• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.881-898
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• 2018

This article deals with implementation of a high-order finite difference scheme for numerical solution of the incompressible Navier-Stokes equations on curvilinear grids. The numerical scheme is based on pseudo-compressibility approach. A fifth-order upwind compact scheme is used to approximate the inviscid fluxes while the discretization of metric and viscous terms is accomplished using sixth-order central compact scheme. An implicit Euler method is used for discretization of the pseudo-time derivative to obtain the steady-state solution. The resulting block tridiagonal matrix system is solved by approximate factorization based alternating direction implicit scheme (AF-ADI) which consists of an alternate sweep in each direction for every pseudo-time step. The convergence and efficiency of the method are evaluated by solving some 2D benchmark problems. Finally, computed results are compared with numerical results in the literature and a good agreement is observed.

• 한국방재학회:학술대회논문집
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• 2008.02a
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• pp.431-434
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• 2008

Pratical dispersion-correction scheme is applicated to simulate the distant propagation of tsunami. This scheme is based on the leap-frog finite difference scheme for the linear shallow-water equations. The new scheme has the advantage of using the constant spatial grid size and time step size even in area of variable depths. And this new model constructed by using the 2nd upwind scheme, dynamic linking method, and staggered grid system. This model is simulated to near Sokcho harbor about The Central East Sea Tsunami in 1983. And this result is compared to tide gage and result of former model.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.311-316
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• 2001

The thin-layer Navier-Stokes equations are solved for the hypersonic flow over blunt cone configurations with applications to laminar as well as turbulent flows. The equations are expressed in the forms of flux-vector splitting and explicit algorithm. The upwind schemes of Steger-Warming and van Leer are investigated in their ability to accurately predict the heating loads along the surface of the body. A comparison with the second order extensions of these schemes is made and a hybrid scheme incorporating a combination of central differencing and flux-vector-splitting is presented. This scheme is also investigated in its ability to accurately predict heat transfer distributions.

• 한국전산유체공학회:학술대회논문집
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• 2001.10a
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• pp.91-97
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• 2001

The thin-layer Navier-Stokes equations are solved for the hypersonic flow over blunt cone configurations with applications to laminar as well as turbulent flows. The equations are expressed in the forms of flux-vector splitting and explicit algorithm. The upwind schemes of Steger-Warming and van Leer are investigated in their ability to accurately predict the heating loads along the surface of the body. A comparison with the second order extensions of these schemes is made and a hybrid scheme incorporating a combination of central differencing and flux-vector-splitting is presented. This scheme is also investigated in its ability to accurately predict heat transfer distributions.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.11
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• pp.1371-1378
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• 1999

Flow through turbomachinery has a very complex structure and Is Intrinsically unsteady. In addition, trend to highly loaded turbomachinery makes the flow extremely complex due to the interaction between rotor and stator. In this study, flows through UTRC LSRR turbine are numerically analyzed using 2 dimensional Navier-Stokes equations. The convective terms of the governing equations are discretized using the Van-Leer's FVS(Flux vector splitting) with an upwind TVD scheme. The conventional central differencing is used to discretize the diffusion terms on the finite volume. The accurate unsteady motion is achieved by using a 2nd order accurate, 3-point Euler implicit scheme. The quasi-conservative zonal scheme is used for calculating the flow variables on the zonal interface between the rotor and stator. The axial gap between stator and rotor has been configured in two variations, 15% and 65% of average chord length. The analysis program is validated using experimental results and the effect of axial gap is examined. The numerical analysis results are presented by time averaged pressure coefficient and pressure magnitude coefficient and compared with experimental results.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.12
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• pp.1555-1569
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• 2000

Numerical simulation of fluid flow with moving free surface has been carried out. For the free surface flow, a VOF(Volume of Fluid)-based algorithm utilizing a fixed grid system has been investigated. In order to reduce numerical smearing at the free surface represented on a fixed grid system, a new free surface tracking algorithm based on the donor-acceptor scheme has been presented. Novel features of the proposed algorithm are characterized as two numerical tools; the orientation vector to represent the free surface orientation in each cell and the baby-cell to determine the fluid volume flux at each cell boundary. The proposed algorithm can be easily implemented in any irregular non-uniform grid systems that are usual in finite element method (FEM). Moreover, the proposed algorithm can be extended and applied to the 3-D free surface flow problem without additional efforts. For computation of unsteady incompressible flow, a finite element approximation based on the explicit fractional step method has been adopted. In addition, the SUPG(streamline upwind/Petrov-Galerkin) method has been implemented to deal with convection dominated flows. Combination of the proposed free surface tracking scheme and explicit fractional step formulation resulted in an efficient solution algorithm. Validity of the present solution algorithm was demonstrated from its application to the broken dam and the solitary wave propagation problems.

• 한국전산유체공학회:학술대회논문집
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• 2001.10a
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• pp.84-90
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• 2001

Secondary instability of flow past a circular cylinder is examined using direct numerical simulation at Reynolds number 220 and 250. The higher-order finite difference scheme is employed for the spatial distributions along with the second order Adams-Bashforth and the first order backward-Euler time integration. In x-y plane, the convection term is applied by the 5th order upwind scheme, and the pressure and viscosity terms are applied by the 4th order central difference. In spanwise, Navier-Stokes equation is distributed using Spectral Method. The critical Reynolds number for this instability is found to be about Re=190. The secondary instability leads re three-dimensionality with a spanwise wavelength about 4 cylinder diameters at onset (A-mode). Results of three-dimensional effect in wake of a circular cylinder are represented with spanwise and streamwise vorticity contours as Reynolds numbers.

• Proceedings of the KSME Conference
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• 2001.11b
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• pp.570-577
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• 2001

Three-dimensional time-dependent flow past a circular cylinder is numerically investigated using direct numerical simulation for Reynolds number 280 and 300. The higher-order finite difference scheme is employed for the spatial distributions along with the second order Adams-Bashforth and the first order backward-Euler time integration. In x-y plane, the convection term is applied by the 5th order upwind scheme and the pressure and viscosity terms are applied by the 4th order central difference. And in spanwise, Navier-Stokes equation is distributed using of Spectral Method. At Reynolds number 259 the two-dimensional wake becomes linearly unstable to a second branch of modes with wavelength about 1.0 diameters at onset (B-mode). Present results of three-dimensional effects of in wake of a circular cylinder is represented with spanwise and streamwise vorticity contours as Reynolds numbers.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.10
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• pp.1384-1391
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• 2001

Three-dimensional flow analysis is implemented to investigate the flow through transonic axial-flow compressor rotor(NASA R67) and to evaluate the performances of Abid's low-Reynolds-number k-$\omega$ and Baldwin-Lomax turbulence models. A finite volume method is used fur spatial discretization. The equations are solved implicitly in time by the use of approximate factorization. The upwind difference scheme is used for inviscid terms and viscous terms are approximated with central difference. The flux-difference-splitting method of Roe is used to obtain fluxes at the cell faces. Numerical analysis is performed near peak efficiency and near stall. The results are compared with the experimental data for NASA R67 rotor. Blade-to-Blade Mach number distributions are compared to confirm the accuracy of the code. From the results, it is concluded that Abid'k-$\omega$ model is better for the calculation of flow rate and efficiency than Baldwin-Lomax model. But, the predictions for Mach number and shock structure are almost the same.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.45 no.3
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• pp.233-240
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• 2017

The flowfield around transonic wing-body configuration was simulated using in-house CFD code and compared with the experimental data to understand the influence of several features of CFD(Computational Fluid Dynamics) ; grid dependency, turbulence models, spatial discretization, and viscosity. The wing-body configuration consists of a simple planform RAE Wing 'A' with an RAE 101 airfoil section and an axisymmetric body. The in-house CFD code is a compressible Euler/Navier-Stokes solver based on unstructured grid. For the turbulence model, the $k-{\omega}$ model, the Spalart-Allmaras model, and the $k-{\omega}$ SST model were applied. For the spatial discretization method, the central differencing scheme with Jameson's artificial viscosity and Roe's upwind differencing scheme were applied. The results calculated were generally in good agreement with experimental data. However, it was shown that the pressure distribution and shock-wave position were slightly affected by the turbulence models and the spatial discretization methods. It was known that the turbulent viscous effect should be considered in order to predict the accurate shock wave position.