Wyniki wyszukiwania - Biblioteka Nauki

1

Conditions for the solvability of a nonlinear boundary value problem of the flow of a viscous fluid

100%

Studziński J.

Mathematica Applicanda

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1985

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tom 12

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nr 24

PL

.

EN

The author presents a discussion of existence, uniqueness and convergence of finite difference approximations for Navier-Stokes equations with convection in a two-dimensional rectangle with sufficiently small data.

2

On the magnetization-based Lagrangian methods for 2D and 3D viscous flows. Part 1 - theoretical background

51%

Styczek A. , Szumbarski J.

Journal of Theoretical and Applied Mechanics

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2002

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tom Vol. 40 nr 2

339-355

EN

The paper presents the background of an alternative formulation of the Navier-Stokes equation using a variable called the magnetization. Several variants of governing equations, based on different choices of a particular gauge transform, are discussed. The remaining part of the paper is devoted to the formulation of a Lagrangian approach to 2D and 3D viscous flows. First, the carrier of the magnetization (the magneton) is defined and the corresponding induction law is derived. The instantaneous velocity field is constructed as a superposition of contributions from a large set of magnetons and a uniform stream. An essential feature of the method is a one-time-step operator splitting, consisting in the consecutive solution of three sub-problems: generation of the magnetization on solid boudaries, advection-diffusion of the magnetization and sretching.

PL

W artykule przedstawione jest sformułowanie problemu granicznego dla równań Naviera-Stokesa z użyciem tzw. pola magnetyzacji. Sformułowanie nie jest jednoznaczne, lecz wiąże się z przyjętą transformacją cechowania. Rozważane są różne postacie tej transformacji i dokonuje się wyboru odpowiednich wariantów. Pole magnetyzacji przedstawione jest w formie lagrangeowskiej. Wprowadza się cząstki będące źródłami tego pola i określa się związane z ich zbiorem pole prędkości. Cząstki magnetyzacji (zwane magnetonami) poruszają się w indukowanym polu prędkości, wykonują ruch losowy odpowiadający dyfuzji i podlegają przekształceniu w sposób opisany członem źródłowym (tzw. stretching). Warunek brzegowy sformułowany na opływanym ciele jest realizowany przez tworzenie w każdej chwili nowych cząstek ulokowanych w bliskim otoczeniu powierzchni ciała.

3

Computations of an unsteady viscous flow in a three dimensional system of ducts. Part I: Formulation of the mathematical problem and numerical method

51%

Szumbarski J. , Olszewski P. , Styczek A. , Rokicki J.

Journal of Theoretical and Applied Mechanics

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2004

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tom Vol. 42 nr 1

21-39

EN

Numerical modeling of an unsteady flow of a viscous incompressible fluid inside a branched pipe system is considered. The mathematical formulation is given with special emphasis on inlet/outlet conditions. The equivalent weak form of the initial-boundary value problem is presented. The numerical method based on solutions to particular Stokes problems is proposed and described in some details. Finally, some general remarks about the implementation issues within the framework of the spectral element discretization are made.

PL

W pracy rozważono problem numerycznego wyznaczania nieustalonego przepływu cieczy lepkiej w układzie trójwymiarowych przewodów. Podano sformułowanie wariacyjne zagadnienia uwzględniające uogólnione warunki brzegowe na wlotach/wylotach do obszaru ruchu. Opisano metodę obliczeniową, opartą na zastosowaniu wskaźników Lagrange'a i superpozycji szczególnych problemów Stokesa w każdym kroku czasowym.

4

Influence of Liquid Metal Movements on the Casting Creation

51%

Sowa L. , Skrzypczak T. , Kwiatoń P.

Archives of Metallurgy and Materials

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2021

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tom Vol. 66, iss. 2

489--495

EN

Knowledge about complex physical phenomena used in the casting process simulation requires continuous complementary research and improvement in mathematical modeling. The basic mathematical model taking into account only thermal phenomena often becomes insufficient to analyze the process of metal solidification, therefore more complex models are formulated, which include coupled heat-flow phenomena, mechanical or shrinkage phenomena. However, such models significantly complicate and lengthen numerical simulations; therefore the work is limited only to the analysis of coupled thermal and flow phenomena. The mathematical description consists then of a system of Navier-Stokes differential equations, flow continuity and energy. The finite element method was used to numerically modeling this problem. In computer simulations, the impact of liquid metal movements on the alloy solidification process in the casting-riser system was assessed, which was the purpose of this work, and the locations of possible shrinkage defects were pointed out, trying to ensure the right supply conditions for the casting to be free from these defects.

5

Tests on a new method for numerical solution to the Navier-Stokes equations*. Part I: plane unsteady flow in finite, rectangular domains

51%

Klonowska M. E. , Kołodziejczyk M.

Applied Mechanics and Engineering

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1999

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tom Vol. 4, no 2

311-339

EN

The paper deals with a new method (Prosnak and Kosma, 1991) for the determination of unsteady, plane flows of viscous incompressible fluids. The characteristic feature of the method consists in elimination of pressure from the system of the Navier-Stokes equations governing the flow - in such a manner that the order of the resulting system is not increased in comparison with the original one. Furthermore, the mathematical problem posed for the resulting system is reduced in the frame of the method to an initial problem for a system of first order ordinary differential equations, wherein time represents the only independent variable. The nonlinearities of the Navier-Stokes equations do not cause any difficulties by virtue of such an approach. In this paper, the method has been applied to flows in plane, finite rectangular domains, and domains composed of rectangles. Numerical solutions to such problems are presented in the paper in graphical form, and some conclusions are drawn concerning the results as well as the method.

6

Shape sensitivity analysis of time-dependent flows of incompressible non-Newtonian fluids

51%

Sokołowski J. , Stebel J.

Control and Cybernetics

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2011

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tom Vol. 40, no 4

1077-1097

EN

We study the shape differentiability of a cost function for the flow of an incompressible viscous fluid of power-law type. The fluid is confined to a bounded planar domain surrounding an obstacle. For smooth perturbations of the shape of the obstacle we express the shape gradient of the cost function which can be subsequently used to improve the initial design.

7

On shape sensitivity analysis of the cost functional without shape sensitivity of the state variable

51%

Kasumba H. , Kunisch K.

Control and Cybernetics

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2011

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tom Vol. 40, no 4

989-1017

EN

A general framework for calculating shape derivatives for domain optimization problems with partial differential equations as constraints is presented. The first order approximation of the cost with respect to the geometry perturbation is arranged in an efficient manner that allows the computation of the shape derivative of the cost without the necessity to involve the shape derivative of the state variable. In doing so, the state variable is only required to be Lipschitz continuous with respect to geometry perturbations. Application to shape optimization with the Navier-Stokes equations as PDE constraint is given.

8

On the numerical solution of one inverse problem for a linearized two-dimensional system of Navier-Stokes equations

51%

Jenaliyev M. , Ramazanov M. , Yergaliyev M.

Opuscula Mathematica

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2022

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tom Vol. 42, no. 5

709--725

EN

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.

9

Influence of Liquid Metal Movements on the Casting Creation

51%

Sowa L. , Skrzypczak T. , Kwiatoń P. , Sowa L. , Skrzypczak T. , Kwiatoń P.

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tom 66

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nr 2

10

Algorithms for the exact solution of two matrix equations occurring in the driven cavity problem

51%

Klonowska M. E. , Prosnak W. J.

Oceanologia

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1999

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tom No. 41 (1)

3-23

EN

It is shown that two particular systems of linear equations, derived in an earlier paper by Prosnak and Kosma (1991), can be solved in an exact time- and storage-saving manner. First of all, by the proper elimination of unknowns, each system can be reduced to a smaller one containing only half of the unknowns. In the first case, the matrix of coefficients of the so reduced system turns out to be tridiagonal, its elements consisting of square submatrices. Moreover, the reduced system can be split into two independent ones. In the second case, the matrix of the reduced system can be presented as the product of two triangular ones, each one being partitioned in square submatrices. Corresponding algorithms and computer programs have been developed in order to investigate whether some economy in storage and computing time is really attainable. Affirmative conclusions are drawn from the results of computations. This means that the new method of solving problems governed by the Navier-Stokes equations, presented in the cited paper, can be applied in a more effective manner.

11

A regularity criterion for the Navier-Stokes equations in terms of the pressure gradient

51%

Bosia S. , Conti M. , Pata V.

Open Mathematics

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2014

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tom 12

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nr 7

1015-1025

EN

The incompressible three-dimensional Navier-Stokes equations are considered. A new regularity criterion for weak solutions is established in terms of the pressure gradient.

12

On the magnetization-based Lagrangian methods for 2D and 3D viscous flows. Part 2 - numerical implementation and results

51%

Duszyński P. , Olszewski P. , Poćwierz M. , Styczek A. , Szumbarski J.

Journal of Theoretical and Applied Mechanics

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2002

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tom Vol. 40 nr 4

825-846

EN

The numerical implementation of the Lagrangian method using particles of the magnetization field (magnetons) has been considered. A detailed description of essential elements of the algorithm has been provided. The presentation has focused on computations of stretching, where a novel integral-based rather than point wise approach has been proposed. The results of test computations, carried out for viscous flows past 2D and 3D bodies, have been presented. Difficulties with obtaining stable large-time simulations have been encountered and discussed. It has also been shown that, in contrast to flows around solid bodies, the vortex dynamics in the absence of boundaries can be successfully simulated, however, some consistent remeshing technique may by necessary to achieve appropriate resolution.

PL

W tej części pracy przedstawiono realizację numeryczną i opis wyników wyznaczania ruchów cieczy lepkiej uzyskanych lagrangeowską metodą cząstek magnetyzacji. Podano szczegóły wyznaczenia członu źródłowego (tzw.stretching term). Zaproponowano szczególny nowy sposób postępowania związany z tym efektem. Praca zawiera wyniki symulacji opływów dwu i trójwymiarowych oraz dyskusję napotkanych trudności. Podano też wyniki symulacji ewolucji swobodnych struktur wirowych. Modelowanie takich struktur jest prostsze wobec braku warunku brzegowego.

13

Numerical study of the Yosida method applied to viscous incompressible internal flows with open boundary conditions

51%

Szumbarski J.

Archives of Mechanics

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2016

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tom Vol. 68, nr 2

133--160

EN

The Yosida methods for incompressible viscous flows are investigated numerically in the aspect of local and global errors of volume conservation. Unsteady Stokes and Navier–Stokes flows past an obstacle inserted into 2D channel are used as the test cases. Open boundary conditions are imposed at the channel’s inlet and outlet. The results obtained by the Yosida-based Spectral Element Method (SEM) solvers are compared to the results obtained by the SEM solver using exact factorization of the Uzawa system. Analysis of parametric variation of the velocity divergence and the flow rate errors is presented. It is concluded that switching to higher-order Uzawa methods reduces substantially volume conservation errors and removes numerical artifacts observed at the channel’s inlet when the basic Yosida method is used.

14

Global existence for a one-dimensional model in gas dynamics

51%

Njamkepo S.

Applicationes Mathematicae

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1996-1997

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tom 24

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nr 2

203-221

EN

We prove the existence of a global solution for a one-dimensio- nal Navier-Stokes system for a gas with internal capillarity.

15

Warstwa przyścienna w lepkim naddźwiękowym opływie profilu

44%

Wrzesień S.

Zeszyty Naukowe. Cieplne Maszyny Przepływowe - Turbomachinery / Politechnika Łódzka

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2000

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tom nr 117, vol. 1

137-142

PL

Rozpatrzono naddźwiękowy opływ profilu lepkim gazem przewodzącym ciepło. W algorytmie wykorzystano równania Naviera-Stokesa, równanie ciągłości i energii, oraz zależności dodatkowe. Rozwiązanie problemu wyznaczono metodą, dekompozycji równań z iteracyjną procedurą względem czasu. Zastosowano metodę różnic skończonych z podwójną transformacją obszaru przepływu na pomocniczy obszar. Zastosowana transformacja umożliwia łatwe zagęszczenie siatki różnicowej w obszarze bezpośredniego sąsiedztwa powierzchni profilu. Pozwala to na dokładniejsze zbadanie formującej się w opływie warstwy przyściennej.

EN

Supersonic flow around an airfoil by viscous heat conducted gas were evaluated. The Navier-Stokes set of equation, continuos and energy equation as well as additional dependencies were used in algorithm. The solution of the problem was considered by equation decomposition method with the iteration procedure with respect to time. The differential scheme with a double transformation of a flow zone into auxiliary zone was implemented. Transformation enables for a condense of the differential grid within an airfoil surface zone. It also allows for more precision evaluation of increasing boundary layer.

16

Analytical solutions for the unsteady MHD rotating flow over a rotating sphere near the equator

44%

Sweet E. , Vajravelu K. , Gorder R.

Open Physics

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2011

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tom 9

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nr 1

167-175

EN

In this paper we investigate the three-dimensional magnetohydrodynamic (MHD) rotating flow of a viscous fluid over a rotating sphere near the equator. The Navier-Stokes equations in spherical polar coordinates are reduced to a coupled system of nonlinear partial differential equations. Self-similar solutions are obtained for the steady state system, resulting from a coupled system of nonlinear ordinary differential equations. Analytical solutions are obtained and are used to study the effects of the magnetic field and the suction/injection parameter on the flow characteristics. The analytical solutions agree well with the numerical solutions of Chamkha et al. [31]. Moreover, the obtained analytical solutions for the steady state are used to obtain the unsteady state results. Furthermore, for various values of the temporal variable, we obtain analytical solutions for the flow field and present through figures.

17

Computations of an unsteady viscous flow in a three-dimensional system of ducts. Part II: Implementation of the spectral element method and sample results

44%

Szumbarski J. , Olszewski P. , Wawruch K. , Małota Z.

Journal of Theoretical and Applied Mechanics

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2004

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tom Vol. 42 nr 4

869-903

EN

The second part the paper focuses on implementation issues of the spectral element technique and presents sample results of numerical simulations. Particular algorithms like preconditioning of the presser solver, fast diagonalization method and the projection method for solving sequences of large linear systems are described in some details. The computational results, obtained for both test domains and geometries of medical origin, are presented. The comparison with the results of computations with the FIDAP package is provided. The difficulties and limitations of the spectral method and current implementation are discussed. Attempts of the parallelization of the spectral code and the obtained efficiency are briefly described.

PL

Druga część pracy omawia zagadnienia związane z implementacją metody spektralnych elementów skończonych oraz prezentuje wybrane wyniki obliczeń. Przedstawiono również wybrane algorytmy: skalowanie (ang. preconditioning) procesu iteracyjnego dla ciśnienia, metodę FDM oraz metodę efektywnego rozwiązywania sekwencji układów liniowych dużych rozmiarów z ustaloną macierzą. Omówiono wyniki obliczeń testowych. Przedyskutowano trudności i ograniczenia aktualnej implementacji oraz zaprezentowano wstępne efekty paralelizacji solwera spektralnego.

18

A mixed, scalable domain decomposition method for incompressible flow

44%

Vergnault E. , Allix O. , Maison-le-Poëc S.

Computer Assisted Methods in Engineering and Science

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2012

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tom Vol. 19, no. 2

173-190

EN

This work deals with the construction of a mixed and extensible domain decomposition method for incompressible flows. In the scheme proposed here, the solution is sought at the intersection of two spaces, one containing the solution of the Navier–Stokes equations considered separately in each subdomain, and theother one containing the solutions of the compatibility equations on the interfaces. A solution verifying all the equations of the two spaces is achieved iteratively. One di?culty is that the interface problem is large and dense. In order to reduce its cost while maintaining the extensibility of the method, we defined an interface macroproblem in terms of a few interface macro unknowns. The best option takes advantage of the incompressibility condition to prescribe an interface macroproblem which propagates the information to the whole domain by making use of only two unknowns per interface. Several examples are used to illustrate the main properties of the method.

19

On local existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion

44%

Mucha P. B. , Zajączkowski W.

Applicationes Mathematicae

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2000

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tom 27

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nr 3

319-333

EN

The local-in-time existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion is proved. We show the existence of solutions with lowest possible regularity for this problem such that $u\in W^{2,1}_r(\widetilde{{\mitΩ}}^T)$ with r>3. The existence is proved by the method of successive approximations where the solvability of the Cauchy-Neumann problem for the Stokes system is applied. We have to underline that in the $L_p$-approach the Lagrangian coordinates must be used. We are looking for solutions with lowest possible regularity because this simplifies the proof and decreases the number of compatibility conditions.

20

Steady-state analytical solutions for the lattice boltzmann equation

44%

Házi G.

Open Physics

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2003

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tom 1

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nr 3

453-462

EN

A general class of analytical solutions of the lattice Boltzmann equation is derived for two-dimensional, steady-state unidirectional flows. A subset of the solutions that verifies the corresponding Navier-Stokes equations is given. It is pointed out that this class includes, e.g., the Couette and the Poiseuille flow but not, e.g., the basic Kolmogorov flow. For steady-state non-unidirectional flows, first and second order solutions of the lattice Boltzmann equation are derived. Practical consequences of the analysis are mentioned. Differences between the technique applied here and those used in some earlier works are emphasized.