• Nuclear Engineering and Technology
• /
• v.15 no.2
• /
• pp.98-109
• /
• 1983

A two-step alternating direction explicit method is developed to solve the space-dependent reactor kinetics equations in two space dimensions. As a special case in the general class of alternating direction implicit methods, this method is analysed for accuracy and stability. To test the validity of this method it is compared with the implicit-difference method used in the TWIGL program. It is shown that the two methods are closely related. The time dependent neutron fluxes of the pressurized water reactor (PWR), during control rod insertion, and, of the CANDU-PHW reactor, in case of postulated loss of coolant accident, are obtained from the numerical calculation results.

• 한국전산유체공학회:학술대회논문집
• /
• 2007.10a
• /
• pp.243-248
• /
• 2007

A three-dimensional (3D) unstructured hydrodynamic solver for transient two-phase flows has been developed. A two-fluid three-field model was adopted for the two-phase flows. The three fields represent a continuous liquid, an entrained liquid, and a vapour field. The hydrodynamic solver is for the 3D component of a nuclear system code and the component-scale analysis tools for transient two-phase flows. The finite volume method and unstructured grid are adopted, which are useful for the flows in a complicated geometry. The semi-implicit ICE (Implicit Continuous-fluid Eulerian) numerical scheme has been adapted to the unstructured non-staggered grid. This paper presents the numerical method and the preliminary results of the calculations. The results show that the numerical scheme is robust and predicts the phase change and the flow transitions due to boiling and flashing problems well.

• Transactions of the Korean Society of Automotive Engineers
• /
• v.6 no.3
• /
• pp.143-153
• /
• 1998

In this reaserch, a program for real time simulation of a vehicle is developed. This program uses relative coordinates to save the computation time and BDF(Backward Difference Formula) to integrate system variables. Numerical tests were performed for J-turn and Lane change steering, respectively. The validity of the program is proved by the ADAMS package. Numerical results showed that the proposed implicit method is more stable in carrying out the numerical integration for vehicle dynamics than the explicit method. Hardware requirements for real time simulation are suggested.

• Journal of The Korean Astronomical Society
• /
• v.40 no.4
• /
• pp.91-97
• /
• 2007

The Fokker-Planck (FP) model is one of the commonly used methods for studies of the dynamical evolution of dense spherical stellar systems such as globular clusters and galactic nuclei. The FP model is numerically stable in most cases, but we find that it encounters numerical difficulties rather often when the effects of tidal shocks are included in two-dimensional (energy and angular momentum space) version of the FP model or when the initial condition is extreme (e.g., a very large cluster mass and a small cluster radius). To avoid such a problem, we have developed a new integration scheme for a two-dimensional FP equation by adopting an Alternating Direction Implicit (ADI) method given in the Douglas-Rachford split form. We find that our ADI method reduces the computing time by a factor of ${\sim}2$ compared to the fully implicit method, and resolves problems of numerical instability.

• Journal of computational fluids engineering
• /
• v.14 no.4
• /
• pp.13-22
• /
• 2009

A two-phase (gas and liquid) flow analysis solver, named CUPID, has been developed for a realistic simulation of transient two-phase flows in light water nuclear reactor components. In the CUPID solver, a two-fluid three-field model is adopted and the governing equations are solved on unstructured grids for flow analyses in complicated geometries. For the numerical solution scheme, the semi-implicit method of the RELAP5 code, which has been proved to be very stable and accurate for most practical applications of nuclear thermal hydraulics, was used with some modifications for an application to unstructured non-staggered grids. This paper is concerned with the effects of interpolation schemes on the simulation of two-phase flows. In order to stabilize a numerical solution and assure a high numerical accuracy, the second-order upwind scheme is implemented into the CUPID code in the present paper. Some numerical tests have been performed with the implemented scheme and the comparison results between the second-order and first-order upwind schemes are introduced in the present paper. The comparison results among the two interpolation schemes and either the exact solutions or the mesh convergence studies showed the reduced numerical diffusion with the second-order scheme.

• Journal of Energy Engineering
• /
• v.17 no.4
• /
• pp.218-226
• /
• 2008

A component-scale two-phase analysis code has been developed for a realistic simulation of two-phase flow transients in a light water nuclear reactor component. In the code, a two-fluid three-field model is adopted and the governing equations are solved on an unstructured mesh. For the numerical solution scheme, the semi-implicit method used in the RELAP5 code was selected, which has been proved to be very stable and accurate for most of practical applications. However, some modifications were needed for its application to an unstructured non-staggered grid. This paper presents the modified semi-implicit numerical method for unstructured grid and the preliminary results of the calculations.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.22 no.4
• /
• pp.315-322
• /
• 2009

This paper presents a novel numerical method based on the extended moving least squares finite difference method(MLS FDM) for solving 1-D Stefan problem. The MLS FDM is employed for easy numerical modelling of the moving boundary and Taylor polynomial is extended using wedge function for accurate capturing of interfacial singularity. Difference equations for the governing equations are constructed by implicit method which makes the numerical method stable. Numerical experiments prove that the extended MLS FDM show high accuracy and efficiency in solving semi-infinite melting, cylindrical solidification problems with moving interfacial boundary.

• Journal of applied mathematics & informatics
• /
• v.8 no.1
• /
• pp.165-180
• /
• 2001

This paper presents a new difference scheme for numerical solution of stiff system of ODE’s. The present study is mainly motivated to develop an absolutely stable numerical method with a high order of approximation. In this work a double implicit A-stable difference scheme with the sixth order of approximation is suggested. Another purpose of this study is to introduce automatic choice of the integration step size of the difference scheme which is derived from the proposed scheme and the one step scheme of the fourth order of approximation. The algorithm was tested by means of solving the Kreiss problem and a chemical kinetics problem. The behavior of the gas explosive mixture (H₂+ O₂) in a closed space with a mobile piston is considered in test problem 2. It is our conclusion that a hydrogen-operated engine will permit to decrease the emitted levels of hazardous atmospheric pollutants.

• Proceedings of the KSME Conference
• /
• 2003.04a
• /
• pp.2005-2011
• /
• 2003

Introducing the interfacial pressure jump terms based on the surface tension into the momentum equations of two-phase two-fluid model, the system of governing equations is turned mathematically into the hyperbolic system. The eigenvalues of the equation system become always real representing the void wave and the pressure wave propagation speeds as shown in the previous manuscript. To solve the interfacial pressure jump terms with void fraction gradients implicitly, the conventional semi-implicit method should be modified as an intermediate iteration method for void fraction at fractional time step. This advanced semi-implicit method (ASIM) then becomes stable without conventional additive terms. As a consequence, including the interfacial pressure jump terms with the advanced semi-implicit method, the numerical solutions of typical two-phase problems can be more stable and sound than those calculated exclusively by using any other terms like virtual mass, or artificial viscosity.

• Journal of applied mathematics & informatics
• /
• v.29 no.3_4
• /
• pp.909-920
• /
• 2011

A regularized Newton method for nonlinear ill-posed problems is considered. In each Newton step an implicit iterative method with an appropriate stopping rule is proposed and analyzed. Under certain assumptions on the nonlinear operator, the convergence of the algorithm is proved and the algorithm is stable if the discrepancy principle is used to terminate the outer iteration. Numerical experiment shows the effectiveness of the method.