• Journal of the Korean Mathematical Society
• /
• v.58 no.1
• /
• pp.1-28
• /
• 2021

We study a continuous data assimilation algorithm for the three-dimensional simplified Bardina model utilizing measurements of only two components of the velocity field. Under suitable conditions on the relaxation (nudging) parameter and the spatial mesh resolution, we obtain an asymptotic in time estimate of the difference between the approximating solution and the unknown reference solution corresponding to the measurements, in an appropriate norm, which shows exponential convergence up to zero.

• Structural Engineering and Mechanics
• /
• v.10 no.1
• /
• pp.67-79
• /
• 2000

Critical loads and load-carrying capacities for steel scaffolds used as shoring systems were compared using computational and experimental methods in Part I of this paper. In that paper, a simple 2-D model was established for use in evaluating the structural behavior of scaffold-shoring systems. This 2-D model was derived using an incremental finite element analysis (FEA) of a typical complete scaffold-shoring system. Although the simplified model is only two-dimensional, it predicts the critical loads and failure modes of the complete system. The objective of this paper is to present a closed-form solution to the 2-D model. To simplify the analysis, a simpler model was first established to replace the 2-D model. Then, a closed-form solution for the critical loads and failure modes based on this simplified model were derived using a bifurcation (eigenvalue) approach to the elastic-buckling problem. In this closed-form equation, the critical loads are shown to be function of the number of stories, material properties, and section properties of the scaffolds. The critical loads and failure modes obtained from the analytical (closed-form) solution were compared with the results from the 2-D model. The comparisons show that the critical loads from the analytical solution (simplified model) closely match the results from the more complex model, and that the predicted failure modes are nearly identical.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.30 no.3 s.246
• /
• pp.238-245
• /
• 2006

This paper proposes appropriate conjugate parameters and dimensionless temperatures to analysis the conjugate problem of heat conduction in solid wall coupled with laminar film condensation flow adjacent to horizontal flat plate. An efficient methods for some fluids are proposed for its solution. The momentum and energy balance equations are reduced to a nonlinear system of ordinary differential equations with four parameters: the Prandtl number, Pr, Modified Jacob number, $Ja^*/Pr$, defined by an overall temperature difference, a property ratio $\sqrt{\rho_l{\mu}_l/{\rho_v{\mu}_v}$ and the conjugate parameter $\zeta$. The obtained similarity solution reveals the effect of the conjugate parameter, and the results are compared with the simplified solution. The variations of the heat transfer rates as well as the interface temperature and frictions along the plate are shown explicitly.

• Nuclear Engineering and Technology
• /
• v.32 no.6
• /
• pp.605-617
• /
• 2000

Nodal transport methods are studied for the solution of two dimensional discrete-ordinates, simplified even-parity transport equation(SEP) which is known to be an approximation to the true transport equation. The polynomial expansion nodal method(PEN) and the analytic function expansion nodal method(AFEN）which have been developed for the diffusion theory are used for the solution of the discrete-ordinates form of SEP equation. Our study shows that while the PEN method in diffusion theory can directly be converted without complication, the AFEN method requires a theoretical modification due to the nonhomogeneous property of the transport equation. The numerical results show that the proposed two methods work well with the SEP transport equation with higher accuracies compared with the conventional finite difference method.

• Journal of the Korean Society of Fisheries and Ocean Technology
• /
• v.47 no.1
• /
• pp.46-58
• /
• 2011

A steady-state analysis and a simple dynamic model as simplified methods are developed, and results of energy consumption loads are compared with results obtained using computer to evaluate the analytical solution. Before obtaining simplified model a mathematical model is formulated for the effect of wall mass on the thermal performance of four different houses having various wall construction. This analytical study was motivated by the experimental work of Burch et al. An analytical solution of one-dimensional, linear, partial differential equation for wall temperature profiles and room air temperatures is obtained using the Laplace transform method. Typical Meteorological Year data are processed to yield hourly average monthly values. This study is conducted using weather data from four different locations in the United States: Albuquerque, New mexico; Miami, Florida; Santa Maria, California; and Washington D.C. for both winter and summer conditions. The steady state analysis that does not include the effect of thermal mass can provide an accurate estimate of energy consumption in most cases except for houses #2 and #4 in mild weather areas. This result shows that there is an effect of mass on the thermal performance of heavily constructed house in mild weather conditions. The simple dynamic model is applicable for high cycling rates and accurate values of inside wall temperature and ambient air temperature.

• Earthquakes and Structures
• /
• v.24 no.1
• /
• pp.65-79
• /
• 2023

A simplified analytical solution for seismic response of tunnel cross section in horizontally layered ground subjected to oblique incidence of SH wave is deduced in this paper. The proposed analytical solution consists of two main steps: free-field response in layered field and tunnel response. The free field responses of the layered ground are obtained by one-dimensional finite element method in time domain. The tunnel lining is treated as a thick-wall cylinder to calculate the tunnel response, which subject to free field stress. The analytical solutions are verified by comparing with the dynamic numerical results of two-dimensional ground-lining interaction analysis under earthquake in some common situations, which have a good agreement. Then, the appropriate range of the proposed analytical solution is analyzed, considering the height of the layered ground, the wavelength and incident angle of SH wave. Finally, by using the analytical solutions, the effects of the ground material, burial depth of the tunnel, and lining thickness and the slippage effect at the ground-lining interface on the seismic response of tunnels are investigated. The proposed solution could serve as a useful tool for seismic analysis and design of tunnels in layered ground.

• Proceedings of the Korean Society of Marine Engineers Conference
• /
• 2005.06a
• /
• pp.183-188
• /
• 2005

The effect of heat conduction resistance on laminar film condensation of the pure saturated vapor in forced flow over a flat plate has been investigated as boundary layer solutions. A efficient numerical methods for water are proposed for its solution. The momentum and energy balance equations are reduced to a nonlinear system of ordinary differential equations with four parameters: the Prandtl number, Pr, Modified Jacob number, $Ja^{\ast}/Pr$, defined by an overall temperature difference, a property ratio $\sqrt{P_l{\mu}_l/P_v{\mu}_v}$ and the conjugate parameter ${\zeta}$. The similarity and simplified solutions obtained reveal the effects of the conjugate parameter.

• Proceedings of the Korean Geotechical Society Conference
• /
• 2009.09a
• /
• pp.457-462
• /
• 2009

In this study, seismic analysis is performed using simplified method, analytical solution and numerical analysis based on one-dimensional seismic site response analysis. The results show that analytical solution of tunnel response is predicted more conservative than numerical solution. And simplified method is not appropriate for seismic analysis of tunnel response. In addition, it is reasonable to determine shear-modulus reduction ratio performing seismic site response analysis to consider ground nonlinear-behavior.

• Proceedings of the SAREK Conference
• /
• 2003.07a
• /
• pp.100-100
• /
• 2003

• Journal of applied mathematics & informatics
• /
• v.15 no.1_2
• /
• pp.313-321
• /
• 2004

In this paper we study the problem of three-dimensional layout optimization on the simplified rotating vessel of satellite. The layout optimization model with behavioral constraints is established and some effective and convenient conditions of performance optimization are presented. Moreover, we prove that the performance objective function is locally Lipschitz continuous and the results on the relations between the local optimal solution and the global optimal solution are derived.