• East Asian mathematical journal
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• 제40권1호
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• pp.109-118
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• 2024

This paper proposes a numerical method based on domain decomposition to find approximate solutions for one-dimensional convection-diffusion equations with Neumann boundary conditions. First, the equations are transformed into convection-diffusion equations with Dirichlet conditions. Second, the author introduces the Prediction/Correction Domain Decomposition (PCDD) method and estimates errors for the interface prediction scheme, interior scheme, and correction scheme using known error estimations. Finally, the author compares the PCDD algorithm with the fully explicit scheme (FES) and the fully implicit scheme (FIS) using three examples. In comparison to FES and FIS, the proposed PCDD algorithm demonstrates good results.

• 한국전산유체공학회지
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• 제4권1호
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• pp.8-18
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• 1999

In devising a numerical approximation for the convective spatial transport of a fluid mechanical quantity, it is noted that the convective motion of a scalar quantity occurs in one-way, or from upstream to downstream. This consideration leads to a new scheme termed a pure upwind difference scheme (PUDS) in which an estimated value for a fluid mechanical quantity at a control surface is not influenced from downstream values. The formal accuracy of the proposed scheme is third order accurate. Two typical benchmark problems of a wall-driven fluid flow in a square cavity and a buoyancy-driven natural convection in a tall cavity are computed to evaluate performance of the proposed method. for comparison, the widely used simple upwind scheme, power-law scheme, and QUICK methods are also considered. Computation results are encouraging: the proposed PUDS sensitized to the convection direction produces the least numerical diffusion among tested convection schemes, and, notable improvements in representing recirculation of fluid stream and spatial change of a scalar. Although the formal accuracy of PUDS and QUICK are the same, the accuracy difference of approximately a single order is observed from the revealed results.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2002년도 추계 학술대회논문집
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• pp.64-69
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• 2002

A numerical study has been peformed for evaluation of convection schemes for thermal hydraulic analysis in a liquid metal reactor Four convection schemes, HYBRID, QUICK, SMART and HLPA included in the CFX-4 code are considered. The performances of convection schemes are evaluated by applying them to the five test problems. The accuracy, stability and convergence are tested. It is shown that the HYBRID scheme is too diffusive, and the QUICK scheme exhibits overshoots and undershoots, and the SMART scheme shows convergence oscillations, and the HLPA scheme preserves the boundedness without causing convergence oscillations. The accuracies of SMART, QUICK and HLPA schemes are comparable. Thus, the use of HLPA scheme is highly recommended for thermal hydraulic analysis in a liquid metal reactor.

• 설비공학논문집
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• 제2권1호
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• pp.63-73
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• 1990

A numerical analysis of initial unsteady state flow and heat transfer in an enclosed cavity has been performed by the Modified QUICK Scheme. The stable QUICK Scheme which modified the coefficient always to be positive is included in this numerical analysis. The implicit method is applied to solve the unsteady state flow; between iterations the PISO (Pressure - Implicit with Splitting of Operators) algorithm is employed to correct and update the velocity and pressure fields on a staggered grid. The accuracy of the Modified QUICK Scheme is proved by applying fewer grid systems than those which Ghia et al. and Davis applied. The initial unsteady mixed convection in an enclosed cavity is analyzed using the above numerical procedure. This study focuses on the development of the large main vortex and secondary vortex in forced convection, the effects of the Rayleigh Number in natural convection and the relative direction of the forced and natural convection.

• Journal of applied mathematics & informatics
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• 제36권1_2호
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• pp.135-154
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• 2018

In this paper, an almost second order overlapping Schwarz method for singularly perturbed third order convection-diffusion type problem is constructed. The method splits the original domain into two overlapping subdomains. A hybrid difference scheme is proposed in which on the boundary layer region we use the combination of classical finite difference scheme and central finite difference scheme on a uniform mesh while on the non-layer region we use the midpoint difference scheme on a uniform mesh. It is shown that the numerical approximations which converge in the maximum norm to the exact solution. We proved that, when appropriate subdomains are used, the method produces convergence of second order. Furthermore, it is shown that, two iterations are sufficient to achieve the expected accuracy. Numerical examples are presented to support the theoretical results. The main advantages of this method used with the proposed scheme are it reduce iteration counts very much and easily identifies in which iteration the Schwarz iterate terminates.

• Journal of applied mathematics & informatics
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• 제36권3_4호
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• pp.181-203
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• 2018

In this paper, we have constructed an overlapping Schwarz method for singularly perturbed second order convection-diffusion equations. The method splits the original domain into two overlapping subdomains. A hybrid difference scheme is proposed in which on the boundary layer region we use the central finite difference scheme on a uniform mesh while on the non-layer region we use the mid-point difference scheme on a uniform mesh. It is shown that the numerical approximations which converge in the maximum norm to the exact solution. When appropriate subdomains are used, the numerical approximations generated from the method are shown to be first order convergent. Furthermore it is shown that, two iterations are sufficient to achieve the expected accuracy. Numerical examples are presented to support the theoretical results. The main advantages of this method used with the proposed scheme is it reduces iteration counts very much and easily identifies in which iteration the Schwarz iterate terminates.

• Journal of Mechanical Science and Technology
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• 제20권10호
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• pp.1773-1778
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• 2006

Steady-state natural convection heat transfer characteristics from cylinders in a multiply-connected bounded region are clarified. A spectral finite difference scheme (spectral decomposition of the system of partial differential equations, semi-implicit time integration) is applied in numerical analysis, with a boundary-fitted conformal coordinate system through a Jacobian elliptic function with a successive transformation to formulate a system of governing equations in terms of a stream function, vorticity and temperature. Multiplicity of the domain is expressed explicitly.

• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.491-505
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• 2022

This paper is concerned with singularly perturbed convection-diffusion parabolic partial differential equations which have time-delayed. We used the Crank-Nicolson(CN) scheme to build a fitted operator to solve the problem. The underling method's stability is investigated, and it is found to be unconditionally stable. We have shown graphically the unstableness of CN-scheme without fitting factor. The order of convergence of the present method is shown to be second order both in space and time in relation to the perturbation parameter. The efficiency of the scheme is demonstrated using model examples and the proposed technique is more accurate than the standard CN-method and some methods available in the literature, according to the findings.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2000년도 춘계 학술대회논문집
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• pp.33-38
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• 2000

A Numerical study of laminar vortex-shedding past a circular cylinder has been performed widely by many researchers. Many factors, such as numerical technique and domain size, number and shape of grid, affected predicting vortex shedding and Strouhal number. In the present study, the effect of convection scheme, time discretization methods and grid dependence were investigated. The present paper presents the finite volume solution of unsteady flow past circular cylinder at Re=200, 400. The Strouhal number was predicted using UDS, CDS, Hybrid, Power-law, LUDS, QUICK scheme for convection term, implicit and crank-nicolson methods for time discretization. The grid dependence was investigated using H-type mesh and O-type mesh. It also studied that the effect of mesh size of the nearest adjacent grid of circular cylinder. The effect of convection scheme is greater than the effect of time discretization on predicting Strouhal. It has been found that the predicted Strouhal number changed with mesh size and shape.

• 한국전산유체공학회지
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• 제11권1호
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• pp.36-42
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• 2006

The existing numerical approximations of convection flux, especially the spatial higher-order difference schemes, in unstructured cell-centered finite volume methods are examined in detail with each other and evaluated with respect to the accuracy through their application to a 2-D benchmark problem. Six higher-order schemes are examined, which include two second-order upwind schemes, two central difference schemes and two hybrid schemes. It is found that the 2nd-order upwind scheme by Mathur and Murthy(1997) and the central difference scheme by Demirdzic and Muzaferija(1995) have more accurate prediction performance than the other higher-order schemes used in unstructured cell-centered finite volume methods.