I. Kvasnica¹, P. Kvasnica²

CMES-Computer Modeling in Engineering & Sciences, Vol.107, No.6, pp. 447-462, 2015, DOI:10.3970/cmes.2015.107.447

Abstract The issue of simulation of decentralized mathematical models is discussed in the paper. The authors’ knowledge is based on a theory of design of decentralized computer control systems. Their knowledge is gained in the process of designing mathematical models that are simulated. A decomposed control system is required to meet the conditions of observation and control. The methodology of a multi-model design is based on main principles of object orientation such as abstraction, hierarchy, and modularity. Modelling on a parallel architecture has an impact on a simulator system. The system is defined by the equations shown below. An important part… More >

Ş. Emrah Amrahov¹, N. A. Gasilov², A. G. Fatullayev²

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.5, pp. 351-369, 2014, DOI:10.3970/cmes.2014.099.351

Abstract In this paper, we present a new approach to a time-optimal control problem with uncertainties. The dynamics of the controlled object, expressed by a linear system of differential equations, is assumed to be crisp, while the initial and final phase states are fuzzy sets. We interpret the problem as a set of crisp problems. We introduce a new notion of fuzzy optimal time and transform its calculation to two classical time-optimal control problems with initial and final sets. We examine the proposed approach on an example which is a problem of fuzzy control of mathematical pendulum. More >

J. A. Ferreira¹, P. de Oliveira², P. M. da Silva³

CMES-Computer Modeling in Engineering & Sciences, Vol.76, No.3&4, pp. 163-174, 2011, DOI:10.3970/cmes.2011.076.163

Abstract In two previous papers the authors presented mathematical models that simulate the mass of drug delivered, in vitro Ferreira, Oliveira, Silva, Carreira, Gil and Murta (2010) and in vivo Ferreira, Oliveira, Silva and Murta (2011), from a therapeutic contact lens. In the present paper the time it takes to reach an equilibrium state is studied. A closed formula based on the concept of effective time is derived and the influence of the parameters of the model is analyzed. More >

G. Prater, Jr.¹

CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.3, pp. 299-312, 2002, DOI:10.3970/cmes.2002.003.299

Abstract A vapor compressor's performance is affected by pressure and mass flow fluctuations resulting from acoustic effects in the suction and discharge manifolds. Through proper geometric design of the manifolds, these pulsations can be modified to increase efficiency and reduce noise. This paper documents the development of a computer simulation program used to tune stationary-vane refrigeration compressors. The program models the mechanical, fluid, thermodynamic, kinematic, and acoustical processes occurring in such compressors, and calculates suction and discharge chamber pressures, mass flow rates, valve displacements, and acoustic input and transfer impedances. Experimental acoustic pressure measurements from a refrigerator test stand provide validation… More >

H.W. Tang¹, Y.T. Yang¹, C.K. Chen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.3, pp. 193-206, 2012, DOI:10.3970/cmes.2012.085.193

Abstract In this article, a new method combining the Mathematical Programming and the Method of Weighted Residual called MP-MWR is presented. Under the validation of maximum principle, and up on the collocation method, the differential equation can be transferred into a bilateral inequality problem. Applying the genetic algorithms helps to find optimal solutions of upper and lower bounds which satisfy the inequalities. Here, the method is verified by analyzing the deflection of superelliptical clamped plate problem. By using this method, the good approximate solution and its error bounds can be obtained effectively and accurately. More >

J. Bonilla¹, L.J. Yebra¹, S. Dormido²

CMES-Computer Modeling in Engineering & Sciences, Vol.67, No.1, pp. 13-38, 2010, DOI:10.3970/cmes.2010.067.013

Abstract This paper presents and discusses a mean densities method applied to a steam-water two-phase flow mathematical model which uses a finite volume method and a staggered grid for discretizing a rigid volume in control volumes, where the thermodynamic properties are calculated. This method is based on the concepts of uniform pressure among all the control volumes and mean density in each control volume, allowing smooth thermodynamic properties, hence avoiding discontinuity at phase boundaries. This method wipes out the chattering problem due to the continuous and differentiable modelling of density and its partial derivatives, which leads to faster simulations and increases… More >

Hsiang-Wen Tang, Cha’o-Kung Chen¹, Chen-Yu Chiang

CMES-Computer Modeling in Engineering & Sciences, Vol.65, No.1, pp. 95-106, 2010, DOI:10.3970/cmes.2010.065.095

Abstract Up to now, solving some nonlinear differential equations is still a challenge to many scholars, by either numerical or theoretical methods. In this paper, the method of the maximum principle applied on differential equations incorporating the Residual Correction Method is brought up and utilized to obtain the upper and lower approximate solutions of nonlinear heat transfer problem of the non-Fourier fin. Under the fundamental of the maximum principle, the monotonic residual relations of the partial differential governing equation are established first. Then, the finite difference method is applied to discretize the equation, converting the differential equation into the mathematical programming… More >

Chia-Yi Cheng, Cha’o-Kuang Chen¹, Yue-Tzu Yang

CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.3, pp. 203-218, 2009, DOI:10.3970/cmes.2009.044.203

Abstract This paper seeks to utilize the residual correction method in coordination with the evolutionary monotonic iteration technique to obtain upper and lower approximate solutions of non-linear heat transfer problem of the annular hyperbolic profile fins whose thermal conductivity vary with temperature. First, the monotonicity of a non-linear differential equation is reinforced by using the monotone iterative technique. Then, the cubic spline method is applied to discretize and convert the differential equation into the mathematical programming problems. Finally, based on the residual correction concept, the complicated constraint inequality equations can be transferred into the simple iterative equations. As verified by this… More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.1, pp. 25-38, 2008, DOI:10.3970/cmes.2008.038.025

Abstract In this paper a complex matrix operator and a complex field are used to express the Maxwell equations, of which the complex field embraces all field variables and the matrix operator embraces the time and space differential operators. By left applying the operator on the complex field one can get all the four Maxwell equations, which are usually expressed by the vector form. The new formulation matches the Lorenz gauge condition, and its mathematical advantage is that it can incorporate the Maxwell equations into a single equation. The introduction of four-potential is possible only under the Lorenz gauge. In terms… More >

Shishir Sinha¹, Praveen Ch.

CMES-Computer Modeling in Engineering & Sciences, Vol.32, No.2, pp. 85-102, 2008, DOI:10.3970/cmes.2008.032.085

Abstract Fluid catalytic cracking (FCC) unit plays most important role in the economy of a modern refinery that it is use for value addition to the refinery products. Because of the importance of FCC unit in refining, considerable effort has been done on the modeling of this unit for better understanding and improved productivity. The process is characterized by complex interactions among feed quality, catalyst properties, unit hardware parameters and process conditions. \newline The traditional and global approach of cracking kinetics is lumping. In the present paper, five lump kinetic scheme is considered, where gas oil crack to give lighter fractions… More >