• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.27 no.6
• /
• pp.821-827
• /
• 2003

Fully developed turbulent flow in a square duct is numerically predicted with two nonlinear low-Reynolds-number ${\kappa}-{\varepsilon}$ models. Typical predicted quantities such as axial and secondary velocities, turbulent kinetic energy and Reynolds stresses are compared in detail with each other. It is found that the nonlinear low-Reynolds-number ${\kappa}-{\varepsilon}$ model adopted in a commercial code is unable to predict accurately duct flows involving turbulence-driven secondary motion with the prediction level of secondary flows one order less than that of the experiment.

• Steel and Composite Structures
• /
• v.38 no.5
• /
• pp.497-521
• /
• 2021

In this study, an effective numerical method is introduced for nonlinear inelastic analyses of rectangular concrete-filled steel tubular (CFST) frames for the first time. A steel-concrete composite fiber beam-column element model is developed that considers material, and geometric nonlinearities, and residual stresses. This is achieved by using stability functions combined with integration points along the element length to capture the spread of plasticity over the composite cross-section along the element length. Additionally, a multi-spring element with a zero-length is employed to model the nonlinear semi-rigid beam-to-column connections in CFST frame models. To solve the nonlinear equilibrium equations, the generalized displacement control algorithm is adopted. The accuracy of the proposed method is firstly verified by a large number of experiments of CFST members subjected to various loading conditions. Subsequently, the proposed method is applied to investigate the nonlinear inelastic behavior of rectangular CFST frames with fully rigid, semi-rigid, and hinged connections. The accuracy of the predicted results and the efficiency pertaining to the computation time of the proposed method are demonstrated in comparison with the ABAQUS software. The proposed numerical method may be efficiently utilized in practical designs for advanced analysis of the rectangular CFST structures.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.1
• /
• pp.219-244
• /
• 2020

In this paper, we approximate the solution of the coupled nonlinear Schrödinger equations by using a fully discrete finite element scheme based on the standard Galerkin method in space and implicit midpoint discretization in time. The proposed scheme guarantees the conservation of the total mass and the energy. First, a priori error estimates for the fully discrete Galerkin method is derived. Second, the existence of the approximated solution is proved by virtue of the Brouwer fixed point theorem. Moreover, the uniqueness of the solution is shown. Finally, convergence orders of the fully discrete Crank-Nicolson scheme are discussed. The end of the paper is devoted to some numerical experiments.

• Nuclear Engineering and Technology
• /
• v.41 no.7
• /
• pp.885-892
• /
• 2009

This manuscript will discuss a numerical method where the six equations of two-phase flow, the solid heat conduction equations, and the two equations that describe neutron diffusion and precursor concentration are solved together in a tightly coupled, nonlinear fashion for a simplified model of a nuclear reactor core. This approach has two important advantages. The first advantage is a higher level of accuracy. Because the equations are solved together in a single nonlinear system, the solution is more accurate than the traditional "operator split" approach where the two-phase flow equations are solved first, the heat conduction is solved second and the neutron diffusion is solved third, limiting the temporal accuracy to $1^{st}$ order because the nonlinear coupling between the physics is handled explicitly. The second advantage of the method described in this manuscript is that the time step control in the fully implicit system can be based on the timescale of the solution rather than a stability-based time step restriction like the material Courant limit required of operator-split methods. In this work, a pilot code was used which employs this tightly coupled, fully implicit method to simulate a reactor core. Results are presented from a simulated control rod movement which show $2^{nd}$ order accuracy in time. Also described in this paper is a simulated rod ejection demonstrating how the fastest timescale of the problem can change between the state variables of neutronics, conduction and two-phase flow during the course of a transient.

• Land and Housing Review
• /
• v.1 no.1
• /
• pp.59-65
• /
• 2010

The paper presents a comparison between a semi-implicit time integration linear finite element implementation and fully-implicit nonlinear Newton-Raphson finite element implementation of a triphasic small strain mixture formulation of an elastic partially saturated porous medium. The pore air phase pressure pa is assumed atmospheric, i.e., $p_a$ = 0, although the formulation and implementation are general to handle increase in pore air pressure as a result of loading, if needed. The solid skeleton phase is assumed linear isotropic elastic and partially saturated 'consolidation' in the presence of surface infiltration and traction is simulated. The verification of the implementation against an analytical solution for partially saturated pore water flow (no deformation) and comparison between the two implementations is presented and the important of the porosity-dependent nature of the partially saturated permeability is assessed on comparison with a commercial code for the partially saturated flow with deformation. As a result, the response of partially saturated permeability subjected to the porosity influences on the saturation of a soil, and the different behaviors of the partially saturated soil between staggered and monolithic coupled programs is worth of attention because the negative pore water pressure in the partially saturated soil depends on the difference.

• Journal of Ocean Engineering and Technology
• /
• v.24 no.6
• /
• pp.34-40
• /
• 2010

Bragg reflection of nonlinear waves is simulated by a 2D fully nonlinear numerical wave tank (NWT). The developed NWT was based on the Boundary Element Method (BEM) with potential theory and the mixed Eulerian-Lagrangian (MEL) time marching scheme with Runge-Kutta 4th-order time integration. A spatial variation of wave elevations and their Fourier amplitudes of each component are compared to investigate the effect of sea bottom ripples and their relative heights. The incident waves over an undulated sea bottom are partially reflected and changed to partial standing waves due to Bragg reflection. The present results are verified with linear calculations and experimental data. It is found that the 1st-order wave component is mainly affected by Bragg reflection and its spatial modulation is significant in front of the bottom ripples.

• KIPS Transactions on Software and Data Engineering
• /
• v.11 no.1
• /
• pp.1-10
• /
• 2022

Deep neural networks are widely used to solve various problems. In a fully connected neural network, the nonlinear activation function is a function that nonlinearly transforms the input value and outputs it. The nonlinear activation function plays an important role in solving the nonlinear problem, and various nonlinear activation functions have been studied. In this study, we propose a combined parametric activation function that can improve the performance of a fully connected neural network. Combined parametric activation functions can be created by simply adding parametric activation functions. The parametric activation function is a function that can be optimized in the direction of minimizing the loss function by applying a parameter that converts the scale and location of the activation function according to the input data. By combining the parametric activation functions, more diverse nonlinear intervals can be created, and the parameters of the parametric activation functions can be optimized in the direction of minimizing the loss function. The performance of the combined parametric activation function was tested through the MNIST classification problem and the Fashion MNIST classification problem, and as a result, it was confirmed that it has better performance than the existing nonlinear activation function and parametric activation function.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
• /
• 2000.04a
• /
• pp.140-145
• /
• 2000

The spectral method which is composed of an eigenfunction expansion of free modes in the wave number domain is used to produce two dimensional unsteady inviscid wave simulation such as progressive waves in a numerical pneumatic wave tank. A spatial and time dependent free surface elevation and the potential are calculated by integrating ODE derived from fully nonlinear kinematic and dynamic free surface boundary condition at each time step. The nonlinear characteristics in the waves by this method were notable as increasing wave steepness. This method is very useful and powerful in terms of saving computational time caused by rapid convergence exponentially with increasing number of nodes, even preserving accurate numerical results. Moreover, it will given us many possibilities to apply to naval and ocean engineering fields.

• International Journal of Naval Architecture and Ocean Engineering
• /
• v.4 no.3
• /
• pp.281-290
• /
• 2012

Hydrodynamic analysis of a surface-piercing body with an open chamber was performed with incident regular waves and forced-heaving body motions. The floating body was simulated in the time domain using a 2D fully nonlinear numerical wave tank (NWT) technique based on potential theory. This paper focuses on the hydrodynamic behavior of the free surfaces inside the chamber for various input conditions, including a two-input system: both incident wave profiles and forced body velocities were implemented in order to calculate the maximum surface elevations for the respective inputs and evaluate their interactions. An appropriate equivalent linear or quadratic viscous damping coefficient, which was selected from experimental data, was employed on the free surface boundary inside the chamber to account for the viscous energy loss on the system. Then a comprehensive parametric study was performed to investigate the nonlinear behavior of the wave-body interaction.

• Publications of The Korean Astronomical Society
• /
• v.7 no.1
• /
• pp.107-148
• /
• 1992

This paper presents a cosmological perturbation analysis in a Newtonian framework, using the Newtonian multi component version of the relativistic covariant equations. This work considers the fully nonlinear evolution of the perturbations, and is generalized to multicomponent systems and imperfect fluids. Known nonlinear solutions are presented in a general framework. Quasi-nonlinear analysis, considering both the compressible and rotational modes, is presented, including cases already known in the literature. The Fourier space representation of the conservation equations is also derived in a general context, with various decompositions of the velocity field. Commonly accepted cosmogonical frameworks are critically examined in the context of nonlinear evolution. This work may be regarded as the Newtonian counterpart of a recently presented general relativistic covariant formulation.