• Journal of applied mathematics & informatics
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• 제8권2호
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• pp.371-386
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• 2001

In this work we investigate the finite element preconditioning method for the $C^1$-cubic spline collocation discretizations for an elliptic operator A defined by $Au := -{\Delta}u + a_1u_x+a_2u_y+a_0u$ in the unit square with some boundary conditions. We compute the condition number and the numerical solution of the preconditioning system for the several example problems. Finally, we compare the this preconditioning system with the another preconditioning system.

• 한국전산유체공학회지
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• 제15권2호
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• pp.55-61
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• 2010

A dependence of weighting parameter in preconditioning method for solving low Mach number flow with incompressible flow nature is investigated. The present preconditioning method employs a finite-difference method applied Roe‘s flux difference splitting approximation with the MUSCL-TVD scheme and 4th-order Runge-Kutta method in curvilinear coordinates. From the computational results of benchmark flows through a 2-D backward-facing step duct it is confirmed that there exists a suitable value of the weighting parameter for accurate and stable computation. A useful method to determine the weighting parameter is introduced. With this method, high accuracy and stable computational results were obtained for the flow with low Mach number in the range of Mach number less than 0.3.

• 한국군사과학기술학회지
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• 제9권2호
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• pp.152-160
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• 2006

Time marching methods are well-suited for high speed compressible flow computations. However, it is well known that the time marching methods suffer a slow down in convergence due to disparity in Eigenvalues. A local preconditioning method is one of numerical methods to enhance convergence characteristics of low mach number flows by modifying Eigenvalues of the governing equations. In this paper, the local preconditioning method of Weiss is applied to a 2 dimensional Navier-Stokes code and the efficiency of the preconditioning method is shown through a number of computational examples.

• Journal of applied mathematics & informatics
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• 제6권2호
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• pp.523-538
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• 1999

A new preconditioning method is investigated to reduce the roundoff error in computing derivatives using Chebyshev col-location methods(CCM). Using this preconditioning causes ration of roundoff error of preconditioning method and CCm becomes small when N gets large. Also for accuracy enhancement of differentiation we use a domain decomposition approach. Error analysis shows that for this domain decomposition method error reduces proportional to the length of subintervals. Numerical results show that using domain decomposition and preconditioning simultaneously gives super accu-rate approximate values for first derivative of the function and good approximate values for moderately high derivatives.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2009년 춘계학술대회논문집
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• pp.269-276
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• 2009

The local preconditioning method has both robust convergence and accurate solutions by using local flow properties for parameters in the preconditioning matrix. Preconditioning methods have been very effective to low speed inviscid flows. In the viscous and turbulent flows, deterioration of convergence should be overcame on the high aspect ratio grids to get better convergence and accuracy. In the present study, the local time stepping and min-CFL/max-VNN definitions are applied to compare the results and we propose the method that switches between two methods. The min-CFL definition is applied for inviscid flow problems and the min-CFL/max-VNN definition is implemented to viscous and turbulent flow problems.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2004년도 추계 학술대회논문집
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• pp.7-14
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• 2004

It is well known that preconditioning methods are efficient for convergence acceleration at compressible low Mach number flows. In this study, the original Euler equations and three preconditioners nondimensionalized differently are implemented in two dimensional inviscid bump flows using the 3rd order MUSCL and DADI schemes as flux discretization and time integration respectively. The multigrid and local time stepping methods are also used to accelerate the convergence. The test case indicates that a properly modified local preconditioning technique involving concepts of a global preconditioning one produces Mach number independent convergence. Besides, an asymptotic analysis for properties of preconditioning methods is added.

• 대한기계학회논문집B
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• 제22권6호
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• pp.788-802
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• 1998

A numerical method using dual time stepping and preconditioning procedure for efficient computations of unsteady low speed compressible flow problems is developed. The time-derivative preconditioning method which is valid at low speed flow conditions cannot maintain temporal accuracy because of the modification of the time-derivative term in Navier-Stokes equations. The dual time stepping procedure is incorporated to enable the time accurate computations and this procedure introduces a pseudo-time derivative in addition to the physical time derivative. At a given physical time, an inner iteration can be carried out until a steady state in pseudo-time is achieved. This will effectively yield a time accurate solution. Computational capabilities of the above algorithm are demonstrated through computation of a variety of practical fluid flows and it is shown that the algorithms is efficient in the essentially incompressible flows and low Mach number compressible flows with heat source.

• 대한기계학회논문집
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• 제18권7호
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• pp.1840-1850
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• 1994

Enhancement of numerical algorithms for low speed compressible flow will be considered. Contemporary time-marching algorithm has been widely accepted and applied as the method of choice for transonic, supersonic and hypersonic flows. In the low Mach number regime, time-marching algorithms do not fare as well. When the velocity is small, eigenvalues of the system of compressible equations differ widely so that the system becomes very stiff and the convergence becomes very slow. This characteristic can lead to difficulties in computations of many practical engineering problems. In the present approach, the time-derivative preconditioning method will be used to control the eigenvalue stiffness and to extend computational capabilities over a wide range of flow conditions (from very low Mach number to supersonic flow). Computational capabilities of the above algorithm will be demonstrated through computation of a variety of practical engineering problems.

• 한국항공우주학회지
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• 제33권8호
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• pp.8-17
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• 2005

저속 압축성 유동에서 사용하는 예조건화 기법은 수렴성 증진에 효과적이다. 본 연구에서는 일반적인 오일러 지배 방정식과 각각 다르게 무차원화한 세 가지 종류의 예조건화 기법을 3차 공간 정확도의 MUSCL, DADI, 다중 격자, 국소 시간 전진 기법을 이용하여 2차원 비점성 bump 유동에 적용하였다. 결과적으로 국소 예조건화 기법에 전역 예조건화 기법의 압력 항 무차원화 방법을 적용하면, 마하수에 무관한 수렴 특성을 얻을 수 있다. 또한, 점근해석을 이용하여 각 예조건화 기법의 특성에 대해 언급하였다.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2004년도 춘계 학술대회논문집
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• pp.91-98
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• 2004

In two dimensional incompressible flows, a preconditioning technique called Hierarchical Iterative Procedure(HIP) has been implemented on a stabilized finite element formulation. The stabilization has been peformed by a modified residual method proposed by Illinca et. al.[3]. The stabilization which is necessary to escape from the LBB constraint renders an equal order formulation. In this paper, we increased the order of interpolation whithin an element up to cubic. The conjugate gradient squared(CGS) method is used for the outer iteration, and the HIP for the preconditioning for the incompressible Navier-Stokes equation. The hierarchical elements has been used to achieve a higher order accuracy in fluid flow analyses, but a proper efficient iterative procedure for higher order finite element formulation has not been available so far. The numerical results by the present HIP for the lid driven cavity flow showed the present procedure to be stable, very efficient and useful in flow analyses in conjunction with hierarchical elements.