• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2005년도 추계 학술대회논문집
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• pp.111-116
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• 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
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• 제16권1호
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• pp.1-10
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• 1984

2상 유동에 대한 일반적인 시간과 공간에 대해 평균된 보존방정식과 jump condition을 유도했다. 단상난류 유동 방정식에 사용되는 방법을 써서, 한부분에서 순간적으로 이루어지는 평형 방정식 (local instant balance eq.)으로부터 2상유동내 단상영역에 관한 시간에 대해 평균된 방정식을 유체체적에 대해 적분하여 얻어진 결과는 공간적으로 두차례에 걸쳐 평균된다. 즉, 한 유체체적내에서 일차적으로 k번째 상의 단상영역에 대해 평균하고 다음에 k번째 상 전체체적에 대해 평균한다. 질량, 운동량 그리고 에너지 보존 방정식은 일반적인 시간과 공간에 대해 평균된 방정식으로부터 얻어진다. 이 모델의 장점은 Ishii모델, 그리고 Banerjee의 model과 비교하여 설명된다. 마지막으로, THERMIT-6S의 방정식에 포함된 가정과 근사항들에 대해 박혀둔다.

• Water Engineering Research
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• 제4권2호
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• pp.69-85
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• 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
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• 제3권2호
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• pp.131-149
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• 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.

• 상하수도학회지
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• 제13권3호
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• pp.42-55
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• 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
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• 제4권4호
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• pp.175-185
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• 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

• 물과 미래
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• 제23권3호
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• pp.319-328
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• 1990

2차원 하구모델의 매개변수 동정을 BF좌표계로 변환된 ADI-FDM출력 수치모형을 사용하여 수행하였다. 모형에서 기본 방정식을 동수역학식과 수송방정식이 복합된 방정식을 사용하였다. Thompson식이 지배방정식을 사각평면으로 변환 하는데 사용도이ㅓㅆ으며 Thompson의 Elliptic 격자발생기법이 BF 좌표계에서 곡선격자망을 발생하는데 사용되었다. 지배방정식에서 동정될 매개변수는 마찰계수와 분산 정수이다. 출력수치모형은 BF좌표계에서 조석평균 염도 모형이 사용되었다. 최적화 기법으로 영향계수 알고리즘을 적용하였다. 또한 Lumped 모형이 동정에 고려 되었다. 본 연구는 새로운 출력 수치모형이 하구염도 모형의 매개변수 동정에 있어 유용한가를 검토 하는데 중점을 두었다. 제안된 기법은 간단한 가상모형에 실험적인 적용을 통하여 검토되었다. 검토한 결과는 제안된 기법이 하구모형에서 매개변수 동정시 도입될 수 있음을 보여주었다.

• 충청수학회지
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• 제25권3호
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• pp.381-391
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• 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.

• 대한기계학회논문집
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• 제18권7호
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• pp.1751-1758
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• 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
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• 제14권1호
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• pp.33-45
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• 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.