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The Lagrange multiplier and the stationary Stokes equations

Ożański W. S.

Journal of Applied Analysis

2017

Vol. 23, nr 2

137--140

We briefly discuss the notion of the Lagrange multiplier for a linear constraint in the Hilbert space setting, and we prove that the pressure p appearing in the stationary Stokes equations is the Lagrange multiplier of the constraint div u = 0.

More accurate determination of a pressure function in long hydrodynamical bearings

Zapoměl J.

Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska

2002

z. 19

173-178

Fluid-film bearings are usually incorporated into computational models by means of nonlinear force couplings. Calculation of components the hydraulical force through which the layer of lubricant acts on the rotor journal and bearing shell requires to determine a pressure distribution ( a pressure function ) in the bearing gap which is described by a set of Navier-Stokes equations. Because their solution (together with the equation of continuity) is considerably time consuming, a new approach to calculation of the pressure function has been developed. It consists in averaging the terms in the Navier-Stokes equation corresponding to the direction of prevailing pressure gradient (in long bearings it is in the circumferential direction ). To perform this manipulation velocity profiles obtained from solving a Reynolds' equation are applied. As the pressure function is 2π-periodic, it is approximated by a finite number of terms of a Fourier series and the Fourier coefficients are calculated by means of a trigonometric collocation method.