• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.495-501
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• 1996

There is currently a regain of interest in ADI (Alternating Direction Implicit) method as a preconditioner for iterative Method for solving large sparse linear systems, because of its suitability for parallel computation. However the classical ADI is not applicable to FE(Finite Element) matrices. In this paper wer propose a Block-ADI method, which is applicable to Finite Element metrices. The new approach is a combination of classical ADI method and domain decompositi on. Also, we provide a partial proof of the convergence based on the results from the regular splittings, in case the discretization metrix is symmetric positive definite.

• Proceedings of the IEEK Conference
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• 2002.07a
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• pp.137-140
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• 2002

In this paper, a new algorithm for two-dimensional (2-D) finite-difference time-domain (FDTD) method is presented. By this new method, the maximum time step size can be increased over the Courant-Friedrich-Levy (CFL) condition restraint. This new algorithm is adapted from an Alternating-Direction Implicit FDTD (ADI-FDTD) method. However, unlike the ADI-FDTD algorithm. the alternation is performed with respect to the blocks of fields rather than with respect to each respective coordinate direction. Moreover. this method can be efficiently simulated with parallel computation. and it is more efficient than the conventional FDTD method in terms of CPU time. Numerical formulations are shown and simulation results are presented to demonstrate the effectiveness and efficiency of our proposed method.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.33 no.9
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• pp.34-40
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• 2005

In present study, a two dimensional unsteady Navier-Stokes solver has been developed using the Diagonalized ADI (DADI) method and implicit dual time stepping method. The jacobian matrices in steady state Navier-Stokes equations are introduced from inviscid flux terms. The implicit treatment of artificial dissipation terms results in a block penta-diagonal matrix system and it becomes a scalar penta-diagonal matrix by diagonalization. In steady state equations about fictitious time, a new residual including a real time derivative term is introduced. From a converged solution about fictitious time, a real time unsteady solution can be obtained, which is called 'implicit dual time stepping method'. For code validation, an oscillating flat plate, a regular Karman vortices past a circular cylinder and shock buffeting around a bicircular airfoil problems are numerically solved. And they are compared with a theoretical solution, experiments and other researcher's computations.

• 한국전산유체공학회:학술대회논문집
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• 2000.05a
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• pp.91-98
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• 2000

The three-dimensional unsteady compressible Full Navier-Stokes equation solver with sliding multi-block method has been applied to analyze three dimensional characteristics of the flow field and compression wave around the high speed train which Is entering into a tunnel. The numerical scheme of AF + ADI was used to efficiently solve Navier-Stokes equations in the curvilinear coordinate system. The vortex formation around the nose region was found and the generation of compression wave due to the blockage effects was observed ahead of the train in the form of plane wave. The three dimensional characteristics of the flow field compared to the analytic results were discussed in detail. The variation of pressure of tunnel wall surface and velocity profile of the train are identified as the train enters into a tunnel. The changes in aerodynamic forces and streamlines of each specific sections are also discussed and presented.

• Journal of computational fluids engineering
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• v.5 no.3
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• pp.23-31
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• 2000

The three-dimensional unsteady compressible Full Navier-Stokes equation solver with sliding multi-block method has been applied to analyze three dimensional characteristics of the viscous flow field and compression wave around the high speed train which is entering into a tunnel. The numerical scheme of AF + ADI was used to efficiently solve Navier-Stokes equations in the curvilinear coordinate system. The vortex formation owing to the viscous interaction around the train was found and the generation of compression wave due to the blockage effects was observed ahead of the train in the form of plane wave. The three dimensional characteristics of the flow field compared to the analytic results were discussed in detail. The variation of pressure of tunnel wall surface and velocity profile of the train are identified as the train enters into a tunnel. The changes in aerodynamic forces and streamlines of each specific sections are also discussed.

• The Transactions of the Korea Information Processing Society
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• v.2 no.4
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• pp.535-542
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• 1995

In this paper we present two preconditioners for solving large sparse linear systems arising from elliptic partial differential equations on massively parallel machines, such as the CM-5. Most massively parallel machines do heavily rely on the message-passing for the interprocessor communications. but according to the current manufacturing standards the cost of communications is very high compared to that of floating point arithmetic computations. Due to this we need an algorithm which minimizes the amount of interprocessor communication on the massively parallel machines. We will show that Block SOR(Successive Over Relaxation) method coupled with the multi-coloring technique is one of such preconditioner on the massively parallel machines, by conducting experiments in the CM-5. Also, we implemented the ADI(Alternation Direction Implicit) method in the CM-5, which has been conventionally one of the most powerful parallel preconditioner. Our experiment shows that Block SOR method coupled with the multi-coloring technique could yield a speedup with 50% efficiency with the range of number of processors form 16 to 512 for a matrix with dimension 512x512. On the other hand, the ADI method shows a very poor performance.

• The Korean Journal of Pain
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• v.14 no.2
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• pp.193-198
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• 2001

Background: Anterior atlantoaxial subluxation (AAS) is a frequent phenomenon in rheumatoid arthritis (RA). AAS compresses the C2 ganglion or nerve and is a cause of posterior neck pain or occipital headache. Methods: We selected RA patients that had developed posterior neck pain or occipital headache caused by AAS. AAS was diagnosed by an increase of ADI (atlantodental interval). A distance of 3 mm or more was considered significant. Patients with vertical subluxation or symptoms suggestive of myelopathy were excluded. Before C2 RF ganglionotomy, we proceeded with a C2 ganglion block or greater occipital nerve block used by local anesthetics. For C2 RF ganglionotomy, the patient was placed in the supine position on a fluoroscopic table. A 100 mm, 4 mm active tip electrode was chosen. Following sensory stimulation at 0.2 to 0.6 V, the lesion was performed at a temperature of $60^{\circ}C$ to $65^{\circ}C$ for 60 sec. We followed up the patient after 6 months later. Results: All cases were female and the average duration of RA was 8.5 years. The duration of posterior neck pain or occipital headache was 1-8 months. The average ADI was 4.2 mm and the McGregor index was 3.3 mm on the average. In all cases, the score on the 4 point Likert scale was 4 (pain free) during the follow-up period. Conclusions: We found that the occipital headache or posterior neck pain caused by AAS in rheumatoid arthritis patients was alleviated over a short term follow up. C2 RF ganglionotomy is suggested as an effective palliative treatment for AAS in RA patients.

• Journal of Industrial Technology
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• v.17
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• pp.183-189
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• 1997

The computation of the flow around a supercritical airfoil with a divergent trailing edge(DTE) modification(DLBA 243) is compared to that of original supercritical airfoil(DLBA 186). For this computation, Reynolds-Averaged Navier-Stokes equations are solved with a linearized block implicit ADI method and a mixing length turbulence model. Results show the effects of the shock and separated flow regions on drag reduction due to DTE modification. Results also show that DTE modification accelerates the boundary layer flow near the trailing edges which has an effect similar to a chordwise extension that increases circulation and is consistent with the calculated increase in the recirculation region in the wake. Airfoil with DTE modification achieves the same lift coefficient at a lower incidence and thus at a lower drag coefficient, so that lift-to-drag ratio is increased in transonic cruise conditions compared to the original airfoil. The reduction in drag due to DTE modification is associated with weakening of shock strength and delay of shock which is greater than the increase in base drag.

• 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.

• 한국전산유체공학회:학술대회논문집
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• 2005.04a
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• pp.123-127
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• 2005

The numerical analyses of the complicated flows are widely attempted in these days. Because of the enormous demanding memory and calculation time, parallel processing is used for these problems. In order to obtain calculation efficiency, it is important to choose proper domain decomposition technique and numerical algorithm. In this research we enhanced the efficiency of the CFDS code developed by ADD, using parallel computation and newly developed numerical algorithms. For the huge amount of data transfer between blocks non-blocking method is used, and newly developed data transfer algorithm is used for non-aligned block interface. Recently developed RoeM scheme is adpoted as a spatial difference method, and AF-ADI and LU-SGS methods are used as a time integration method to enhance the convergence of the code. Analyses of the flows around the ONERA M6 wing and the high angle of attack missile configuration are performed to show the efficiency improvement.