• Proceedings of the KSME Conference
• /
• 2004.04a
• /
• pp.1869-1874
• /
• 2004

Acoustic pressure field around the cross-flow fan is predicted by a hydrodynamic-acoustic splitting method. Unsteady flow field is obtained by solving the incompressible Navier-Stokes equations using an unstructured finite-volume method on the triangular meshes, while the acoustic waves generated inside the cross-flow fan are predicted by solving the perturbed compressible equations(PCE) with a 6th-order compact finite difference method. Computational results show that the acoustic waves of BPF tone are generated by interactions of the blades wakes with the stabilizer, which then are reflected from the rear-guider and mainly propagate towards the fan inlet. Also, a directivity of BPF noise predicted by the PCE is noticeably different from that of the FW-H equations, in which a fan casing effect cannot be included.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.25 no.4
• /
• pp.224-261
• /
• 2021

The interest in implicit-explicit (IMEX) integration methods has emerged as an alternative for dealing in a computationally cost-effective way with stiff ordinary differential equations arising from practical modeling problems. In this paper, we introduce implicit-explicit second derivative linear multi-step methods (IMEX SDLMM) with error control. The proposed IMEX SDLMM is based on second derivative backward differentiation formulas (SDBDF) and recursive SDBDF. The IMEX second derivative schemes are constructed with order p ranging from p = 1 to 8. The methods are numerically validated on well-known stiff equations.

• Steel and Composite Structures
• /
• v.42 no.5
• /
• pp.711-722
• /
• 2022

In this paper, hyperbolic shear deformation plate theory is developed for thermal buckling of functionally graded plates with porosity by dividing transverse displacement into bending and shear parts. The present theory is variationally consistent, and accounts for a quadratic variation of the transverse shearstrains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. Three different patterns of porosity distributions (including even and uneven distribution patterns, and the logarithmic-uneven pattern) are considered. The logarithmic-uneven porosities for first time is mentioned. Equilibrium and stability equations are derived based on the present theory. The non-linear governing equations are solved for plates subjected to simply supported boundary conditions. The thermal loads are assumed to be uniform, linear and non-linear distribution through-the-thickness. A comprehensive parametric study is carried out to assess the effects of volume fraction index, porosity fraction index, aspect ratio and side-to-thickness ratio on the buckling temperature difference of imperfect FG plates.

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.1
• /
• pp.93-115
• /
• 2024

In this paper, the Gauge-Uzawa methods for the Darcy-Brinkman equations driven by temperature and salt concentration (DBTC) are proposed. The first order backward difference formula is adopted to approximate the time derivative term, and the linear term is treated implicitly, the nonlinear terms are treated semi-implicit. In each time step, the coupling elliptic problems of velocity, temperature and salt concentration are solved, and then the pressure is solved. The unconditional stability and error estimations of the first order semi-discrete scheme are derived, at the same time, the unconditional stability of the first order fully discrete scheme is obtained. Some numerical experiments verify the theoretical prediction and show the effectiveness of the proposed methods.

• Nutrition Research and Practice
• /
• v.12 no.4
• /
• pp.283-290
• /
• 2018

BACKGROUND/OBJECTIVES: Indirect calorimetry is the gold-standard method for the measurement of resting energy expenditure. However, this method is time consuming, expensive, and requires highly trained personnel. To overcome these limitations, various predictive equations have been developed. The objective of this study was to assess the validity of predictive equations for resting energy expenditure (REE) in Korean non-obese adults. SUBJECTS/METHODS: The present study involved 109 participants (54 men and 55 women) aged between 20 and 64 years. The REE was measured by indirect calorimetry. Nineteen REE equations were evaluated for validity, by comparing predicted and measured REE results. Predictive equation accuracy was assessed by determining percent bias, root mean squared prediction error (RMSE), and percentage of accurate predictions. RESULTS: The measured REE was significantly higher in men than in women (P < 0.001), but the difference was not significant after adjusting for body weight (P > 0.05). The equation developed in this study had an accuracy rate of 71%, a bias of 0%, and an RMSE of 155 kcal/day. Among published equations, the $FAO_{weight}$ equation gave the highest accuracy rate (70%), along with a bias of -4.4% and an RMSE of 184 kcal/day. CONCLUSIONS: The newly developed equation provided the best accuracy in predicting REE for Korean non-obese adults. Among the previously published equations, the $FAO_{weight}$ equation showed the highest overall accuracy. Regardless, at an individual level, the equations could lead to inaccuracies in a considerable number of subjects.

• Nuclear Engineering and Technology
• /
• v.52 no.2
• /
• pp.230-237
• /
• 2020

In this part, an implicit time dependent solution is presented for the Boltzmann transport equation discretized by the analytic coarse mesh finite difference method (ACMFD) over the spatial domain as well as the simplified P₃ (SP₃) for the angular variable. In the first part of this work we proposed a SP₃-ACMFD approach to solve the static eigenvalue equations which provide the initial conditions for temp dependent equations. Having solved the 3D multi-group SP₃-ACMFD static equations, an implicit approach is resorted to ensure stability of time steps. An exponential behavior is assumed in transverse integrated equations to establish a relationship between flux moments and currents. Also, analytic integration is benefited for the time-dependent solution of precursor concentration equations. Finally, a multi-channel one-phase thermal hydraulic model is coupled to the proposed methodology. Transient equations are then solved at each step using the GMRES technique. To show the sufficiency of proposed transient SP₃-ACMFD approximation for a full core analysis, a comparison is made using transport peers as the reference. To further demonstrate superiority, results are compared with a 3D multi-group transient diffusion solver developed as a byproduct of this work. Outcomes confirm that the idea can be considered as an economic interim approach which is superior to the diffusion approximation, and comparable with transport in results.

• Korean Journal of Mathematics
• /
• v.23 no.4
• /
• pp.665-732
• /
• 2015

Existence results for multiple positive solutions of two classes of boundary value problems for bilateral difference systems are established by using a fixed point theorem under convenient assumptions. It is the purpose of this paper to show that the approach to get positive solutions of boundary value problems of finite difference equations by using multi-fixed-point theorems can be extended to treat the bilateral difference systems with one-dimensional Laplacians. As an application, the sufficient conditions are established for finding multiple positive homoclinic solutions of a bilateral difference system. The methods used in this paper may be useful for numerical simulation. An example is presented to illustrate the main theorems. Further studies are proposed at the end of the paper.

• Korea-Australia Rheology Journal
• /
• v.17 no.4
• /
• pp.149-156
• /
• 2005

A simple constitutive model for viscoelastic suspensions is discussed in this paper. The model can be used to predict the rheological properties (relative viscosity and all stresses) for viscoelastic suspensions in shear and elongational flow, and the constitutive equations combine a 'viscoelastic' behaviour component and a 'Newtonian' behaviour component. As expected, the model gives a prediction of positive first normal stress difference and negative second normal stress difference; the dimensionless first normal stress difference strongly depends on the shear rate and decreases with the volume fraction of solid phase, but the dimensionless second normal stress difference (in magnitude) is nearly independent of the shear rate and increases with the volume fraction. The relative viscosities and all the stresses have been tested against available experimental measurements.

• Journal of the Ergonomics Society of Korea
• /
• v.27 no.2
• /
• pp.1-7
• /
• 2008

This study quantified 7 trunk muscles' physiological cross-sectional areas (PCSAs) and developed prediction equations for the physiological cross-sectional area as a function of anthropometic variables for Korean people. Nine females and nine males were participated in the magnetic resonance imaging (MRI) scans approximately from S1 through T8. Muscle fiber angle corrected cross-sectional areas (anatomical cross sectional areas: ACSAs) were recorded at each vertebral level and maximum value of ACSAs were determined as physiological cross sectional area (PCSA). There was a significant gender difference in PCSAs of all muscles (p<0.05). Stepwise linear regression techniques using anthropometric measures (e.g., height, weight, trunk depths and widths) as independent variables were conducted to develop prediction equations for the PCSA for each muscle. For males, six muscles' significant prediction equations (p<0.05) were developed except quadratus lumborum. For females, three prediction equations were developed for psoas, quadratus lumborum, and erector spinae muscles (p<0.05).

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
• /
• 2003.09a
• /
• pp.6-6
• /
• 2003

In this work we consider the mathematical formulation and numerical resolution of the linear feedback control problem for Boussinesq equations. The controlled Boussinesq equations is given by $$\frac{{\partial}u}{{\partial}t}-{\nu}{\Delta}u+(u{\cdot}{\nabla}u+{\nabla}p={\beta}{\theta}g+f+F\;\;in\;(0,\;T){\times}\;{\Omega}$$, $${\nabla}{\cdot}u=0\;\;in\;(0,\;T){\times}{\Omega}$$, $$u|_{{\partial}{\Omega}=0,\;u(0,x)=\;u_0(x)$$ $$\frac{{\partial}{\theta}}{{\partial}t}-k{\Delta}{\theta}+(u{\cdot}){\theta}={\tau}+T,\;\;in(0,\;T){\times}{\Omega}$$ $${\theta}|_{{\partial}{\Omega}=0,\;\;{\theta}(0,X)={\theta}_0(X)$$, where $\Omega$ is a bounded open set in $R^{n}$, n=2 or 3 with a $C^{\infty}$ boundary ${\partial}{\Omega}$. The control is achieved by means of a linear feedback law relating the body forces to the velocity and temperature field, i.e., $$f=-{\gamma}_1(u-U),\;\;{\tau}=-{\gamma}_2({\theta}-{\Theta}}$$ where (U,$\Theta$) are target velocity and temperature. We show that the unsteady solutions to Boussinesq equations are stabilizable by internal controllers with exponential decaying property. In order to compute (approximations to) solution, semi discrete-in-time and full space-time discrete approximations are also studied. We prove that the difference between the solution of the discrete problem and the target solution decay to zero exponentially for sufficiently small time step.