• Nuclear Engineering and Technology
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• v.54 no.4
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• pp.1195-1205
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• 2022

Recent developments on spectral diffusion algorithms, i.e., algorithms which exploit the projection of the solution on the eigenfunctions of the Laplacian operator, demonstrated their effective applicability in fast transient conditions. Nevertheless, the numerical error introduced by these algorithms, together with the uncertainties associated with model parameters, may impact the reliability of the predictions on short-lived volatile fission product release from nuclear fuel. In this work, we provide an upper bound on the numerical error introduced by the presented spectral diffusion algorithm, in both constant and time-varying conditions, depending on the number of modes and on the time discretization. The definition of this upper bound allows introducing a methodology to a priori bound the numerical error on short-lived volatile fission product retention.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.603-618
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• 2022

In this paper, a numerical solution of the generalized diffusion equation with a delay has been obtained by a numerical technique based on the Galerkin finite element method by applying the cubic B-spline basis functions. The time discretization process is carried out using the forward Euler method. The numerical scheme is required to preserve the delay-independent asymptotic stability with an additional restriction on time and spatial step sizes. Both the theoretical and computational rates of convergence of the numerical method have been examined and found to be in agreement. As it can be observed from the numerical results given in tables and graphs, the proposed method approximates the exact solution very well. The accuracy of the numerical scheme is confirmed by computing L₂ and L_∞ error norms.

• Korea-Australia Rheology Journal
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• v.19 no.4
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• pp.211-219
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• 2007

Here we demonstrate complex transient behavior of viscoelastic liquid described numerically with the Leonov model in straight and contraction channel flow domains. Finite element and implicit Euler time integration methods are employed for spatial discretization and time marching. In order to stabilize the computational procedure, the tensor-logarithmic formulation of the constitutive equation with SUPG and DEVSS algorithms is implemented. For completeness of numerical formulation, the so called traction boundaries are assigned for flow inlet and outlet boundaries. At the inlet, finite traction force in the flow direction with stress free condition is allocated whereas the traction free boundary is assigned at the outlet. The numerical result has illustrated severe forward-backward fluctuations of overall flow rate in inertial straight channel flow ultimately followed by steady state of forward flow. When the flow reversal occurs, the flow patterns exhibit quite complicated time variation of streamlines. In the inertialess flow, it takes much more time to reach the steady state in the contraction flow than in the straight pipe flow. Even in the inertialess case during startup contraction flow, quite distinctly altering flow patterns with the lapse of time have been observed such as appearing and vanishing of lip vortices, coexistence of multiple vortices at the contraction comer and their merging into one.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.13 no.4
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• pp.1895-1899
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• 2012

Formulation of finite difference method for analyzing consolidation were carried out. It can be seen that the differences in settlement with time obtained by FDM and Terzaghi method are diminished by fine discretization of time increment. Excess pore pressures predicted by the derived finite difference equation were same as those calculated by Olson's method. Predicted time-settlement behavior from the derived finite difference method were almost same as those calculated by Terzaghi's method and Olson's method. Analysis results obtained from the assumed multi-step time dependent loading are thought to be reasonable.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.5 s.176
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• pp.1075-1083
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• 2000

The prediction of the inelastic behavior of the structure is an essential part of reliability assessment procedure, because most of the failures are induced by the inelastic deformation, such as creep and plastic deformation. During decades, there has been much progress in understanding of the inelastic behavior of the materials and a lot of inelastic constitutive equations have been developed. These equations consist of the definition of inelastic strain and the evolution of the state variables introduced to quantify the irreversible processes occurred in the material. With respect to the definition of the inelastic strain, the inelastic constitutive models can be categorized into elastoplastic model, unified viscoplastic model and separated viscoplastic model and the different integration methods have been applied to each category. In the present investigation, the generalized integration method applicable for various types of constitutive equations is developed and implemented into ABAQUS by means of UMAT subroutine. The solution of the non-linear system of algebraic equations arising from time discretization with the generalized midpoint rule is determined using line-search technique in combination with Newton method. The strategy to control the time increment for the improvement of the accuracy of the numerical integration is proposed. Several numerical examples are considered to demonstrate the efficiency and applicability of the present method. The prediction of the inelastic behavior of the structure is an essential part of reliability assessment procedure, because most of the failures are induced by the inelastic deformation, such as creep and plastic deformation. During decades, there has been much progress in understanding of the inelastic behavior of the materials and a lot of inelastic constitutive equations have been developed. These equations consist of the definition of inelastic strain and the evolution of the state variables introduced to quantify the irreversible processes occurred in the material. With respect to the definition of the inelastic strain, the inelastic constitutive models can be categorized into elastoplastic model, unified viscoplastic model and separated viscoplastic model and the different integration methods have been applied to each category. In the present investigation, the generalized integration method applicable for various types of constitutive equations is developed and implemented into ABAQUS by means of UMAT subroutine. The solution of the non-linear system of algebraic equations arising from time discretization with the generalized midpoint rule is determined using line-search technique in combination with Newton method. The strategy to control the time increment for the improvement of the accuracy of the numerical integration is proposed. Several numerical examples are considered to demonstrate the efficiency and applicability of the present method.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.46 no.2
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• pp.52-60
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• 2009

This paper proposes a digital controller for a nonlinear multi-input/multi-output(MIMO) system with time-delayed input. A nonlinear system with multi-input time delay is discretized using Taylor's discretization method, and the discretized system can be converted into a general nonlinear system. Consequently, general nonlinear controller synthesis can be applied to the discretized time-delay system We adopted MAC controller synthesis and verified the performance of the proposed method by conducting computer simulations. The results of the simulation showed that the proposed controller synthesis performs well and the proposed method is useful for controlling a nonlinear time-delay system.

• Korea-Australia Rheology Journal
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• v.19 no.4
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• pp.233-242
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• 2007

We performed a numerical investigation to find out the optimal choice of the spatial discretization in the distributed-Lagrangian-multiplier/fictitious-domain (DLM/FD) method for the solid/fluid interaction problem. The elastic solid bar attached on the bottom in a pressure-driven channel flow of a Newtonian fluid was selected as a model problem. Our formulation is based on the scheme of Yu (2005) for the interaction between flexible bodies and fluid. A fixed regular rectangular discretization was applied for the description of solid and fluid domain by using the fictitious domain concept. The hydrodynamic interaction between solid and fluid was treated implicitly by the distributed Lagrangian multiplier method. Considering a simplified problem of the Stokes flow and the linearized elasticity, two numerical factors were investigated to clarify their effects and to find the optimum condition: the distribution of Lagrangian multipliers and the solid/fluid interfacial condition. The robustness of this method was verified through the mesh convergence and a pseudo-time step test. We found that the fluid stress in a fictitious solid domain can be neglected and that the Lagrangian multipliers are better to be applied on the entire solid domain. These results will be used to extend our study to systems of elastic particle in the Stokes flow, and of particles in the viscoelastic fluid.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.4 no.3
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• pp.27-42
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• 1984

The complexity and expensiveness of water resources projects have made optimum operation and design by computer-based techniques of increasing interest in recent years. Water resources problems in real world need many decisions under numerous constraints. In addition there are nonlinearities in the state and return function. This mathematical and technical troublesome must be overcome so that the optimum operation polices are determined. Then traditional dynamic optimization method encountered two major-cruxes: variable discretization and appearance of constraints. Even several recent methods which based on the Differential Dynamic Programming(DDP) have some difficulties in handling of constraints. This paper has presented New DDP which is applicable to multi-reservoir control. It is intended that the method suggested here is superior to abailable alternatives. This belief is supported by analysis and experiments(New DDT does not suffer course of dimensionality and requires no discretization and is able to handle easily all constraints nonlinearity).

• Journal of Korea Society of Industrial Information Systems
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• v.23 no.3
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• pp.49-57
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• 2018

In a previous article, for analyzing a stochastic activity network, Cho proposed a method for estimating the moments (mean, variance, skewness, kurtosis) of the project completion time under the assumption that the durations of activities are independently and normally distributed. Developed in the present article is a method for estimating those moments for stochastic activity networks which allow any type of distributions for activity durations. The proposed method uses the moment matching approach to discretize the distribution function of activity duration, and then a discrete inverse-transform method to determine activity durations to be used for calculating the project completion time. The proposed method can be easily applied to large-sized activity networks, and computationally more efficient than Monte Carlo simulation, and its accuracy is comparable to that of Monte Carlo simulation.

• Journal of the Korea Society of Computer and Information
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• v.20 no.12
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• pp.67-74
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• 2015

The heat conduction equation, a type of a Poisson equation which can be applied in various areas of engineering is calculating its value with the iteration method in general. The equation which had difference discretization of the heat conduction equation is the simultaneous equation, and each line has the characteristic of expressing in sparse matrix of the equivalent number of none-zero elements with neighboring grids. In this paper, we propose a data structure for sparse matrix that can calculate the value faster with less memory use calculate the heat conduction equation. To verify whether the proposed data structure efficiently calculates the value compared to the other sparse matrix representations, we apply the representative iteration method, CG (Conjugate Gradient), and presents experiment results of time consumed to get values, calculation time of each step and relevant time consumption ratio, and memory usage amount. The results of this experiment could be used to estimate main elements of calculating the value of the general heat conduction equation, such as time consumed, the memory usage amount.