• The Pure and Applied Mathematics
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• v.19 no.2
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• pp.147-169
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• 2012

We introduce a Heaviside-function formulation of the interaction between incompressible two-phase fluid and a non-deformable solid. Fluid and solid interact in two ways : fluid satises the Dirichlet boundary condition imposed by the velocity field of solid, and solid is accelerated by the surface traction exerted by fluid. The two-way couplings are formulated by the Heaviside function to the interface between solid and fluid. The cumbersome treatment of interface is taken care of by the Heaviside function, and the interaction is discretized in a simple manner. The discretization results in a stable and accurate projection method.

• 한국전산유체공학회:학술대회논문집
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• 1996.05a
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• pp.46-51
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• 1996

The flow field around a three dimensional minivan-like body has been simulated. This study solves 3-D unsteady incompressible Navier-Stokes equations on a non-orthogonal curvilinear coordinate system using second-order accurate schemes for the time derivatives, and third/second-order scheme for the spatial derivatives. The Marker-and-Cell concept is applied to efficiently solve continuity equation. The fourth -order artificial damping is added to the continuity equation for numerical stability. A H-H type multi-block grid system is generated around a three dimensional minivan-like body. Turbulent flows have been modeled by the Baldwin-Lomax turbulent model. The simulation shows three dimensional vortex-pair just behind body. And the flow separation is also observed the rear of the body. It has concluded that the results of present study properly agree with physical flow phenomena.

• 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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• 1997.10a
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• pp.73-80
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• 1997

Objective of the present study is to examine the convergence characteristics of the various multi-stage Runge-Kutta methods in solving the incompressible Navier-Stokes equations of a time-marching from casted by the artificial compressibility method. Convergence characteristics are examined over 2-stage, 4-stage and hybrid type (using 4-, 3-, 2-stages sequentially) Runge-Kutta methods for a laminar lid-driven cavity flow, and also for a turbulent bump channel flow using Chien's low-Reynolds number turbulence model. Efforts are made to establish a stable and fast convergent multi-stage Runge-Kutta method with minimal artificial dissipations.

• 한국전산유체공학회:학술대회논문집
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• 2009.11a
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• pp.223-227
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• 2009

In the present study, a least square weighted residual method and Taylor-Galerkin method were formulated and tested for the discretization of the two hyperbolic type equations of level set method; advection and reinitialization equations. The two approaches were compared by solving a time reversed vortex flow and three-dimensional broken dam flow by employing a four-step splitting finite element method for the solution of the incompressible Navier-Stokes equations. From the numerical experiments, it was shown that the least square method is more accurate and conservative than Taylor-Galerkin method and both methods are approximately first order accurate when both advection and reinitialization phase are involved in the evolution of free surface.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2003.10a
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• pp.192-197
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• 2003

Three-dimensional cavity flow is analyzed with the code by using unstructured grid. Incompressible Navier-Stokes equations are used as governing equations, and governing equations are discretized by Finite Volume Method. Artificial compressibility method, proposed by Chorin, and developed by Soh, is used for coupling a pressure and a velocity. Cell-centered scheme is adopted in the code, this has the effect of having denser grid than nodal scheme when the same grid is used. Weighted Averaging scheme is used for the value at a nodal point. Cavity flow is analyzed, and this computed results are compared with the results in the research report

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.1869-1874
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• 2004

Acoustic pressure field around the cross-flow fan is predicted by a hydrodynamic-acoustic splitting method. Unsteady flow field is obtained by solving the incompressible Navier-Stokes equations using an unstructured finite-volume method on the triangular meshes, while the acoustic waves generated inside the cross-flow fan are predicted by solving the perturbed compressible equations(PCE) with a 6th-order compact finite difference method. Computational results show that the acoustic waves of BPF tone are generated by interactions of the blades wakes with the stabilizer, which then are reflected from the rear-guider and mainly propagate towards the fan inlet. Also, a directivity of BPF noise predicted by the PCE is noticeably different from that of the FW-H equations, in which a fan casing effect cannot be included.

• 한국전산유체공학회:학술대회논문집
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• 2010.05a
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• pp.389-396
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• 2010

In this paper, a new computational code was developed using Chorin's artificial compressibility method to solve the two-dimensional incompressible Navier-Stokes equations. In spatial derivatives, Roe's flux difference splitting was used for the inviscid flux, while central differencing was used for the viscous flux. Furthermore, AF-ADI with dual time stepping method was implemented for accurate unsteady computations. Two-equation turbulence models, Menter's $k-{\omega}$ SST model and Coakley's $q-{\omega}$ model, hae been adopted to solve high-Reynolds number flows. A number of numerical simulations were carried out for steady laminar and turbulent flow problems as well as unsteady flow problem. The code was verified and validated by comparing the results with other computational results and experimental results. The results of numerical simulations showed that the present developed code with the artificial compressibility method can be applied to slve steady and unsteady incompressible flows.

• 한국전산유체공학회:학술대회논문집
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• 2002.05a
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• pp.8-15
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• 2002

For the large scale computation of turbulent flows around an arbitrarily shaped body, a parallel LES (large eddy simulation) code has been recently developed in which domain decomposition method is adopted. METIS and MPI (message Passing interface) libraries are used for domain partitioning and data communication between processors, respectively. For unsteady computation of the incompressible Wavier-Stokes equation, 4-step splitting finite element algorithm [1] is adopted and Smagorinsky or dynamic LES model can be chosen fur the modeling of small eddies in turbulent flows. For the validation and performance-estimation of the parallel code, a three-dimensional laminar flow generated by natural convection inside a cube has been solved. Then, we have solved the turbulent flow around MIRA (Motor Industry Research Association) model at $Re = 2.6\times10^6$, which is based on the model height and inlet free stream velocity, using 32 processors on IBM SMP cluster and compared with the existing experiment.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.410-415
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• 2001

An analytical and numerical examination of second-order fractional-step methods and boundary condition for the incompressible Navier-Stokes equations is presented. In this study, the compatibility condition for pressure Poisson equation and its boundary conditions, stability, and numerical accuracy of canonical fractional-step methods has been investigated. It has been found that satisfaction of compatibility condition depends on tentative velocity and pressure boundary condition, and that the compatible boundary conditions for type D method and approximately compatible boundary conditions for type P method are proper for divergence-free velocity for type D and approximately divergence-free for type P method. Instability of canonical fractional-step methods is induced by approximation of implicit viscous term with explicit terms, and the stability criteria have been founded with simple model problems and numerical experiments of cavity flow and Taylor vortex flow. The numerical accuracy of canonical fractional-step methods with its consistent boundary conditions shows second-order accuracy except $D_{MM}$ condition, which make approximately first-order accuracy due to weak coupling of boundary conditions.