• 한국전산유체공학회:학술대회논문집
• /
• 2005.10a
• /
• pp.111-116
• /
• 2005

Two coupling methods for the Navier-Stokes equations and a two-equation turbulence model equations are compared. They are the strongly coupled method and the loosely coupled method. The strongly coupled method solves the Navier-Stokes equations and the two-equation turbulence model equations simultaneously, while the loosely coupled method solves the Navier-Stokes equation with the turbulence viscosity fixed and subsequently solves the turbulence model equations with all the flow quantities fixed. In this paper, performances of two coupling methods are compared for two and three-dimensional problems.

• Nuclear Engineering and Technology
• /
• v.16 no.1
• /
• pp.1-10
• /
• 1984

General time-volume averaged conservation equations and jump conditions for two-phase flows are derived here. The time-averaged equations for a single phase region in two-phase flow are obtained from local instant balance equations by a technique often used for single phase turbulent flow equations. The results obtained by integrating the time averaged equations over a flow volume are spatially averaged twice; first, they are averaged over a single phase region of the k-th phase and then averaged over the total volume of the k-th phase, in a flow volume. The mass, momentum, and energy conservation equations are obtained from the general time-volume averaged equations. The advantages of the present model are explained by comparing it with Ishii's model (1) and Banerjee's model (2). Finally, the assumptions and approximate terms of the equations of the THERMIT-6S are clarified.

• Water Engineering Research
• /
• v.4 no.2
• /
• pp.69-85
• /
• 2003

Previously developed empirical equations used to calculate the parameters of the transient storage model are analyzed in depth in order to evaluate their behavior in representing solute transport in the natural streams with storage zone. A comparative analysis of the existing theoretical and experimental equations used to predict parameters of the transient storage (TS) model is reported. New simplified equations for predicting 4 key parameters of the TS model using hydraulic data sets that are easily obtained in the natural streams are also developed. The weighted one-step Huber method, which is one of the nonlinear multi-regression methods, is applied to derive new parameters equation. These equations are proven to be superior in explaining mixing characteristics of natural streams with the transient storage zone more precisely than the other existing equations.

• Advances in environmental research
• /
• v.3 no.2
• /
• pp.131-149
• /
• 2014

Two different model selection indices, the Akaike information criterion (AIC) and the coefficient of determination ($R^2$), are used to discriminate competing isotherm equations for aqueous pollutant removal systems. The former takes into account model accuracy and complexity while the latter considers model accuracy only. The five types of isotherm shape in the Brunauer-Deming-Deming-Teller (BDDT) classification are considered. Sorption equilibrium data taken from the literature were correlated using isotherm equations with fitting parameters ranging from two to five. For the isotherm shapes of types I (favorable) and III (unfavorable), the AIC favors two-parameter equations which can easily track these simple isotherm shapes with high accuracy. The $R^2$ indicator by contrast recommends isotherm equations with more than two parameters which can provide marginally better fits than two-parameter equations. To correlate the more intricate shapes of types II (multilayer), IV (two-plateau) and V (S-shaped) isotherms, both indices favor isotherm equations with more than two parameters.

• Journal of Korean Society of Water and Wastewater
• /
• v.13 no.3
• /
• pp.42-55
• /
• 1999

A mathematical model for biological nutrient removal in a sequencing batch reactor process, which is based on the IAWQ Activated Sludge Model No. 2 with a few modifications, has been developed. Twenty water quality components and twenty three kinetic equations are incorporated in the model. The model is structured in the matrix form based on the law of mass conservation using stoichiometry and kinetic equations. Stoichiometric coefficients and kinetic parameters included in the model equations are chosen from the literature. A multistep predictor-corrector algorithm of variable step-size is adopted for solving the vector nonlinear ordinary differential equations. The simulation for experimental results is conducted to evaluate the validity of the model and to calibrate coefficients and parameters. The simulation using the model well represents the experimental results from laboratory. The mathematical model developed in this study may be utilized for the design and operation of a sequencing batch reactor process under the steady and unsteady-state at various environmental conditions.

• Water Engineering Research
• /
• v.4 no.4
• /
• pp.175-185
• /
• 2003

A numerical model to analyze dam break flows has been developed based on approximate Riemann solver. The governing equations of the model are the nonlinear shallow-water equations. The governing equations are discretized explicitly by using finite volume method and the numerical flux are reconstructed with weighted averaged flux (WAF) method. The developed model is verified. The first verification problem is about idealized dam break flow on wet and dry beds. The second problem is about experimental data of dam break flow. From the results of the verifications, very good agreements have been observed

• Water for future
• /
• v.23 no.3
• /
• pp.319-328
• /
• 1990

The Parameter Identification of 2-demensional estuarine model was carried out using new output ADI-FDM numerical semi-implicit schem transformed in boundary fitted(BF) - coordinate. The hydrodynamic equations which is coupled with the transport equations were used as basic equations in the model. Thompson's equations were used to transform governing equations into rectangular plane equations and his elliptic grid generation scheme was used to generate curvilinear grid system. in BF - coordinates. The parameters to be identified are friction coefficient and disperse coefficient embedded in the governing equations. The numerical output scheme is tidally averaged salinity model in BF - coordinates. The algorithm to optimize norm of error between observations and calculations is the influence coefficinet algorithm associated with least square criterion. The lumped model is conssidered in identification. This paper was concetrated on checking whether the new output scheme might be useful to identify parameters in estuarine salinity model or not. The proposed method was tested through experimental application with hypothetical simple model. The result of the test shows that the proposed method can be used for parameter identification in estuarine model.

• Journal of the Chungcheong Mathematical Society
• /
• v.25 no.3
• /
• pp.381-391
• /
• 2012

In this paper, the formal linearization method is used to construct multisoliton solutions for three model of shallow water waves equations. The three models are completely integrable. The formal linearization method is an efficient method for obtaining exact multisoliton solutions of nonlinear partial differential equations. The method can be applied to nonintegrable equations as well as to integrable ones.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.18 no.7
• /
• pp.1751-1758
• /
• 1994

A new set of governing equations is derived for the dynamic analysis of the Free-Piston Stirling Engines(EPSE). Equations from the ideal adiabatic model for the thermodynamic analysis of the working fluid are incoporated with the equations of motion for the moving masses of the system, resulting in a set of nonlinear differential equations. The coupled set of equations are numerically integrated with proper intial conditions to obtain a steady state response of the engine. The proposed method is compared with the conventional method of analyzing EPSE based mainly on the ideal isothermal model. The results clearly shows the limitationsl of the conventional methods and the relative advantages of the method proposed in the present study.

• Korea-Australia Rheology Journal
• /
• v.14 no.1
• /
• pp.33-45
• /
• 2002

Recent results obtained for the port-pom model and the constitutive equations with time-strain separability are examined. The time-strain separability in viscoelastic systems Is not a rule derived from fundamental principles but merely a hypothesis based on experimental phenomena, stress relaxation at long times. The violation of separability in the short-time response just after a step strain is also well understood (Archer, 1999). In constitutive modeling, time-strain separability has been extensively employed because of its theoretical simplicity and practical convenience. Here we present a simple analysis that verifies this hypothesis inevitably incurs mathematical inconsistency in the viewpoint of stability. Employing an asymptotic analysis, we show that both differential and integral constitutive equations based on time-strain separability are either Hadamard-type unstable or dissipative unstable. The conclusion drawn in this study is shown to be applicable to the Doi-Edwards model (with independent alignment approximation). Hence, the Hadamardtype instability of the Doi-Edwards model results from the time-strain separability in its formulation, and its remedy may lie in the transition mechanism from Rouse to reptational relaxation supposed by Doi and Edwards. Recently in order to describe the complex rheological behavior of polymer melts with long side branches like low density polyethylene, new constitutive equations called the port-pom equations have been derived in the integral/differential form and also in the simplifled differential type by McLeish and carson on the basis of the reptation dynamics with simplifled branch structure taken into account. In this study mathematical stability analysis under short and high frequency wave disturbances has been performed for these constitutive equations. It is proved that the differential model is globally Hadamard stable, and the integral model seems stable, as long as the orientation tensor remains positive definite or the smooth strain history in the flow is previously given. However cautious attention has to be paid when one employs the simplified version of the constitutive equations without arm withdrawal, since neglecting the arm withdrawal immediately yields Hadamard instability. In the flow regime of creep shear flow where the applied constant shear stress exceeds the maximum achievable value in the steady flow curves, the constitutive equations exhibit severe instability that the solution possesses strong discontinuity at the moment of change of chain dynamics mechanisms.