• 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.

• Journal of Powder Materials
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• v.2 no.2
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• pp.120-134
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• 1995

The behavior of the flow about gas atomizers with a supersonic nozzle containing an under-expanded or over-expanded jet is very important with respect to performance and stability characteristics. Since detailed experiments are expensive, computational fluid mechanics have been applied recently to various relating flow field. In this study, a higher order upwind method with the 3rd order MUSCL type TVD scheme is used to solve the full Reynolds Wavier-Stokes equations. To delineate the purely exhaust jet effects, the melt flow is not considered. Comparison is made with some experimental data in terms of density fields. The influence of the exhaust-jet-to freestream pressure ratio and the effect of the protrusion length of the melt orifice are studied. The present study leads us to believe that the computational fluid mechanics should be considered as powerful tool in predicting the gas atomizer flows.

• 유체기계공업학회:학술대회논문집
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• 2006.08a
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• pp.353-356
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• 2006

A set of solutions of the Navier-Stokes equation for the gas inside a spherical bubble with heat transfer through the bubble wall permits to predict correctly behavior of an ultrasonically driven bubble in aqueous solutions of sulfuric acid. Calculation results of the minimum velocity of bubble wall and the peak temperature and pressure are in excellent agreement with the observed ones. Further the calculated bubble radius-time curve displays alternating pattern of bubble motion as observed in experiment.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.1
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• pp.31-39
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• 2007

A pedagogic model for blood flow is introduced to help medicine majors understand a simplified version of Navier-Stokes equations which is known to be a good tool for interpreting the phenomena in blood flow. The pressure gradient consists of a time-independent part known as Hagen-Poiseuille's gradient and a time-dependent part known as Sexl's, and the model formula for the volume rate of blood flow is reduced to a very simple form. For demonstration, the blood rate in human aorta system is analyzed in connection with the time-dependence of pressure gradient. It is shown for Sexl's part that the flow rate lags the pressure gradient by ${\pi}/2$, which is thought to be due to the relaxation process involved.

• Journal for History of Mathematics
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• v.15 no.3
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• pp.59-64
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• 2002

This paper investigates a history of Fourier Series for the heat equation and how deeply it is related to modern famous three equations, Navier-Stokes equations in fluid dynamics, drift-diffusion equations in semiconductor, and Black-Scholes equation in finance. We also propose improved models for the heat equation with finite propagation speeds.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.10
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• pp.1915-1927
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• 1992

A three-dimensional Navier-Stokes code has been developed for analysis of viscous flows through turbomachinery blade rows or other internal passages. The Navier-Stokes equations are written in a cartesian coordinate system, then mapped to a general body-fitted coordinate system. Streamwise viscous terms are neglected and turbulent effects are modeled using the baldwin-Lomax model. Equations are discretized using finite difference method on the stacked C-type grids and solved using LU-ADI decomposition scheme. calculations are made for a two-dimensional cascade in a transonic wind-tunnel to see the infuence of the endwalls. The flow pattern of the three-dimensional flow near the endwall is found to be different from that of the two-dimensional flow due to the existence of the endwalls.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.8
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• pp.1950-1963
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• 1995

A modification of the approximate-factorization method is made to accelerate the convergency rate and to take sufficiently large Courant number without loss of accuracy. And a stable implicit finite-difference scheme for solving the incompressible Navier-Stokes equations employed above modified method is developed. In the present implicit scheme, the volume fluxes with contravariant velocity components and the pressure formulation in curvilinear coordinates is adopted. In order to satisfy the continuity condition completely and to remove spurious errors for the pressure, the Navier-Stokes equations are solved by a modified SMAC scheme using a staggered gird. The upstream-difference scheme such as the QUICK scheme is also employed to the right hand side. The implicit scheme is unconditionally stable and satisfies a diagonally dominant condition for scalar diagonal linear systems of implicit operator on the left hand side. Numerical results for some test calculations of the two-dimensional flow in a square cavity and over a backward-facing step are obtained using both usual approximate-factorization method and the modified one, and compared with each other. It is shown that the present scheme allows a sufficiently large Courant number of O(10$^{2}$) and reduces the computing time.

• Journal of computational fluids engineering
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• v.19 no.1
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• pp.27-33
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• 2014

A new and efficient implicit scheme is proposed to obtain a steady-state solution in time integration and the comparison of characteristics with the approximation ways for the implicit method to solve the incompressible Navier-Stokes equations is provided. The conservative, finite-volume cell-vertex upwind scheme and artificial compressibility method using dual time stepping for time accuracy is applied in this paper. The numerical results obtained indicate that the direct application of Jacobian matrix to the Lower and upper sweeps of implicit LU-SGS leads to better performance as well as convergence regardless of CFL number and true time step than explicit scheme and approximation of Jacobian matrix. The flow simulation around box in uniform flow with unstructured meshes is demonstrated to check the validity of the current formulation.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.2
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• pp.93-114
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• 2019

In this article, we introduce a finite difference method for solving the Navier-Stokes equations in rectangular domains. The method is proved to be energy stable and shown to be second-order accurate in several benchmark problems. Due to the guaranteed stability and the second order accuracy, the method can be a reliable tool in real-time simulations and physics-based animations with very dynamic fluid motion. We first discuss a simple convection equation, on which many standard explicit methods fail to be energy stable. Our method is an implicit Runge-Kutta method that preserves the energy for inviscid fluid and does not increase the energy for viscous fluid. Integration-by-parts in space is essential to achieve the energy stability, and we could achieve the integration-by-parts in discrete level by using the Marker-And-Cell configuration and central finite differences. The method, which is implicit and second-order accurate, extends our previous method [1] that was explicit and first-order accurate. It satisfies the energy stability and assumes rectangular domains. We acknowledge that the assumption on domains is restrictive, but the method is one of the few methods that are fully stable and second-order accurate.

• Korean Journal of Mathematics
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• v.16 no.1
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• pp.25-40
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• 2008

We are concerned with a free boundary problem for the 2D Stokes channel flows, which determines the profile of the wing for the channel, so that the given traction force is to be distributed along the wing of the channel. Using the domain embedding technique, the free boundary problem is transferred into the shape optimization problem through the compliant formulation by releasing the traction condition along the variable boundary. The justification of the formulation will be discussed.