• Journal of the Korean Mathematical Society
• /
• v.38 no.1
• /
• pp.1-23
• /
• 2001

This paper is concerned with an optimal shape control problem for the stationary Navier-Stokes system. A two-dimensional channel flow of an incompressible, viscous fluid is examined to determine the shape of a bump on a part of the boundary that minimizes the viscous drag. by introducing an artificial compressibility term to relax the incompressibility constraints, we take the penalty method. The existence of optima solutions for the penalized problem will be shown. Next, by employing Lagrange multipliers method and the material derivatives, we derive the shape gradient for the minimization problem of the shape functional which represents the viscous drag.

• 유체기계공업학회:학술대회논문집
• /
• 2001.11a
• /
• pp.293-299
• /
• 2001

Since the previous cut-and-try design algorithm require much cost and time, it has recently been concerned the automatic design technique using the CFD and optimum design algorithm. In this study, the Navier-Stokes equations is solved to consider the more detail viscous flow informations of cascade interaction and O-H multiblock grid system is generated to impose an accurate boundary condition. The cubic-spline interpolation is applied to handle a relative motion of a rotor to the stator. To validate present procedure, the time averaged aerodynamic loads are compared with experiment and good agreement obtained. Once the N-S equations have been solved, the computed aerodynamic loads may be used to computed the sensitivities of the aerodynamic objective function. The Modified Method of feasible Direction(MMFD) is usef to compute the

• 한국전산유체공학회:학술대회논문집
• /
• 1995.10a
• /
• pp.203-212
• /
• 1995

In this paper the upwind flux difference splitting Navier-Stokes method has been applied to study the perfect gas and the equilibrium chemically reacting hypersonic flow over an axisymmetric sphere-cone($5^{\circ}$) geometry. The effective gamma($\bar{r}$), enthalpy to internal energy ratio was used to couple chemistry with the fluid mechanics for equilibrium chemically reacting air. The test case condition was at altitude(30Km) and Mach number(15). The equilibrium shock thickness over the blunt body region was much thinner than that of perfect gas shock. The pressure difference between perfect gas and equilibrium gas was about $3\sim5$ percent. The skin friction coefficient and heat transfer coefficient were also calculated.

• International Journal of Aeronautical and Space Sciences
• /
• v.17 no.2
• /
• pp.149-156
• /
• 2016

The hypersonic flow on the stagnation streamline of a blunt body is analyzed with quasi one-dimensional (1-D) Navier-Stokes equations approximated by adopting the local similarity to the two-dimensional (2-D)/axisymmetric Navier-Stokes equations. The governing equations are solved using the implicit finite volume method. The computational domain is confined from the stagnation point to the shock wave, and the shock fitting method is used to find the shock position. We propose a boundary condition at the shock, which employs the shock wave angle in the vicinity of the stagnation streamline using the shock shape correlation. As a result of numerical computation conducted for the hypersonic flow over a sphere, the proposed boundary condition is shown to improve the accuracy of the prediction of the shock standoff distance. The quasi 1-D Navier-Stokes code is efficient in computing time and is reliable for the flow analysis along the stagnation streamline and the prediction of heat flux at the stagnation point in the hypersonic blunt body flow.

• 한국전산유체공학회:학술대회논문집
• /
• 1999.05a
• /
• pp.171-176
• /
• 1999

In the present paper, three types of the flow solvers were used to investigate the influence on the airfoil shape optimization. The adopted equations, i.e., Euler , thin layer Navier- Stokes and full Navier-Stokes ones, are solved using implicit LU-ADI decomposition scheme. The feasible direction algorithm with the sinusoidal function was used as an optimization algorithm. The present numerical method was applied to the drag minimization problems under the initial shape of NACA0012 airfoils.

• 유체기계공업학회:학술대회논문집
• /
• 1999.12a
• /
• pp.27-32
• /
• 1999

A numerical study based on the three-dimensional thin-layer Navier-Stokes solver is carried out to analyze the flowfield through a single stage transonic compressor. Explicit four-step Runge-Kutta scheme with spatially variable time step and implicit residual smoothing is used. The governing equations are discretized with exploit finite difference method. Mixed-out average method is used at the interface between rotor and stator. And, an artificial dissipation model is used to assure the stability of solution. The results with k-$\omega$ turbulence model were compared to the results with Baldwin-Lomax model, and physical phenomena of transonic compressor are presented. The two turbulence models give the results that show reasonably good agreements with experimental data.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.24 no.7
• /
• pp.907-915
• /
• 2000

The preconditioned Krylov subspace methods were applied to the incompressible Navier-Stoke's equations for convergence acceleration. Three of the Krylov subspace methods combined with the five of the preconditioners were tested to solve the lid-driven cavity flow problem. The MILU preconditioned CG method showed very fast and stable convergency. The combination of GMRES/MILU-CG solver for momentum and pressure correction equations was found less dependency on the number of the grid points among them. A guide line for stopping inner iterations for each equation is offered.

• Journal of computational fluids engineering
• /
• v.10 no.1
• /
• pp.67-72
• /
• 2005

This research is based on the iterative space-marching method for incompressible and compressible Navier-Stokes equations[1-4]. A principle of parallel computational schemes construction for steady and unsteady problems is suggested. It is analytically proven that convergence of these schemes is unconditional for incompressible case. When the parallel scheme is used the total volume of computations is the sum of a large number of independent and equal parts. Estimation of the speed-up K shows that K > 1000 in ideal case. First results of using the parallel schemes are presented.

• Proceedings of the KSME Conference
• /
• 2002.08a
• /
• pp.35-38
• /
• 2002

The convergence acceleration methods for the compressible Wavier-Stokes equations are studied ,which are multigrid method and implicit preconditioned multistage time stepping method. In this paper, the performance of implicit preconditioning methods are studied for the full-coarsening multigrid methods on the high Reynolds number compressible flow computations. The effect of numerical flux on the convergence are investigated for the inviscid and viscous calculations.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
• /
• v.1
• /
• pp.181-186
• /
• 2006

In this paper, generation mechanisms of ocean freak waves are briefly introduced in the context of wave-current interaction phenomena. The present model of the fluid motion is based on the Navier-Stokes equations incorporating velocity-pressure formulation because of need to model the nonlinear wave interaction with spatially non-uniform current field. In order to deal with the free surface motion, an Arbitrary Lagrangian-Eulerian (ALE) description is adopted. As an accurate and efficient numerical tool, the spectral element method is presented with general features and specific treatment for the wave-current interaction problem. As an intermediate stage of development, solution procedure and characteristics aspects of the present modeling and numerical method are addressed in detail, and preliminary numerical results prove its accuracy and convergence.