has been developed using the Diagonalized ADI (DADI) method and implicit dual time stepping method. The jacobian matrices in steady state Navier-Stokes equations are introduced from inviscid flux terms. The implicit treatment of artificial dissipation terms results in a block penta-diagonal matrix system and it becomes a scalar penta-diagonal matrix by diagonalization. In steady state equations about fictitious time, a new residual including a real time derivative term is introduced. From a converged solution about fictitious time, a real time unsteady solution can be obtained, which is called 'implicit dual time stepping method'. For code validation, an oscillating flat plate, a regular Karman vortices past a circular cylinder and shock buffeting around a bicircular airfoil problems are numerically solved. And they are compared with a theoretical solution, experiments and other researcher's computations.

• Journal of the Korea institute for structural maintenance and inspection
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• v.22 no.5
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• pp.13-22
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• 2018

In this study, a governing differential equation for the bending problem of orthotropic rectangular plate is drived. It's exact solution for various boundary conditions is presented. This solution follows traditional method like Navier's solution or Levy's solution that transforms the governing differential equation into an algebraic equation by using trigonometric series. To obtain a solution by Levy's method, it is required that two opposite edges of the plate be simply supported. And the boundary conditions, for which the Navier's method is applicable, are simply supported edge at all edges. In this study, it overcomes the limitations of the previous Navier's and Levy's methods.This solution is applicable for any combination of boundary conditions with simply supported edge and clamped edge in x, y direction. The plate could be subjected to uniform, partially uniform, and line loads. The advantage of the solution is that it is the exact solution as well as it overcomes the limitations of the previous Navier's and Levy's methods. Calculations are presented for orthotropic plates with nonsymmetric boundary conditions. Comparisons between the result of this paper and the result of Navier, Levy and Szilard solutions are made for the isotropic plates. The deflections were in excellent agreement.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.11
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• pp.1581-1593
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• 2001

An efficient variable-reordering method for finite element meshes is used and the effect of variable-reordering is investigated. For the element renumbering of unstructured meshes, Cuthill-McKee ordering is adopted. The newsy reordered global matrix has a much narrower bandwidth than the original one, making the ILU preconditioner perform bolter. The effect of variable reordering on the convergence behaviour of saddle point type matrix it studied, which results from P2/P1 element discretization of the Navier-Stokes equations. We also propose and test 'level(0) preconditioner'and 'level(2) ILU preconditioner', which are another versions of the existing 'level(1) ILU preconditioner', for the global matrix generated by P2/P1 finite element method of incompressible Navier-Stokes equations. We show that 'level(2) ILU preconditioner'performs much better than the others only with a little extra computations.

• 한국전산유체공학회:학술대회논문집
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• 1997.10a
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• pp.38-42
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• 1997

A multiblock grid generation has been applied to a Navier-Stokes design procedure of a axial-flow compressors. A multiblock structure simplifies the creation of structured H-grids about complex turbomachinery geometries and facilitate the creation of a grid in the tip flow region. The numerical algorithm adopts the combination of the algebraic and elliptic method to create the internal grids efficiently and quickly. The input module is made of the results of the preliminary design, i.e., flow-path, aerodynamic conditions along the spanwise direction, and the blade profile data. The final grids generated from each module of the system are used as the preprocessor for the performance prediction of the sectional blade, the blade-stacking process and the three-dimensional flow simulation inside the blade passage. Application to the blade design of the LP compressor was demonstrated to be very reliable and practical in support of design activities. This customized system are coupled strongly with the design procedure of the turbomachinery cascades using the Navier-Stokes technique.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.1
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• pp.43-56
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• 2010

The representative numerical algorithms to solve the time dependent Navier-Stokes equations are projection type methods. Lots of projection schemes have been developed to find more accurate solutions. But most of projection methods [4, 11] suffer from inconsistency and requesting unknown datum. E and Liu in [5] constructed the gauge method which splits the velocity $u=a+{\nabla}{\phi}$ to make consistent and to replace requesting of the unknown values to known datum of non-physical variables a and ${\phi}$. The errors are evaluated in [9]. But gauge method is not still obvious to find out suitable combination of discrete finite element spaces and to compute boundary derivative of the gauge variable ${\phi}$. In this paper, we define 4 gauge algorithms via combining both 2 decomposition operators and 2 boundary conditions. And we derive variational derivative on boundary and analyze numerical results of 4 gauge algorithms in various discrete spaces combinations to search right discrete space relation.

• Journal of computational fluids engineering
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• v.1 no.1
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• pp.64-70
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• 1996

Three dimensional turbulent flow fields around ships are simulated by a numerical method. Reynolds Averaged Navier-Stokes equations are used where Reynolds stresses are approximated by Baldwin-Lomax and Sub-Grid Scale(SGS) turbulence models. Body-fitted coordinate system is introduced to conform three dimensional ship geometries. The governing equations are discretized by a finite volume method. Temporal derivatives are approximated by the forward differencing and the convection terms are approximated by the QUICK or Kawamura scheme. The 2nd-order centered differencing is used for other spatial derivatives. Pressure and velocity fields are simultaneously iterated by the Highly Simplified Marker-And-Cell method. To verify the numerical method and turbulence models, flow fields around ships are simulated and compared to the experiments.

• Journal of computational fluids engineering
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• v.2 no.2
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• pp.35-43
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• 1997

An efficient inverse method for 1.he supersonic/hypersonic axisymmetric body design is developed for the parabolized Navier-Stokes equations. The developed method is examined numerically for three extreme testcases in the supersonic(M/sub ∞/=3.0) and hypersonic(M/sub ∞/=6.28) speeds. The first one is a negative pressure distribution near a vacuum pressure and the second one is a positive pressure distribution over the whole region of the body. The last one is the case of abrupt change of pressure distribution to zero in the forward region of the body. These testcases show the robustness of the method. By introducing a regular-falsi method and by using a not-fully converged inverse solution, the convergence behavior was greatly improved.