Circuital Model and Proper Eigenvalue Solution for a Fluid Mechanical Problem

R.C. Callarotti (Venezuela)


Circuital modeling, numerical procedures, transient response


We apply the proper eigenvalue procedure to a system of two concentric rotating cylinders enclosing a viscous fluid. The linear partial differential equations that rule the system in the absence of gravity, and in the low Reynolds limit, are solved a) analytically, b) through direct space and time iteration, and c) by using the eigenvalue procedure which avoids numerical time iterations. In this method the time dependent response of the system is obtained directly from the trivial Laplace transform inversion, once the zeros and poles of the system are known. The method arises from the analysis of the Laplace transform of a given variable (the velocity of the liquid in the present paper), as given by application of the determinant rule according to Cramer. The determinants involved are evaluated efficiently in terms of a generalized eigenvalue problem, which determines the poles and zeros for the system. We compare the computational time required in the three approaches, showing the advantages of the eigenvalue calculation. This approach might be particularly useful in engineering and science teaching in multidimensional problems since it not only saves computer time, but also provides a valuable physical insight through the knowledge of the pole and zero constellation

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