• 대한수학회지
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• 제58권3호
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• pp.553-569
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• 2021

In this paper, we present and analyze a fully discrete numerical method for solving the time-fractional diffusion wave equation: ∂^β_tu - div(a∇u) = f, 1 < β < 2. We first construct a difference formula to approximate ∂^β_tu by using an interpolation of derivative type. The truncation error of this formula is of O(△t^2+δ-β)-order if function u(t) ∈ C^2,δ[0, T] where 0 ≤ δ ≤ 1 is the Hölder continuity index. This error order can come up to O(△t^3-β) if u(t) ∈ C³ [0, T]. Then, in combinination with the linear finite volume discretization on spatial domain, we give a fully discrete scheme for the fractional wave equation. We prove that the fully discrete scheme is unconditionally stable and the discrete solution admits the optimal error estimates in the H¹-norm and L₂-norm, respectively. Numerical examples are provided to verify the effectiveness of the proposed numerical method.

• Nuclear Engineering and Technology
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• 제51권5호
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• pp.1181-1194
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• 2019

A new moving-mesh Finite Volume Method (FVM) for the efficient solution of the two-dimensional neutron diffusion equation is introduced. Many other moving-mesh methods developed to solve the neutron diffusion problems use a relatively large number of sophisticated mathematical equations, and so suffer from a significant complexity of mathematical calculations. In this study, the proposed method is formulated based on simple mathematical algebraic equations that enable an efficient mesh movement and CV deformation for using in practical nuclear reactor applications. Accordingly, a computational framework relying on a new moving-mesh FVM is introduced to efficiently distribute the meshes and deform the CVs in regions with high gradient variations of reactor power. These regions of interest are very important in the neutronic assessment of the nuclear reactors and accordingly, a higher accuracy of the power densities is required to be obtained. The accuracy, execution time and finally visual comparison of the proposed method comprehensively investigated and discussed for three different benchmark problems. The results all indicated a higher accuracy of the proposed method in comparison with the conventional fixed-mesh FVM.

• 한국전산유체공학회지
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• 제15권2호
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• pp.71-78
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• 2010

As a step toward accurate prediction of droplet impingement and ice accretion on aircraft, an Eulerian-based droplet impingement and ice accretion code for air flows around an airfoil containing water droplets is developed. A CFD solver based on the finite volume method was also developed to solve the clean airflow. The finite-volume-based approach for simulating droplet impingement on an airfoil was employed owing to its compatibility with the CFD solver and robustness. For ice accretion module, a simple model based on the control volume is combined with the droplet impingement module that provides the collection efficiency. To validate the present code, it is compared with NASA Glenn IRT (Icing Research Tunnel) experimental data and other well-known icing codes such as LEWICE and FENSAP-ICE. It is shown that the collection efficiency and shape of ice accretion are in good agreement with previous experimental and simulation results.

• International Journal of Aerospace System Engineering
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• 제2권2호
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• pp.40-43
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• 2015

A hybrid mesh based finite volume compressible flow code (PolySim) has been developed recently. Instead of the simple average method for the gradients of variables at each face, the volume average is applied for the calculation of the viscous flux. What is more, an improved Green Gauss method for the calculation of the gradient is also presented. These two techniques will improve both the accuracy and robustness of the code. The aerodynamic performance of this in-house cell centered code is examined by several widely-used bench-mark test cases. These cases include flows over flat plate and RAE 2822 etc. The comparisons on results between calculation and experiment are conducted. They show that the code can produce good numerical results which agree well with the corresponding experiment data.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 추계학술대회논문집B
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• pp.551-556
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• 2001

The filling pattern technique based on the finite element method and Eulerian mesh advancement approach has been developed to analyze incompressible transient viscous flow with free surfaces. The governing equation for flow analysis is Navier-Stokes equation including inertia and gravity effects. The penalty and predictor-corrector methods are used effectively for finite element formulation. The flow front surface and the volume inflow rate are calculated using the filling pattern technique to select an adequate pattern among four filling patterns at each triangular control volume. Using the proposed numerical technique, the collapse of a dam has been analyzed to predict flow phenomenon of fluid and the predicted front positions versus time have been compared with the reported experimental result.

• 한국수자원학회논문집
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• 제31권3호
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• pp.279-290
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• 1998

충격파의 높이나 속도는 홍수제어조작이나 수로벽과 빠른 유속을 가지는 하천에서 교량의 설계에 중요한 자료가 된다. 따라서 광범위한 조건에서 흐름의 불연속면을 모의할 수 있는 수치모형이 요구된다. 본 연구에서는 천수방정식을 지배방정식으로 한 Godunov 형 유한체적법 모형을 개발하였다. Riemann 해법으로 Roe(1981)의 해법이 사용된다. 이 모형은 본 연구에서 비구조적격자(unstructured grids)를 사용하기 위해 개발된 수정 MUSCL을 도입하였다. 양해법을 쓰는 본 모형은 시간간격을 자동 계산한다. 개발된 모형을 전형적인 이차원 댐 붕괴파 모의, 수리모형 실험에서 행해진 붕괴파 모의, 그리고 수리모형 실험에서 행해진 만곡수로에서의 정상상태 모의 등에 적용하였다. 그 적용결과에 의해 다음과 같이 결론을 내었다. 1)유한체적법은, 충격파 모의를 위한 수치해석 기법인 Godunov 형 방법과 잘 결합될 수 있기 때문에 충격파를 모의하기에 적당한 방법이다. 2)수정 MUSCL과 결합된 유한체적법 모형이 충격파를 잘 포착함으로써 수정 MUSCL의 적용성이 입증되었다.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2003년도 The Fifth Asian Computational Fluid Dynamics Conference
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• pp.6-6
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• 2003

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 1994년도 추계학술대회 논문집
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• pp.133-140
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• 1994

In this paper, we have proposed a new method to determine the initial billet for the forged products using a function approximation in neural networks. the architecture of neural network is a three-layer neural network and the back propagation algorithm is employed to train the network. By utilizing the ability of function approximation of neural network, an optimal billet is determined by applying nonlinear mathematical relationship between shape ratio in the initial billet and the final products. A volume of incomplete filling in the die is measured by the rigid-plastic finite element method. The neural network is trained with the initial billet shape ratio and that of the un-filled volume. After learning, the system is able to predict the filling region which are exactly the same or slightly different to results of finite element method. It is found that the prediction of the filling shape ratio region can be made successfully and the finite element method results are represented better by the neural network.

• 대한기계학회논문집
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• 제18권4호
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• pp.1009-1018
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• 1994

An attempt is made to develop a kind of hybrid numerical method for computations of the thermal stresses during a solidification process. In this algorithm, the phase-change heat transfer analysis is perrformed by a finite volume method(FVM) and the thermal stress analysis in a solidifying body by a finite element method(FEM). The temperatures at the grid points calculated in the heat transfer analysis are transferred to those of gauss points in elements by a bi-cubic surface patch technique for the thermal stress analysis. A hyperbolic-sine constitutive law is used to prescribe the inelastic strain rate of material. Results for the unidirectional solidification process of a pure aluminum are compared with those of others and shows good agreement.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2006년도 추계 학술대회논문집
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• pp.57-60
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• 2006

This paper presents an assessment of vertex-centered and cell-centered finite-volume methods on unstructured meshes. The results indicate that the vertex-centered method is more reliable than the cell-centered method.