Wyniki wyszukiwania - Biblioteka Nauki

1

Numerical modelling of heat transfer in spherical domains by means of the BEM using discretisation in time

100%

Mochnacki B. , Szopa R.

Journal of Theoretical and Applied Mechanics

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2002

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tom Vol. 40 nr 2

357-370

EN

A combined variant of the BEM called in literature the BEM using discretization in time consists in an approximation of the time derivative appearing in Fourier's equation by an adequate differential quotient. The next steps of mathematical manipulations and also the numerical algorithm are similar to a typical boudary element approach. In the paper the method is applied to numerical computations concerning a non-steady heat diffusion in homogeneous and non-homogeneous spherical domains. In the final part of the paper the results of computations are presented.

PL

Kombinowany wariant metody elementów skończonych, nazywany w literaturze MEB, z dyskretyzacją czasu polega na zastąpieniu występującej w równaniu Fouriera pochodnej temperatury po czasie odpowiednim ilorazem różnicowym. Dalsze etapy przekształceń matematycznych i konstrukcji algorytmu numerycznego nie odbiegają od typowego podejścia charakteryzującego klasyczną metodę elementów brzegowych. W pracy metodę kombinowaną wykorzystano do modelowania nieustalonej dyfuzji ciepła w obszarach sferycznych jednorodnych i niejednorodnych. W końcowej części przedstawiono przykłady obliczeń numerycznych.

2

Analysis of thermal processes occuring in tissue with a tumor region using bem

100%

Majchrzak E. , Mochnacki B.

Journal of Theoretical and Applied Mechanics

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2002

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tom Vol. 40 nr 1

101-112

EN

In the paper a numerical algorithm based on the boundary element method is used for temperature field computations in the non-homogeneous domain being a composition of healthy tissue and a tumor region. Thermophysical parameters of subdomains, in particular the perfusion coefficients and metabolic heat sources are different. From the mathematical point of view the problem is described by a system of two Poisson's equations with temperature-dependent source functions. These equations are supplemented by adequate boundary conditions. The discussed algorithm allows one to determine the temperature distribution on the surface of the skin. In this way it is possible to analyse the dependence brtween the geometrical features of the tumor region and the external thermal effects. The results can be useful as the information for noninvasive diagnostics. In the final part of the paper examples of computations are shown.

PL

Algorytm numeryczny bazujący na metodzie elementów brzegowych wykorzystano do obliczeń rozkładów remperatury w obszarze niejednorodnym, składającym się ze zdrowej tkanki i podobszaru nowotworowego. Parametry termofizyczne tych podobszarów są zróżnicowane, a w szczególności różnią się współczynniki perfuzji krwi oraz składniki źródłowe związane z metabolizmem. Z matematycznego punktu widzenia rozważane zagadnienie opisane jest układem dwóch równań z zależnymi od temperatury składnikami źródłowymi. Równania te uzupełniają odpowiednie warunki brzegowe. Przedstawiony algorytm pozwala określić rozkład temperatury na powierzchni tkanki skórnej. W ten sposób można analizować zależności między wielkością, kształtem i położeniem podobszaru nowotworowego, a zewnętrznymi efektami termicznymi. Uzyskane wyniki mogą być przydatne w diagnostyce nieinwazyjnej. W końcowej części artykułu przedstawiono przykłady obliczeń.

3

Estimation of Time Dependent Boundary Heat Flux Using Sensitivity Coefficients

100%

Majchrzak E. , Mendakiewicz J. , Janisz D.

Zeszyty Naukowe. Mechanika / Politechnika Opolska

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2002

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tom z. 75

141-144

EN

In the paper the method of time dependent boundary heat flux estimation is presented. The algorithm is constructed on the basis of the boundary element method and the least squares criterion in which the sensitivity coefficients are introduced. The theoretical considerations are supplemented by the example of computations.

4

Boundary Element Method For The Poisson Equation

100%

Majchrzak E. , Drozdek J. , Lupa M.

Zeszyty Naukowe. Mechanika / Politechnika Opolska

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2002

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tom z. 75

149-154

EN

Application of the standard boundary element method for numerical solution of the Poisson equation requires discretization not only the boundary but also the interior of the domain considered. In this paper we present the variant of the BEM which requires only the boundary discretization. It is the essential advantage of the algorithm proposed in comparison with the classical one. In the final part of the paper the example of computations is shown.

5

Application of the boundary element method to numerical modelling of solidification. Part I - The one domain approach

100%

Mochnacki B. , Szopa R.

Journal of Theoretical and Applied Mechanics

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1998

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tom nr 2

457-468

EN

In the paper the numerical model of thermal processes proceeding in the system casting-mold is discussed - in particular, the solidification of alloys is analyzed. The model is constructed using the composition of the 1st and 2nd schemes of the BEM. The problem considered is treated as a boundary-initial one and it is formulated on the basis of the one domain method (fixed domain method) (cf Mochnacki and Suchy, 1995; Voller, 1991).

PL

W pracy przedstawiono opis procesów cieplnych zachodzących w układzie odlew-forma, a w szczególności rozważono krzepnięcie stopów. Model numeryczny zbudowano wykorzystując tzw. I i II schemat metody elementów brzegowych. Rozważany problem potraktowano jako zadanie brzegowo-początkowe opisane równaniami odpowiadającymi metodzie jednego obszaru (por. Mochnacki i Suchy, 1995; Voller, 1991).

6

Application of the boundary element method to numerical modelling of solidification. Part II - The micro-macro approach

100%

Szopa R.

Journal of Theoretical and Applied Mechanics

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1998

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tom nr 2

469-478

EN

In the paper a numerical model of solidification and cooling processes proceeding in the casting domain is discussed. The model is constructed on the basis of the boundary-initial one and it is formulated in a micro / macro convention; i.e. the component describing a capacity of internal heat sources in an adequate differential equation (the so-called source function) results from the analysis of crystallization process on a microscopic level.

PL

W pracy przedstawiono opis procesów cieplnych (krzepnięcie i krystalizacja) zachodzących w układzie odlew-forma. Model numeryczny zbudowano wykorzystując kombinowany wariant metody elementów brzegowych. Zadanie potraktowano jako problem brzegowo-początkowy sformułowany w konwencji mikro-makro, tzn. składnik opisujący wydajność źródeł wewnętrznych w równaniu energii wynika z analizy procesu krystalizacji na poziomie mikroskopowym.

7

Boundary Element method in dynamic crack analysis

100%

Fedliński P.

Journal of Theoretical and Applied Mechanics

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1998

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tom nr 2

403-421

EN

The boundary element method applications to dynamic fracture mechanics are presented. In the present approach displacement and traction boundary integral equations are used for crack representation. The timedependent solutions are obtained using the time domain method, integral transform method or dual reciprocity method. The dynamic stress intensity factors are calculated using crack opening displacements and the path-independent J-integral. Some new applications of these methods are also shown.

PL

W pracy przedstawiono zastosowanie metody elementów brzegowych w analizie dynamicznej pęknięć. W przyjętym sformułowaniu stosuje się brzegowe równanie całkowe przemieszczeń i sił powierzchniowych dla pęknięcia. Rozwiązania zależne od czasu wyznaczono metodą rozwiązań w dziedzinie czasu, metodą transformacji całkowych i metodą podwójnej zasady wzajemności. Dynamiczne współczynniki intensywności naprężeń obliczono na podstawie przemieszczeń powierzchni pęknięcia i całki J niezależnej od drogi całkowania. Przedstawiono nowe przykłady zastosowania metod.

8

Estimation of boundary temperature using the energy minimization method

100%

Majchrzak E. , Freus K. , Jasiński M.

Zeszyty Naukowe. Mechanika / Politechnika Opolska

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2004

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tom z. 78

235-240

EN

The inverse problem consisting in identification of temperature on the part of boundary limiting the domain considered in discussed. In order to solve the problem the energy minimization method coupled with the boundary element method is used. The computations have been realized for different numbers and positions of control points, the possible disturbances of 'measured' temperatures have been also taken into account. The theoretical considerations are supplemented by the examples of computations verifying the correctness of the algorithm proposed.

9

Numerical solution of a two-dimensional inverse heat transfer problem in gas turbine blade cooling

80%

Frąckowiak A. , Ciałkowski M. , Wolfersdorf J.

Archives of Thermodynamics

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2006

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tom Vol. 27, no. 4

91-98

EN

The problem presented in the paper pertains to cooling of gas turbine blades for known values of external heat transfer coefficient and temperature distributions at the blade outer surface. Taking into account that two conditions are given at the same boundary, such a problem is ill-posed in the Hadamard sense. This means that the difficulties related to solving the inverse problems do not depend on the method used for it. The paper presents a solution to the problem attained with the help of the Boundary Element Method for 2-D multiply connected regions (a three cooling channel gas turbine blade). The problems that arose during the numerical computation and the methods of their solution are presented. The obtained numerical results confirm efficiently the assumptions made for the particular example.

10

Application of 1-D and 2-D discrete wavelet transform to crack identification in statically and dynamically loaded plates

80%

Knitter-Piatkowska A. , Guminiak M.

Engineering Transactions

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2020

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tom Vol. 68, iss. 2

137--157

EN

The paper presents the problem of damage detection in thin plates while considering the influence of static and dynamic characteristics, especially with regard to the modes of vibration as well as the excitation by static loads. The problem of Kirchhoff plate bending is described and solved by the Boundary Element Method (BEM). Rectangular plates supported on boundary or plates supported on boundary and resting on the internal columns are examined. A defect is introduced by the additional edges forming a crack in the plate domain. The analyses of static and dynamic structural responses are carried out with the use of Discrete Wavelet Transform (DWT). Signal decomposition according to the Mallat pyramid algorithm is applied. To obtain a more adequate input function subjected to DWT the white noise disturbing the signal is considered together with the structural response. In the dynamic experiments the plate undergoes vibrations similar to natural modes. The measured variables are static deflections and vertical displacement amplitudes. All of them are established at internal collocation points distributed alongside the line parallel to selected plate edge.

11

Sensitivity of conti-casting process with respect to cooling conditions

80%

Mochnacki B. , Majchrzak E.

Journal of Theoretical and Applied Mechanics

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2002

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tom Vol. 40 nr 1

129-147

EN

In the first part of this paper mathematical description of heat transfer processes proceeding in the domain of continuous casting is presented. The approach called the second generation modelling is taken into account. In particular, the capacity of a source function in the energy equation is determined by the nucleation and growth laws and the Johnson-Mehl-Avrami-Kolmogorow theory. Next, on the basis of the methods of sensitivity analysis the influence of cooling conditions of the cast slab surface on the course of solidification process is analyzed. At the stage of numerical computations the boundary element method has been used. In the final part of the paper an example of computations is presented.

PL

W pierwszej części pracy przedstawiono opis matematyczny krzepnięcia wlewka ciągłego wytwarzanego z czystego matalu. Do opisu wykorzystano podeście nazywane modelem drugiej generacji. W szczególności, wydajność wewnętrznych źródeł ciepła będąca składnikiem równania energii jest wyznaczana na podstawie praw zarodkowania i wzrostu oraz teorii Johnsona-Mehla-Avrami-Kołomogorowa. Następnie, wykorzystując metodę bezpośrednią analizy wrażliwości, badano wpływ warunków chłodzenia powierzchni wlewka na proces jego krzepnięcia. Na etapie obliczeń numerycznych zastosowano metodę elementów brzegowych. W końcowej części pracy pokazano przykład obliczeń numerycznych.

12

Application of the Coupled Boundary Element Method With Atomic Model in the Static Analysis

80%

Mrozek A. , Burczyński T.

Computer Methods in Materials Science

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2007

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tom Vol. 7, No. 2

284-288

EN

1. Introduction The models of material behaviour in the atomistic scale allows us to understand the micro and macroscopic events. The algorithm based on the boundary element method (BEM) coupled with a discrete atomistic model is presented in this paper. In this approach, the material behaviour at the molecular level can be simulated and the total number of degrees of freedom is reduced, because in most cases only a small part of the mulitiscale model contains molecules and BEM doesn’t need discretization of the continuum’s domain. 2. The molecular model The discrete molecular model is applied to simulate deformations of the atomistic lattice under loads. This model is based on the equilibrium equations of atomic interaction forces. These pair-wise interaction forces between each two molecules in the lattice are computed as derivative of the interatomic potential respect to the distance between two atoms. In this work, the empirical Lennard-Jones and the Morse potentials were used to describe interatomic behaviour [4]. The force equilibrium equations are computed for all the nearest-neighbour atoms interactions and then, assembled into the global non-linear system of equations [2]. Constraints are applied using elimination method. The Newton-Raphson method is used to solve that system of equations. The main concept is to assume some initial positions of molecules (eg. undeformed lattice) and obtain final, stable equilibrium configuration of atoms. The equilibrium state of the lattice corresponds to the minimal value of the total potential energy of the atomic structure. The process of minimization of the potential energy can be also done by using the evolutionary algorithm [3]. The applications of these algorithms in prediction of atoms distribution give a great probability of finding the global optimal solutions. 3. The mulitiscale model The multiscale model is composed from three main blocks: the continuum model, the interface domain and the discrete atomic model. The boundary element method [1] is used to simulate material behaviour at the continuum level. The interface domain contains so-called embedded atoms which coordinates are equal to the corresponding nodes of boundary elements. Firstly, the macroscale boundary conditions are applied and the BEM model is solved. Displacements of the interface atoms are obtained and introduced as initial displacements of the outer boundary of the atomic lattice. In the next step, equilibrium positions of the atoms in the nanoscale model are computed, using the method described above. Finally, forces acting on interface atoms are computed and introduced as a nodal forces to the BEM model. These computations are repeated until achieved displacements are satisfactory small. 3. Final remarks Some simulations of a dislocation behaviour and deformations of the atomic lattice are performed. Both hexagonal and orthogonal configurations of the lattice are considered. The convergence of the Newton-Raphson method and the total number of iterations strongly depend on the initial positions of the atoms and their displacements taken form BEM. However, for small deformations of the atomic structure, the Newton-Raphson method is faster than the evolutionary algorithm. This kind of analysis gives possibility of simulation, e.g. slips, crack behaviour and fracture at the molecular level and also may be used in modelling some technological processes in material science. The application of loads and displacements to the BEM continuum model is easier then direct in the molecular level. 4. Acknowledgement: The research is financed by the Foundation for Polish Science (2005-2008). 5. References [1] T. Burczynski (1995), The Boundary Element Method in Mechanics, WNT, Warsaw (in Polish) [2] Y. W. Kwon (2003). Discrete atomic and smeared continuum modelling for static analysis Engineering Computations, Vol. 20 No. 8. 964–978. [3] A. Mrozek, W. Kus, P. Orantek, T. Burczynski (2005). Prediction of the aluminium atoms distribution using evolutionary algorithm, Recent Developments in Artificial Intelligence Methods, ed. T. Burczynski, W. Cholewa, M. Moczulski, AI-METH Series, Gliwice. 127-130. [4] R. Sunyk, P. Steinmann (2002). On higher gradients in continuum-atomistic modelling, International Journal of Solids and Structures, No. 40. 6877-6896.

13

Modelling of tissue thermal injury formation process with application of direct sensitivity method

80%

Jasiński M.

Journal of Theoretical and Applied Mechanics

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2014

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tom Vol. 52 nr 4

947--957

EN

In the paper, numerical analysis of thermal processes proceeding in a biological tissue is presented. The tissue is subjected to the external heat impulse and a 2D problem is taken into account. In order to determine the influence of variations of thermophysical parameters of the tissue on the value of tissue injury integral and the area of the lesion, a direct approach of sensitivity analysis is applied. The process of thermal injury formation is also analyzed. At the stage of numerical simulation, the boundary element method is used. In the final part of the paper, an example of numerical simulation is shown.

14

Analysis of hydrodynamic pressure fields of motorboats and pontoons in shallow water

80%

Bielański J.

Hydroacoustics

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2016

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tom Vol. 19

9--16

EN

The article presents the results of calculations of the pressure fields generated by a motorboat at the bottom of a shallow sea. Calculations were made using the boundary elements method (BEM), arranged on the surface of the boat and the bottom of the sea. This method is described in [3], and applied on a free surface linearized boundary condition. Results for four different lengths of motorboats, from 2.85 m to 9.5 m, sea depth from 1 m to 10 m, are presented in the form of a surface, approximated by a polynomial function whose coefficients are given. These functional relations allow one to calculate the maximum and minimum hydrodynamic pressure generated by the motor boat length, in the range as above, and the sea depth to about 10 m when flying at speeds of up to 20 m / s. Given functional dependencies can be used, in the field of security and anti-terrorism defences, and can serve to identify the type and size of speedboats, up to about 10 meters and a displacement of about 8 tons.

15

A singular and non-singular BEM analysis of thin plates considering modified boundary conditions

80%

Guminiak M.

Foundations of Civil and Environmental Engineering

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2011

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tom No. 14

5--45

EN

A static analysis of Kirchhoff plates using the boundary element method is presented in the paper. In this approach, physical boundary conditions are imposed. The Bettie theorem is used to derive the boundary integral equation. The collocation version of the boundary element method is presented. Typical and simplified, curved constant boundary elements are introduced.

16

Exact solutions of integrals to be used in computing the magnetic field by boundary-integral technique

80%

Pawluk K.

Prace Instytutu Elektrotechniki

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2009

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tom Z. 241

9-27

EN

Exact analytical formulae suitable to integrate the boundary quantity over a rectangular boundary element are given. They can be used in algorithms of the boundary-integral technique when some field quantity at the vicinity of the boundaries is searched for. The special computer test software was accomplished which enabled to compare the approximate integrations by Gauss quadrature to those ones obtained by the exact formulae. The error of the numerical approach increases significantly when a distance of field points from the boundary element becomes comparable with the size of it. For the larger distance, both kind of integration are equivalent. The above statement seems to be important when the boundary-integral technique should be applied to compute the magnetic field within the air gap of electric machines.

PL

Podano dokładne wzory do całkowania wielkości brzegowej po prostokątnym elemencie brzegowym. Mogą one znaleźć zastosowanie w algorytmach technik całkowo-brzegowych, gdy obliczenie dotyczy wielkości polowych w pobliżu samego elementu brzegowego. Specjalnie przygotowane testowe programy komputerowe umożliwiły przeprowadzenie porównań wyników obliczeń całkowania przeprowadzonego numerycznie kwadraturą Gaussa z całkowaniem za pomocą podanych wzorów analitycznych. Błąd obliczenia numerycznego wzrasta znacząco dla punktów polowych, gdy ich odległość od elementu brzegowego staje się współmierna z rozmiarem samego elementu. Dla większych odległości obydwa rodzaje całkowania są równoważne. Powyższe stwierdzenie jest szczególnie istotne, gdy technika całkowo-brzegowa ma być zastosowana do obliczania pola magnetycznego w szczelinie powietrznej maszyny elektrycznej.

17

Computational modelling of head-related transfer function

80%

Dobrucki A. B. , Plaskota P.

Archives of Acoustics

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2007

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tom Vol. 32, No. 3

659--682

EN

Measuring the Head-Related Transfer Function (HRTF) is an efficient method that takes into consideration the influence of the human body on the sound spectrum. The data base used in reproduction of the sound source position is built using the measurement results. The base is individual for each person, which makes it impossible to make a versatile base for all listeners. In this paper a numerical model of artificial head is presented. The model allows to determine the value of HRTF without making measurements. The model includes both geometrical and acoustical parameters. A method which is often used to determine the acoustical field parameters is the boundary element method, which was used to calculate the values of HRTF in this work. In the conclusion results of the calculations are presented and the correctness of the previous assumption made while constructing the geometric part of the numerical human head model is discussed.

18

Elongation determination using finite element and boundary element method

80%

Kisała P. , Wójcik W. , Smailov N. , Kalizhanova A. , Harasim D.

International Journal of Electronics and Telecommunications

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2015

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tom Vol. 61, No. 4

389-394

EN

This paper presents an application of the finite element method and boundary element method to determine the distribution of the elongation. Computer simulations were performed using the computation of numerical algorithms according to a mathematical structure of the model and taking into account the values of all other elements of the fiber Bragg grating (FBG) sensor. Experimental studies were confirmed by elongation measurement system using one uniform FBG.

19

The application of fundamental solutions in static analysis of thin plates resting on the internal elastic support

80%

Pawlak Z. , Guminiak M.

Foundations of Civil and Environmental Engineering

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2008

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tom No. 11

67-96

EN

A static analysis of Kirchhoff plates rested on the elastic internal supports has been discussed in the paper. The Finite Strip Method and Boundary Element Method have been used as an engineering tool in the analysis. Suitable fundamental solutions are applied in these method. Using BEM modified approach, there is no need to introduce the Kirchhoff forces at the plate corner and equivalent shear forces at the plate boundary. Two unknown and independent variables are considered at the boundary element node. The collocation points are located slightly outside the plate boundary, hence the quasidiagonal integrals of fundamental functions are non-singular. The constant type of boundary element has been used. According to the finite strip method a continuous structure is divided into a set of identical elements simply supported on opposite edges. The unknowns are the deflections and the transverse slope amplitudes along the nodal lines. The difference equation formulation is applied to express the equilibrium conditions of the discrete system. This reduces the number of degrees of freedom to be analyzed. The solution of one equilibrium difference equation yields the fundamental function of the considered plate strip. The fundamental solution derived in this way, can be used to solve the static problem of finite plate in analogically as in the boundary element method for continuous systems.

20

Application of the Boundary Element Method for the Simulation of Two-dimensional Viscous Incompressible Flow

80%

Prybytak D.

Archives of Hydro-Engineering and Environmental Mechanics

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2014

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tom Vol. 61, nr 3-4

163–-173

EN

The paper presents the application of an indirect variant of the boundary element method (BEM) to solve the two-dimensional steady flow of a Stokes liquid. In the BEM, a system of differential equations is transformed into integral equations. This makes it possible to limit discretization to the border of the solution. Numerical discretization of the computational domain was performed with linear boundary elements, for which a constant value of unknown functions was assumed. The verification was carried out for the case of flow in a square cavity with one moving wall. The results obtained show that the use of approximations by simple linear functions is relatively easy for different shapes of the area, but the result may be affected by significant errors.