Convergence characteristics and efficiency of three implicit approximate factorization schemes(ADI, DDADI and MAF) are examined using 2-Dimensional compressible upwind Navier-Stokes code. Second-order CSCM(Conservative Supra Characteristic Method) upwind flux difference splitting method with Fromm scheme is used for the right-hand side residual evaluation, while generally first-order upwind differencing is used for the implicit operator on the left-hand side. Convergence studies are performed using an example of the flow past a NACA0012 airfoil at steady transonic flow condition, i. e. Mach number 0.8 at $1.25^{\circ}$ angle of attack. The results were compared with other computational results in order to validate the current numerical analysis. The results from the implicit AF algorithms were compared well in low surface with the other computational results; however, not well in upper surface. It might be due to lack of the grid around the shock position. Because the algorithm minimizes the errors of the approximate decomposition, the improved convergence rate with MAF were observed.

In this paper we study numerically the shock-vortex interaction in the shear layer generated by moving shock waves above and below a flat plate. The faster normal shock is diffracted at the tip of the flat plate, producing a starting vortex. The slower normal shock below the flat plate arrives soon later to run across the vortex and make interaction. The two shocks are merged together and reflected back at the closed end of the shock tube to impinge on the shear layer developing multiple vortexlets. The computational simulation based on Euler and Navier-Stokes equations shows good prediction.

A two-dimensional Euler code based on flux vector splitting scheme has been developed to simulate the behavior of supersonic shock wave over the cylinder. AF+ADI scheme was used for time integration. The sliding multiblock technique was implemented to handle the relative motion of the moving cylinder and the stationary tunnel. The code is validated with a problem of subsonic flow around a Naca-0012 airfoil. The Computation results show complex phenomena of the propagation of shock waves and the reflection as expansion wave at tunnel exit.

Shock wave propagating in the particle suspension has important applications. Examples are shock waves occurring in the solid rocket plume and detonation of dusty particles by shock waves. Experimental and numerical investigations on this subject have drawn much attention. More recently, Sivier et al. numerically simulated the experiment of Sommerfeld using the unstructured adaptive grid. They used the Eulerian-Eulerian approach based on the continuum assumption for both gas and particles. In the present paper, a new numerical method using the Lagrangian particle tracing technique and unstructured particle-adaptive grid for the polydisperse system is presented. It is explained why the existing numerical calculation has showed discrepancy with the experimental results by Sommerfeld.

In this study, we adopt the point symmetric Gauss-Seidel relaxation algorithm to obtain the steady state solution of the Navier-Stokes equations for the thermal and chemical nonequilibrium flow of air. All of the inviscid, viscous flux Jacobians and thermochemical source Jacobians are included in the implicit part Numerical simulation is performed for the thermal and chemical nonequilibrium flow over blunt body and computational results are presented. The convergence history and CPU time of the present computation are compared with the LU-SGS scheme which employs the approximate Jacobians.

The Characteristic Flux Difference Splitting (CFDS) scheme designed to adapt the characteristic boundary conditions at the wall and inflow/outflow boundary planes satisfies Roe's property U, although the CFDS Jacobian matrix is decomposed by a product of elaborate transformation matrices and explicit eigenvalue matrix. When the CFDS algorithm, thus a variant of Roe's scheme, is applied straightforwardly to hypersonic flows over a blunt body, the strong bow shock gradually breaks down near the stagnation point. This numerical instability is widely observed by many researchers employing flux-difference method, known in the literature as the carbuncle phenomenon. Many remedies have been proposed and resulted in partial cures. When the idea of Sanders et al. which identifies the minimum eigenvalues near the discontinuity present is applied to CFDS method, it is shown that the instability problem can be controlled successfully. A few flux splitting methods have also been tested and results are compared against the Nakamori's Mach 8 blunt body flow.

The Equations of Chemical kinetics ate very stiff, which forces the use of an implicit scheme. The problem of implicit scheme, however, is that the jacobian must be solved at each time step. In this paper, we examined the approximate chemical jacobian methods such as Gauss-Seidel, Jacobi partial jacobian and diagonalized jacobian that can be stable without full jacobian, We show that Gauss-Seidel jacobian method is stable and accurate as well as full jacobian and that this is more efficient in supersonic combustion problem about $20\%$ than the full jacobian method with same accuracy,

Radiative heating of a liquid rocket base plane due to plume emission is numerically investigated. Calculation of flow and temperature fields around rocket nozzle precedes and thereby realistic plume shape and temperature distribution inside the plume are obtained. Based on the calculated temperature field, radiative transfer equation is solved by discrete ordinate method. The averaged radiative heat flux reaching the base plane is about $5kW/m^2$ at the flight altitude of 10.9km. This value is small compared with radiative heat flux caused by constant-temperature (1500K) plume emission, but it is not negligibly small. At higher altitude (29.8km), view factor between the babe plane and the exhaust plume is increased due to the increased expansion angle of the plume. Nevertheless, the radiative heating disappears since the base plane is heated to high temperature (above 1000K) due to convective heat transfer.

The base flow regions of a three-body sounding rocket containing multiple exhaust plumes were numerically investigated in three dimensions for a free stream Mach number of 2.7 at flight altitude 18.5 km. The flowfields were calculated using the full compressible Navier-Stokes equations with an one-equation turbulence model of Baldwin-Earth. The present calculations were executed based upon a chemically frozen, single perfect gas model assumption. Due to the symmetry of the three-body rocket of each single nozzle, only one fourth of the computational domain was considered for the analysis. The results indicate that a babe heating effect is not considerable due to the small expansion of the plumes. In the base, however, a low speed recirculating flow dominates the region.

Numerical design optimization techniques are implemented for the improvement of the ram accelerator performance. The design object is to find the minimum ram tube length required to accelerate projectile from initial velocity $V_0$ to target velocity $V_e$. The premixture is composed of $H_2,\;O_2,\;N_2$ and the mole numbers of these species are selected as design variables. The objective function and the constraints are linearized during the optimization process and gradient-based Simplex method and SLP(Sequential Linear Programming) have been employed. With the assumption of two dimensional inviscid flow for internal flow field, the analyses of the nonequilibrium chemical reactions for 8 steps 7 species lave been performed. To determined the tube length, ram tube internal flow field is assumed to be in a quasi-steady state and the flow velocity is divided into several subregions with equal interval. Hence the thrust coefficients and accelerations for corresponding subregions are obtained and integrated for the whole velocity region. With the proposed design optimization techniques, the total ram tube length had been reduced $19\%$ within 7 design iterations. This optimization procedure can be directly applied to the multi-stage, multi-premixture ram accelerator design optimization problems.

Transient aerodynamic response of an airfoil to a moving plane-flap is numerically investigated using two-dimensional Euler equations with conservative Chimera grid method. A body moving relative to a stationary grid is treated by an overset grid bounded by a 'dynamic domain-dividing line' the concept of which is developed in this study. A conservative Chimera grid method with a dynamic domain-dividing line technique is applied and validated by solving the flowfield around circular cylinder moving supersonic speed. The unsteady and transient characteristics of the flow solver is also examined by computations of a oscillating airfoil and a ramp pitching airfoil respectively. The transient aerodynamic behavior of an airfoil with a moving plane-flap is analyzed for various flow conditions such as deflecting rate of flap and free stream Mach number.

The spatial error due to the non-conservative interpolation become first-order when second-order conservative schemes are used, discontinuities are located away from the overlapped regions, and if the length of the overlapped region is not proportional to the grid spacing. Therefore, the solution accuracy is ensured if two domains overlap each other with a fixed grid point and the interpolation is occurred in smooth flow regions. To validate the spatial and temporal accuracy due to the non-conservative interpolation, inviscid and viscous problems are tested.

In this paper. a new automatic multi=block grid generation technique for general 2D regions is introduced. According to this simple and robust method, the domain of interest is first triangulated by using Delaunay triangulation of boundary points, and then geometric information of those triangles is used to obtain block topology. Once block boundaries are obtained. structured grid for each block is generated such that grid lines have $C^0-continuity$ across inter-block boundaries. In the final step of the present method, an elliptic grid generation method is applied to smoothen grid distribution for each block and also to re-locale the inter-block boundaries, and eventually to achieve a globally smooth multi-block structured grid system with $C^1-continuity$.

A two-dimensional Navier-Stokes solver using hybrid meshes is parallelized with a domain decompostion method. The focus of this paper is placed on minimizing the amount of effort in parallelizing the serial version of the solver, and this is achieved by adding an additional layer of cells to each decomposed domain. Most subroutines of the serial solver are used without modification, and the information exchange between neighboring domains is achieved using MPI(Message Passing Interface) library. Load balancing among the processors and scheduling of the message passing are implemented to reduce the overhead of parallelization, and the speed-up achieved by parallelization is measured on the transonic invisicd and turbulent flow problems. The parallelization efficiencies of the explicit Runge-Kutta scheme and the implicit point-SGS scheme are compared and the effects of various factors on the results are also studied.

본 연구에서는 2 차원 캐비티 유동에서 경계조건 부여 방법의 차이에 따른 유체유동의 이력이 최종적인 정상상태에 미치는 효과를 수치실험을 통하여 관찰하였다. 그 결과 유동의 Reynolds 수가 작은 경우는 유동장이 가지는 이력이 시간의 경과와 함께 소멸하여 하나의 정상유동 상태를 가지는데 반하여, 큰 Reynolds 수에서는 유동장 이력이 소멸하지 않고 유지됨으로 인하여 다수의 정상유동 형태가 나타남이 확인이 되었다. 엄밀한 이론적 해석은 현재 이루워지지 않았으나 유체 운동량의 증가에 따라 Navier-Stokes 방정식의 비선형성이 영향을 미치고 있다고 여겨진다.

There have been many studies for heat transfer enhancement. Particularly, the study of flow in heat exchangers which have fin device has been main theme in heat transfer area. Practically, the circular tube which has internal fins is widely used for developing heat transfer rate. In this study, flow and heat transfer analysis of the circular tube with fins are investigated. The height and the number of fins are arbitrary. The flow field is assumed to be laminar. The conformal mapping is used for analytic solution of the laminar flow field. Discretization of governing equation, namely, FDM was used for numerical analysis. The velocity field, flow rate and shear stress are calculated for some numbers of fins in circular tube and for some heights of fin. Temperature fields are plotted along the tube length. It can be shown that the numerical solution agrees with the analytical solution.

An Interactive grid generation program(KGRID) with graphical user interface(GUI) has been improved. KGRID works on the UNLX environment and GUI has been implemented with OSF/Motif and X Toolkit and the graphics language is Open GL for visualization of the 3D objects. It supports more convenient user environment to generate 2D and 3D multi-block structured grid systems. It provides various useful field grid generation methods, which are the algebraic methods, the elliptic partial differential equations method and the predictor-corrector method. It also supports 3D surface grid generation with NURBS(Non-Uniform Rational B-Spline) and various stretching functions to control grid points distribution on curves and surfaces. And some menus are added to perform flexible management, for the objects. We generated surface and field grid system about full aircraft configuration using KGRID. The performance and stability of the KGRID is verified through the generation of the grid system about a complex shape.

For the simulation of the blood flow in coronary artery, the system modeling of coronary hemodynamics is combined with CFD technique. The blood flow in coronary artery interacts with the global coronary circulation. Especially in case of the coronary artery with stenosis, the interaction plays an important role in the hemodynamics of the circulation. In this study we present a combined numerical approach using both the CFD technique for flow simulation and the global system model of coronary circulation. We use a lumped parameter model for the global simulation of coronary circulation whereas the finite element method is employed to compute the viscous flow field in stenosed coronary artery, The time variation of the pressure drop due to stenosis is obtained from the proposed numerical method. Numerical results shows that the flow resistance and pressure drop due to stenosis has a relatively large value in systole.

This thesis presents applications of three dimensional visualization technique based on shear-warp volume rendering to medical information. Volume rendering is compared to surface rendering and acceleration technique is also presented. The presented rendering techniques by using three-dimensional arrays of data are a widely used representation for computational fluid dynamics and geological structures as well as medical information.

CAFPlot has been developed for visualizing a wide range of technical data. It offer 2D and 3D plot in a variety of formats.

An Euler-based CFD tool has been developed for the performance evaluation of a thrust reverser mounted on a high bypass ratio turbofan engine. The computational domain surrounded by the ground and non-reflection boundary includes the whole nacelle configuration with a deployed thrust reverser. The numerical algorithm is based on the modified Godunovs scheme to allow the second order accuracy in both space and time. The grid system is generated by using eleven multi-blocks, of which the total cell number is 148,400. The thrust reverser is modeled as if it locates at the nacelle simply in all circumferential direction. The existence of a fan and an OGV(Outlet Guide Vane) is simulated by adopting the actuator disk concept, in which predetermined radial distributions of stagnation pressure ratio and adiabatic efficiency coefficient are used for the rotor type disk, and stagnation pressure losses and flow outlet angles for the stator type disk. All boundary conditions including the fan and OGV simulation are treated by Riemann solver. The developed solver is applied to a turbofan engine with a bypass ratio of about 5.7 and the diameter of the fan cowl of 83 inch. The computational results show that the Euler-based inviscid method is very useful and economical to evaluate the performance of thrust reversers.

Aerodynamic characteristics of tandem airfoil under ground effect is investigated numerically. Some numerical results for NACA 6409 tandem airfoil are presented. The numerical results show that as being decreased distance between airfoils, the lift coefficient of leading airfoil is increased and that of trailing airfoil is decreased. Drag coefficient shows opposite property, At the same distance between leading airfoil and trailing airfoil, lower position of trailing airfoil give better tandem airfoil effect.

The effects of the frequency of upstream gust on the unsteady boundary characteristics on a downstream blade was simulated by using a Navier-Stokes code. The Navier-Stokes code is based on an unstructured finite volume method and uses a low Reynolds k-e turbulence model to close the momentum equations. The MIT flapping foil experiment set-up is used to simulate the interaction between the upstream wake and a blade. The frequency of the upstream wake is simulated by varying rate of pitching motion of the flapping airfoils. Three reduced frequencies. 3.62. 7.24. and 10.86. are simulated. As the frequency increases, the unsteady fluctuation on the surfaces of the downstream hydrofoil is shown to decrease while the upstream flapper wake has larger first harmonics of y-velocity component. The unsteady vortices are shown to interact with each other and. as a result. the upstream wake becomes undiscernible inside the inner layer. The turbulence kinetic energy shows a similar behavior. Limiting streamlines around the trailing edge of the flapper are shown to conform with the unsteady Kutta condition for a round trailing edge. while limiting streamlines around the trailing edge of the hydrofoil conforms with the unsteady Kutta condition for a sharp edge.

A metacomputing system is constructed by integrating the heterogeneous supercomputers at KORDIC supercomputer center. The implementation is directed toward building up an easy-to-use supercomputing environment for Computational Fluid Dynamics (CFD) simulations. The key feature is an automatic resource selection According to the predicted performance, the system assigns the request job to the most suitable resource which satisfies the user's demands. Verification tests are conducted by using example CFD applications. An overview of the system is given and derivation of performance prediction models is described in details. Discussion is made of the test results to illustrate applicability and usefulness of the proposed models.

An unstructured implicit Euler solver is parallelized on a Cray T3E. Spatial discretization is accomplished by a cell-centered finite volume formulation using an unpwind flux differencing. Time is advanced by the Gauss-Seidel implicit scheme. Domain decomposition is accomplished by using the k-way N-partitioning method developed by Karypis. In order to analyze the parallel performance of the solver, flows over a 2-D NACA 0012 airfoil and a 3-D F-5 wing were investigated.

현재 전세계적으로 과한 기술 연산용 리눅스 클러스터에 대한 연구와 개발이 진행되고 있는 추세이다. 본 논문에서는 펜티엄 프로세서와 알파 프로세서 및 고속 이더넷을 이용한 리눅스 클러스터를 구현하고 이를 전산유체역학 분야에 적용하기 위한 선행연구로서 NAS의 병렬 벤치마크 프로그램인 NPB를 사용하여 리눅스 클러스터들의 성능을 비교 분석하였다. NPB 프로그램은 전산유체역학 분야의 해석프로그램에서 널리 이용되는 알고리즘들로 구성된 벤치마크의 프로그램으로 이를 이용한 성능 평가의 결과는 향후 리눅스 클러스터에서 실제 전산유체역학 코드들의 성능을 나타내는 중요한 지표가 될 수 있다. NPB 벤치마크 결과 리눅스 클러스터는 고가의 슈퍼컴퓨터에 비해 전산유체역학 분야에서 높은 가격 대 성능비를 보임을 알 수 있으며 이를 통하여 저비용 슈퍼컴퓨팅의 가능성을 제시하고자 한다.