Wyniki wyszukiwania - BazTech

1

Laminar flow past the bottom with obstacles - a porous medium approximation

Bielski Włodzimierz, Wojnar Ryszard

Journal of Theoretical and Applied Mechanics

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2022

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Vol. 60 nr 3

509--520

EN

We provide a model of a stationary laminar flow in a channel at the bottom of which plants grow in a dense layer. Since this layer of plants is dense, we treat it as a porous medium and we propose to describe the flow in such a medium by Brinkman’s equation. The flow in the fluid layer located above (infiltrated by water) the layers of plants is described by the Stokes equation. We show that such a model gives results consistent with experimental observations. We indicate also that this new model complements the previously given model in which the benthonic plants were considered as a suspension, so the previous model referred to the channel at the bottom of which the plants grew rare. For high permeability of the porous medium, we arrive at the results obtained for the medium filled with a liquid with a suspension.

2

Shape sensitivity of optimal control for the Stokes problem

Abdelbari Merwan, Nachi Khadra, Sokolowski Jan, Szulc Katarzyna

Control and Cybernetics

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2020

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Vol. 49, No. 1

11--40

EN

In this article, we study the shape sensitivity of optimal control for the steady Stokes problem. The main goal is to obtain a robust representation for the derivatives of optimal solution with respect to smooth deformation of the flow domain. We introduce in this paper a rigorous proof of existence of the material derivative in the sense of Piola, as well as the shape derivative for the solution of the optimality system. We apply these results to derive the formulae for the shape gradient of the cost functional; under some regularity conditions the shape gradient is given according to the structure theorem by a function supported on the moving boundary, then the numerical methods for shape optimization can be applied in order to solve the associated optimization problems.

3

Wpływ kształtu cząstek ilastych na wyniki analiz granulometrycznych gruntów spoistych

Gorączko A., Topoliński S.

Przegląd Naukowy Inżynieria i Kształtowanie Środowiska

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2018

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Vol. 27, No. 2

142--151

PL

Pomiar wielkości cząstek za pomocą dyfrakcji laserowej (LDA) jest alternatywną analiz hydrometrycznych (HM) metodą oznaczania składu granulometrycznego gruntów. Przy oznaczaniu frakcji najdrobniejszych, o znacznej zawartości minerałów ilastych, zasadnicze problemy wynikają ze znacznej anizotropii kształtu cząstek. W pracy zawarto porównanie wyników oznaczeń wielkości cząstek iłów neogeńskich z Bydgoszczy. Zaproponowano formuły służące do transformacji wyników metody areometrycznej i metody dyfrakcji laserowej dla badanych gruntów.

EN

Laser diffraction particle sizing is an alternative method to determine grain size analysis in soils. However, for particle with high shape anisotropy LDA measurements usually produce different results than traditional hydrometric methods (HM), based on Stokes equation. The article contains the results of analyzes of Neogene clays characterized by significant lithological differentiation in regard to participation the clay fraction particles. The research was conducted for the clay samples taken in Bydgoszcz. A set of equations to transform LDM results to hydrometric results was proposed.

4

Heuristic derivation of Brinkman's seepage equation

Wojnar R.

Technical Sciences / University of Warmia and Mazury in Olsztyn

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2017

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nr 20(4)

359--374

EN

Brinkman’s law is describing the seepage of viscous fluid through a porous medium and is more acurate than the classical Darcy’s law. Namely, Brinkman’s law permits to conform the flow through a porous medium to the free Stokes’ flow. However, Brinkman’s law, similarly as Schro¨dinger’s equation was only devined. Fluid in its motion through a porous solid is interacting at every point with the walls of pores, but the interactions of the fluid particles inside pores are different than the interactions at the walls, and are described by Stokes’ equation. Here, we arrive at Brinkman’s law from Stokes’ flow equation making use of successive iterations, in type of Born’s approximation method, and using Darcy’s law as a zero-th approximation.

5

The Lagrange multiplier and the stationary Stokes equations

Ożański W. S.

Journal of Applied Analysis

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2017

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Vol. 23, nr 2

137--140

EN

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.

6

Finite element error analysis for state-constrained optimal control of the Stokes equations

Los Reyes J. C. de, Meyer C., Vexler B.

Control and Cybernetics

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2008

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Vol. 37, no 2

251-284

EN

An optimal control problem for 2d and 3d Stokes equations is investigated with pointwise inequality constraints on the state and the control. The paper is concerned with the full discretization of the control problem allowing for different types of discretization of both the control and the state. For instance, piecewise linear and continuous approximations of the control are included in the present theory. Under certain assumptions on the L∞-error of the finite element discretization of the state, error estimates for the control are derived which can be seen to be optimal since their order of convergence coincides with the one of the interpolation error. The assumptions of the L∞-finite-eleinent-error can be verified for different numerical settings. Finally the results of two numerical experiments are presented.

7

Nonstationary two-phase flow through elastic porous medium

Bielski W., Telega J. J., Wojnar R.

Archives of Mechanics

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2001

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Vol. 53, nr 4-5

333-366

EN

The aim of this contribution is to derive macroscopic equations governing the dynamic flow of two immiscible viscous fluids through an elastic microperiodic porous medium. To this end homogenization methods were employed. The procedure used can be justified by the method of two-scale convergence. Passage to the stationary case and illustrative example were also provided.