• Bulletin of the Korean Mathematical Society
• /
• v.45 no.1
• /
• pp.191-205
• /
• 2008

In this paper, we construct the analytic solutions and numerical solutions for a two-dimensional Riemann problem for Burgers' equation. In order to construct the analytic solution, we use the characteristic analysis with the shock and rarefaction base points. We apply the composite scheme suggested by Liska and Wendroff to compute numerical solutions. The result is coincident with our analytic solution. This demonstrates that the composite scheme works pretty well for Burgers' equation despite of its simplicity.

• Journal of applied mathematics & informatics
• /
• v.13 no.1_2
• /
• pp.11-27
• /
• 2003

A fourth order in time and second order in space scheme using a finite-difference method is developed for the non-linear Boussinesq equation. For the solution of the resulting non-linear system a predictor-corrector pair is proposed. The method is analyzed for local truncation error and stability. The results of a number of numerical experiments for both the single and the double-soliton waves are given.

• Architectural research
• /
• v.13 no.1
• /
• pp.17-24
• /
• 2011

Isogeometric solution of Poisson equation is provided. NURBS (NonUniform B-spline Surface) is introduced to express both geometry of structure and unknown field of governing equation. The terms of stiffness matrix and load vector are consistently derived with very accurate geometric definition. The validity of the isogeometric formulation is demonstrated by using two numerical examples such as square plate and L-shape plate. From numerical results, the present solutions have a good agreement with analytical and finite element (FE) solutions with the use of a few cells in isogeometric analysis.

• Communications of the Korean Mathematical Society
• /
• v.22 no.4
• /
• pp.623-640
• /
• 2007

The Lotka-McKendrick model which describes the evolution of a single population is developed from the well known Malthus model. In this paper, we introduce the Lotka-McKendrick model. We approximate the solution to the model using hp-discontinuous Galerkin finite element method. The numerical results show that the presented hp-discontinuous Galerkin method is very efficient in case that the solution has a sharp decay.

• Journal of Ocean Engineering and Technology
• /
• v.14 no.1
• /
• pp.1-5
• /
• 2000

A numerical analysis for wave motion in the shallow water is presented. The method is based on potential theory. The fully nonlinear free surface boundary condition is assumed in an inner domain and this solution is matched along an assumed common boundary to a linear solution in outer domain. In two-dimensional problem Cauchy's integral theorem is applied to calculate the complex potential and its time derivative along boundary.

• Kyungpook Mathematical Journal
• /
• v.28 no.2
• /
• pp.177-183
• /
• 1988

In this work, two numerical schemes arc proposed for solving a general form of Cauchy problem. Here, the problem, to be defined, consists of a system of Volterra integro-differential equations. Picard's and Seiddl'a methods of successive approximations are ued to obtain the approximate solution. The convergence of these approximations is established and the rate of convergence is estimated in every case.

• The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
• /
• v.17 no.4
• /
• pp.377-381
• /
• 1988

Effects of thermal resistance of mold during freezing processes have been investigated. Saturated liquid is chosen to present one-dimensional quasi-steady solution and this solution is compared with numerical solutions. Front tracking finite element method has been applied for the numerical solutions. Results show that mold should be considered as well as phase change material except the cases when the very thin mold with relatively high thermal conductivity is used.

• Journal of applied mathematics & informatics
• /
• v.35 no.3_4
• /
• pp.277-302
• /
• 2017

In this paper, we have proposed a numerical method for Singularly Perturbed Boundary Value Problems (SPBVPs) of reaction-diffusion type of third order Ordinary Differential Equations (ODEs). The SPBVP is reduced into a weakly coupled system of one first order and one second order ODEs, one without the parameter and the other with the parameter ${\varepsilon}$ multiplying the highest derivative subject to suitable initial and boundary conditions, respectively. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference scheme. The weakly coupled system is decoupled by replacing one of the unknowns by its zero-order asymptotic expansion. Finally the present numerical method is applied to the decoupled system. In order to get a numerical solution for the derivative of the solution, the domain is divided into three regions namely two inner regions and one outer region. The Shooting method is applied to two inner regions whereas for the outer region, standard finite difference (FD) scheme is applied. Necessary error estimates are derived for the method. Computational efficiency and accuracy are verified through numerical examples. The method is easy to implement and suitable for parallel computing. The main advantage of this method is that due to decoupling the system, the computation time is very much reduced.

• Nuclear Engineering and Technology
• /
• v.55 no.9
• /
• pp.3301-3312
• /
• 2023

This study incorporates a high-fidelity transient analysis solver based on multigroup CMFD in the MOC code STREAM. Transport modeling with heterogeneous geometries of the reactor core increases computational cost in terms of memory and time, whereas the multigroup CMFD reduces the computational cost. The reactor condition does not change at every time step, which is a vital point for the utilization of CMFD. CMFD correction factors are updated from the transport solution whenever the reactor core condition changes, and the simulation continues until the end. The transport solution is adjusted once CMFD achieves the solution. The flux-weighted method is used for rod decusping to update the partially inserted control rod cell material, which maintains the solution's stability. A smaller time-step size is needed to obtain an accurate solution, which increases the computational cost. The adaptive step-size control algorithm is robust for controlling the time step size. This algorithm is based on local errors and has the potential capability to accept or reject the solution. Several numerical problems are selected to analyze the performance and numerical accuracy of parallel computing, rod decusping, and adaptive time step control. Lastly, a typical pressurized LWR was chosen to study the rod-ejection accident.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.12 no.8
• /
• pp.3374-3383
• /
• 2011

In this study, numerical analyses for slamming impact phenomena have been carried out using a 2-dimensional wedge shaped structure having finite deadrise angles. Fluid is assumed incompressible and entry speed of the structure is kept constant. Geo-reconstruct(or PLIC-VOF) scheme is used for the tracking of the deforming free surface. Numerical analyses are carried out for the deadrise angles of $10^{\circ}$, $20^{\circ}$ and $30^{\circ}$. For each deadrise angle, variations are made for the grid size on the wedge bottom and for the entry speed. The magnitude and the location of impact pressure and the total drag force, which is the summation of pressure distributed at the bottom of the structure, are analyzed. Results of the analyses are compared with the results of the Dobrovol'skaya similarity solutions, the asymptotic solution based on the Wagner method and the solution of Boundary Element Method(BEM).