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    Tytuł:
    Preconditioning in the path-following algorithm for the stokes flow with stick-slip conditions
    Předpodmínění algoritmu sledování cesty pro stokesovo proudění se skluzovou podmínkou
    Autorzy:
    Jarošová, M.
    Kucera, R.
    Šátek, V.
    Powiązania:
    https://bibliotekanauki.pl/articles/112674.pdf
    Data publikacji:
    2017
    Wydawca:
    STE GROUP
    Tematy:
    Stokes problem
    stick-slip condition
    interior point method
    TFETI method
    zagadnienie Stokesa
    stan stick-slip
    metoda punktu wewnętrznego
    metoda TFETI
    Opis:
    The Stokes problem with the stick-slip boundary condition is solved by the mixed finite element method combined with the TFETI method. An interior point method for the minimization subject to box and equality constraints is used. The preconditioned projected conjugate gradient method solves the inner linear systems. The preconditioners are tested experimentally. The aim of our research is to develop efficient solvers for modelling of a flow over hydrophobic walls that exhibits applications in engineering areas including biomedical modelling or transport of fluid.
    Stokesova úloha se skluzovou podmínkou je rešena smíšenou metodou konecných prvku kombinovanou s TFETI metodou. Výpocet rešení se provádí metodou vnitrních bodu urcenou k minimalizaci s oboustraným omezením a rovnostní vazbou. Predpodmínená projektovaná metoda sdružených gradientu se používá pro rešení vnitrních lineárních soustav. Úcinost predpodminovacu se testuje experimentálne. Cílem výzkumu je vyvinout efektivní rešice pro modelování proudení po hydrofobních stenách, což nachází uplatnení v inženýrských oblastech zahrnujících modelování v biomedicíne nebo pri prenosu tekutin.
    Źródło:
    Systemy Wspomagania w Inżynierii Produkcji; 2017, 6, 4; 274-285
    2391-9361
    Pojawia się w:
    Systemy Wspomagania w Inżynierii Produkcji
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Homotopy simulation of non-Newtonian Spriggs fluid flow over a flat plate with oscillating motion
    Autorzy:
    Ray, A. K.
    Vasu, B.
    Gorla, R. S. R.
    Powiązania:
    https://bibliotekanauki.pl/articles/265238.pdf
    Data publikacji:
    2019
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    przepływ nieściśliwy
    przepływy Stokes'a
    płyn nienewtonowski
    incompressible flow
    oscillatory plate
    Stokes second problem
    HAM
    non-Newtonian Spriggs fluid
    Opis:
    An incompressible flow of a non-Newtonian Spriggs fluid over an unsteady oscillating plate is investigated using the Homotopy Analysis Method (HAM). An analytic solution of sine and cosine oscillations of the plate has been obtained. The similarity transformation is introduced to reduce the governing partial differentia equations into a single non-linear dimensionless partial differential equation. The effects of the power index of Spriggs fluid and convergence control parameter of HAM for the flow are studied extensively. The range of the convergence control parameter for convergence of series solution for different values of the power index of Spriggs fluid is obtained. The solution for a Spriggs fluid is noticeably different from the solution obtained for a Newtonian fluid. The influences of the shear thinning and shear thickening fluid on the velocity profile are shown graphically. The transient flow effect is higher for non-Newtonian Spriggs fluid than that of a Newtonian fluid. It is also observed that the interval to reach the steady state for the cosine case is less than the sine case. The applications of Stokes’ second problem have been widely found in the variety of fields of biomedical, medical, chemical, micro and nanotechnology.
    Źródło:
    International Journal of Applied Mechanics and Engineering; 2019, 24, 2; 359-385
    1734-4492
    2353-9003
    Pojawia się w:
    International Journal of Applied Mechanics and Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Energy integral of the Stokes flow in a singularly perturbed exterior domain
    Autorzy:
    Riva, M. D.
    Powiązania:
    https://bibliotekanauki.pl/articles/255971.pdf
    Data publikacji:
    2012
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    boundary value problem for Stokes system
    singularly perturbed exterior domain
    real analytic continuation in Banach space
    Opis:
    We consider a pair of domains Ωb and Ωs in Rn and we assume that the closure of Ωb does not intersect the closure of ε Ωs for ε ∈ (0, ε 0). Then for a fixed ε ∈ (0, ε0)we consider a boundary value problem in Rn\ (Ωb ∪ εΩs) which describes the steady state Stokes flow of an incompressible viscous fluid past a body occupying the domain Ωb and past a small impurity occupying the ε Ωs. The unknown of the problem are the velocity field u and the pressure field p, and we impose the value of the velocity field u on the boundary both of the body and of the impurity. We assume that the boundary velocity on the impurity displays an arbitrarily strong singularity when ε tends to 0. The goal is to understand the behaviour of the strain energy of (u, p) for ε small and positive. The methods developed aim at representing the limiting behaviour in terms of analytic maps and possibly singular but completely known functions of ε, such as ε-1, log &epsilon.
    Źródło:
    Opuscula Mathematica; 2012, 32, 4; 647-659
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the regularity of solution to the time-dependent p-Stokes system
    Autorzy:
    Berselli, Luigi C.
    Ruzicka, Michael
    Powiązania:
    https://bibliotekanauki.pl/articles/255059.pdf
    Data publikacji:
    2020
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    regularity
    evolution problem
    p-Stokes
    Opis:
    n this paper we consider the time evolutionary p-Stokes problem in a smooth and bounded domain. This system models the unsteady motion or certain non-Newtonian incompressible fluids in the regime of slow motions, when the convective term is negligible. We prove results of space/time regularity, showing that first-order time-derivatives and second-order space-derivatives of the velocity and first-order space-derivatives of the pressure belong to rather natural Lebesgue spaces.
    Źródło:
    Opuscula Mathematica; 2020, 40, 1; 49-69
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the numerical solution of one inverse problem for a linearized two-dimensional system of Navier-Stokes equations
    Autorzy:
    Jenaliyev, Muvasharkhan
    Ramazanov, Murat
    Yergaliyev, Madi
    Powiązania:
    https://bibliotekanauki.pl/articles/2216154.pdf
    Data publikacji:
    2022
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Navier-Stokes equations
    inverse problem
    numerical solution
    Opis:
    The paper studies the numerical solution of the inverse problem for a linearized two-dimensional system of Navier-Stokes equations in a circular cylinder with a final overdetermination condition. For a biharmonic operator in a circle, a generalized spectral problem has been posed. For the latter, a system of eigenfunctions and eigenvalues is constructed, which is used in the work for the numerical solution of the inverse problem in a circular cylinder with specific numerical data. Graphs illustrating the results of calculations are presented.
    Źródło:
    Opuscula Mathematica; 2022, 42, 5; 709-725
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Shape sensitivity of optimal control for the Stokes problem
    Autorzy:
    Abdelbari, Merwan
    Nachi, Khadra
    Sokolowski, Jan
    Szulc, Katarzyna
    Powiązania:
    https://bibliotekanauki.pl/articles/2049935.pdf
    Data publikacji:
    2020
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    Stokes equations
    optimal control problem
    coupled partial differential equations
    shape optimization
    shape gradient
    Opis:
    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.
    Źródło:
    Control and Cybernetics; 2020, 49, 1; 11-40
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical Simulation of Nonlinear Water Wave Problems
    Autorzy:
    Lo, D. C.
    Hu, Jia-Shen
    Lin, I-Fu
    Powiązania:
    https://bibliotekanauki.pl/articles/116613.pdf
    Data publikacji:
    2008
    Wydawca:
    Uniwersytet Morski w Gdyni. Wydział Nawigacyjny
    Tematy:
    Weather Navigation
    Numerical Simulation
    Oceanography
    Nonlinear Water Wave Problem
    Navier-Stokes Equations
    Solitary Waves
    Free-Surface Flow Problem
    Streamfunction Vorticity Formulation
    Opis:
    The main purpose of present paper aims at the establishment of a numerical model for solving the nonlinear water wave problems. The model is based on the Navier-Stokes equations with the consideration of a free-surface through the streamfunction-vorticity formulation. The main advantage of the streamfunction-vorticity formulation is that pressure field can be eliminated from the Navier-Stokes equations. To demonstrate the model feasibility, the present studies are first concentrated on problems including the collision of two solitary waves with different amplitudes, and the overtaking collision of two solitary waves. Then, the model is also applied to a solitary wave passes over the submerged obstacle in a viscous fluid. Finally, the application of present study is also to simulate the generation of solitary waves by underwater moving object. All examples give very promising results, those applications reveal that present formulation is a very powerful approach to simulate the fully nonlinear water wave problems.
    Źródło:
    TransNav : International Journal on Marine Navigation and Safety of Sea Transportation; 2008, 2, 2; 137-142
    2083-6473
    2083-6481
    Pojawia się w:
    TransNav : International Journal on Marine Navigation and Safety of Sea Transportation
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the existence for the Cauchy-Neumann problem for the Stokes system in the $L_p$-framework
    Autorzy:
    Mucha, Piotr
    Zajączkowski, Wojciech
    Powiązania:
    https://bibliotekanauki.pl/articles/1205939.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Stokes system
    Marcinkiewicz theorem
    Cauchy-Neumann initial boundary value problem
    the Fourier transform
    existence of solutions
    Opis:
    The existence for the Cauchy-Neumann problem for the Stokes system in a bounded domain $Ω ⊂ ℝ^3$ is proved in a class such that the velocity belongs to $W^{2,1}_r (Ω × (0,T))$, where r > 3. The proof is divided into three steps. First, the existence of solutions is proved in a half-space for vanishing initial data by applying the Marcinkiewicz multiplier theorem. Next, we prove the existence of weak solutions in a bounded domain and then we regularize them. Finally, the problem with nonvanishing initial data is considered.
    Źródło:
    Studia Mathematica; 2000, 143, 1; 75-101
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Two-dimensional vertical Reynolds-Averaged Navier-Stokes equations versus one-dimensional Saint-Venant model for rapidly varied open channel water flow modelling
    Autorzy:
    Szydłowski, M.
    Zima, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/241158.pdf
    Data publikacji:
    2006
    Wydawca:
    Polska Akademia Nauk. Instytut Budownictwa Wodnego PAN
    Tematy:
    mathematical modelling
    Reynolds-averaged Navier-Stokes equations
    Saint-Venant equations
    free surface flow
    rapidly varied flow
    dam-break problem
    Opis:
    The paper concerns mathematical modelling of free surface open channel water flow. In order to simulate the flow two models are used -- two-dimensional vertical Reynolds-Averaged Navier-Stokes equations and one-dimensional Saint-Venant equations. The former is solved with SIPMLE algorithm of finite difference method using Marker and Cell technique to trace a free surface movement. The latter is solved using the finite volume method. The dam-break (water column collapse) problem on horizontal bottom is investigated as a test case. The calculated results are compared with each other. The numerical simulations are examined against laboratory experiment presented by Koshizuka et al (1995). The possibility of using the described models to simulate rapidly varied flow is discussed.
    Źródło:
    Archives of Hydro-Engineering and Environmental Mechanics; 2006, 53, 4; 295-309
    1231-3726
    Pojawia się w:
    Archives of Hydro-Engineering and Environmental Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Mathematical challenges in shape optimization
    Autorzy:
    Henrot, A.
    Sokołowski, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/970146.pdf
    Data publikacji:
    2005
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    optymalizacja kształtu
    optymalizacja topologiczna
    zagadnienie znajdowania wartości własnych
    równanie Naviera-Stokesa
    Navier-Stokes equations
    shape optimization
    topology optimization
    eingenvalue problem
    Opis:
    Activities of the CNRS programme GDR shape optimization are described. Recent developments in shape optimization for eigenvalues and drag minimization are presented.
    Źródło:
    Control and Cybernetics; 2005, 34, 1; 37-57
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
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