Wyniki wyszukiwania - Biblioteka Nauki

1

Implicit versus explicit finite volume schemes for extreme, free surface water flow modelling

100%

Szydłowski M.

Archives of Hydro-Engineering and Environmental Mechanics

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2004

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tom Vol. 51, nr 3

287-303

EN

One explicit and three implicit finite volume method schemes of the Roe type are presented in the paper. The properties and applicability of these methods for modelling unsteady, rapidly varied, open channel flow are investigated. The schemes are used for numerical simulation of one-dimensional extreme flow described by de Saint-Venant equations. The computational results are compared with each other and an analytical (exact) solution to an idealized dam-break problem. The classical versions of general scheme implicit in time - fully implicit and trapezoidal scheme - are not restricted by a stability condition, like an explicit one, however they add some numerical diffusion and dispersion errors to the solution. The modification of parameter , originally proposed for a box scheme of finite difference method, has improved computational properties of the general one-step implicit scheme. This version of finite volume scheme of the Roe type implicit in time can be recommended for modelling and simulation of transient flows in storm sewers and open channel networks.

2

Mixed convection heat transfer of a nanofluid in a square ventilated cavity separated horizontally by a porous layer and discrete heat source

100%

Messaoud H. , Adel S. , Ouerdia O.

Archives of Thermodynamics

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2023

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tom Vol. 44, no 2

87--114

EN

Laminar mixed convection heat transfer in a vented square cavity separated by a porous layer filled with different nanofluids (Fe3O4, Cu, Ag and Al2O3) has been investigated numerically. The governing equations of mixed convection flow for a Newtonian nanofluid are assumed to be two-dimensional, steady and laminar. These equations are solved numerically by using the finite volume technique. The effects of significant parameters such as the Reynolds number (10 ≤ Re ≤ 1000), Grashof number (103 ≤ Gr ≤ 106 ), nanoparticle volume fraction (0.1 ≤ φ ≤ 0.6), porous layer thickness (0 ≤ γ ≤ 1) and porous layer position (0.1 ≤ δ ≤ 0.9) are studied. Numerical simulation details are visualized in terms of streamline, isotherm contours, and average Nusselt number along the heated source. It has been shown that variations in Reynolds and Darcy numbers have an impact on the flow pattern and heat transfer within a cavity. For higher Reynolds (Re > 100), Grashof (Gr > 105 ) numbers and nanoparticles volume fractions the heat transfer rate is enhanced and it is optimal at lower values of Darcy number (Da = 10−5 ). In addition, it is noticed that the porous layer thickness and location have a significant effect on the control of the heat transfer rate inside the cavity. Furthermore, it is worth noticing that Ag nanoparticles presented the largest heated transfer rate compared to other nanoparticles.

3

Unstructured Finite-volume Meshes for Two-dimensional Flow in Variably Saturated Porous Media

100%

Burzyński K. , Szymkiewicz A.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2011

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tom Vol. 15, No 3-4

339-352

EN

This paper presents a numerical algorithm for solving the equation describing variably saturated flow in porous media. The algorithm is based on a control volume finite element approach and can be applied to two-dimensional unstructured meshes consisting of triangular elements. Two methods of defining the dual control volume grid are discussed. We also demonstrate that the method of calculating the average permeability at the control volume face significantly influences numerical results.

4

Improved HLL Scheme for 1D Dam-Break Flows over Complex Topography

100%

Ying X. , Wang S. S. Y.

Archives of Hydro-Engineering and Environmental Mechanics

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2010

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tom Vol. 57, nr 1

31-41

EN

It has been discovered that the shallow water model based on approximate Riemann solvers can produce unrealistic flows in the case of uneven topography and inaccurate solutions of discharge near hydraulic jumps. To overcome these deficiencies, we proposed a new approach to implement the HLL Riemann solver for open channel flows, including: (1) adopting a form of Saint Venant equations which have only one source term representing driving forces; (2) defining discharge at interface and evaluating it according to the flux obtained by the HLL Riemann solver. In this paper, the performance of this new method is evaluated by means of dam-break flows over a channel with triangular cross-section and a natural river valley with complex topography, respectively. Comparisons of computed results with analytic solutions and data measured from the physical model show that the proposed method is capable of satisfactorily reproducing dam-break flows over complex topography.

5

Numerical methods of solving equations of hydrodynamics from perspectives of the code FLASH

100%

Murawski K. , Lee D.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2011

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tom Vol. 59, nr 1

81-91

EN

In this paper we review numerical methods for hydrodynamic equations. Internal complexity make numerical solutions of these equations a formidable task. We present results of advanced numerical simulations for a complex system with a use of a publicly available code, FLASH. These results proof that the numerical methods cope very well with this task.

6

Numerical solutions of magnetohydrodynamic equations

100%

Murawski K. , Murawski K.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2011

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tom Vol. 59, nr 2

219-226

EN

In this paper we review several mathematical aspects in numerical methods for magnetohydrodynamic equations. The intrinsic complexity and the requirements of the selenoidity condition make numerical solutions of these equations a formidable task. We present results of advanced numerical simulations for a complex system, which reveal that the numerical methods cope very well with this task.

7

Numerical modelling the air flow in parts of air jet loom

100%

Adámek K.

Computer Assisted Mechanics and Engineering Sciences

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1999

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tom Vol. 6, No. 3-4

251-261

EN

Paper summarizes the first results of two-dimensional (2D) numerically modelled expansion and flow of compressible and non-viscous gas in typical parts of air jet weaving system ; namely in main nozzle designed as an ejector with various shapes of the mixing zone, in relay (auxiliary) nozzle with substantial flow separation in the rash flow bend directly before the nozzle outlet, and the influence of the reed dent edges shape on the free stream reflection and penetration through reed gaps along a real 'porous' wall. The used Euler's equations are solved by a Finite Volumes Method (FVM) with automatic mesh generation and optimization of unstructured triangle mesh. Graphical results show 2D isolinies of all gas state values, further Mach number, entropy and velocity vectors. 1D profiles of all quantities along chosen cross-section or surfaces can be obtained, too. They give to the designer a large and quick review about the problem. The condicience with experiment, measuring and weaving tests is very good. The advantage of numerical modelling consists in the very quick, simple and user-friendly operation.

8

The basic closures of fluid mechanics in form characteristic for the Finite Volume Method

100%

Sobieski W.

Technical Sciences / University of Warmia and Mazury in Olsztyn

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2013

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tom nr 16(2)

93--107

EN

This short article presents all basic “closures” that are needed to supplementation the general set of balance equations in form characteristic for the Finite Volume Method. In subsequent chapters the equation of state, viscous molecular stress tensor, turbulent stress tensor, molecular heat flux, turbulent heat flux and momentum and energy sources were described. This article is a second part of a cycle dedicated for the mathematical basis of Finite Volume Method. The motivation for writing the article follows from the observation that the Finite Volume Method is usually described in greater detail in monographic books, or very briefly in the basic books dedicated to fluid mechanics. This article is an attempt to center justifications of these approaches, so that in the simplest way show the readers the basic knowledge of the so-called Computational Fluid Mechanics. For this reason this article can be treated as a literature review.

9

Solution of the Dike-break Problem Using Finite Volume Method and Splitting Technique

88%

Gąsiorowski D.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2011

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tom Vol. 15, No 3-4

251-270

EN

In this paper, an approach using the finite volume method (FVM) for the solution of two-dimensional shallow water equations is described. Such equations are frequently used to simulate dam-break and dike-break induced flows. The applied numerical algorithm of the FVM is based on a wave-propagation algorithm, which ensures a stable solution and, simultaneously, minimizes numerical errors. Dimensional decomposition according to the coordinate directions was used to split two-dimensional shallow water equations into one-dimensional equations. Additionally, splitting was also applied with respect to the physical processes. The applied dimensional and physical splitting, together with the wave-propagation algorithm led to an effective algorithm and ensured proper incorporation of source terms into the scheme of the finite volume method. A detailed description of an approximation for numerical fluxes and source terms is presented. The obtained numerical results are compared with analytical solutions, laboratory experiments and other results available in the literature.

10

Simulation of water flow in double-porosity soils on unstructured grids with the finite-volume method

88%

Szymkiewicz A. , Burzyński K.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2007

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tom Vol. 11, No 4

397-410

EN

Double-porosity soils consist of two interacting porous systems corresponding to weakly conductive aggregates and highly conductive inter-aggregate regions. The flow of water in such media can be described with a two-scale model obtained by homogenization. The model consists of a single macroscopic equation for the flow in the highly conductive porous system coupled with a number of micro-scale equations for the flow in the weakly conductive aggregates. In this paper we present a numerical algorithm to solve the resulting system of equations for the case of macroscopically two-dimensional flow. It is based on the finite volume approach for unstructured grid of triangular cells. Special attention is paid to the coupling of the micro- and macro-scale equations. An exemplary calculation is presented, concerning infiltration and redistribution of water in a hill-slope of double-porosity structure with cubic aggregates.

11

Steady-state and transient heat transfer through fins of complex geometry

88%

Taler D. , Taler J.

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2014

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nr 2

12

The Perfect Ménard Pressuremeter Curve

88%

Tarnawski M.

Archives of Hydro-Engineering and Environmental Mechanics

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2004

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tom Vol. 51, nr 4

387-402

EN

As it is commonly known, to obtain a good quality Ménard Pressuremeter Test a perfectly drilled borehole (pocket) is required. It should be of proper size, only slightly greater than the diameter of the pressuremeter probe, and its walls should remain undisturbed. Unsatisfactory shapes of pressuremeter curves result usually from a poor quality drilling. Typical examples of such curves are given in all handbooks dealing with pressuremeters. They correspond to situations when the tested cavity is too large, too mall or its walls are collapsed. There is, however, plenty of room between the pressure and volume axes. An infinite number of various curves can run through this field and only one of them is really the proper one. An interpreter should be able to evaluate the quality of any curve obtained, estimate the source, the direction and the approximate scale of error and finally to draw conclusions on how to improve the drilling technique to avoid or minimize any future errors. To be able to do that, one needs to understand how the perfect curve should look. The present paper is a study on shapes of pressuremeter curves based on the author's 25years' experience.

13

Flow simulations in cross-flow fans using the finite element and finite volume methods

88%

Sowa A.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2004

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tom Vol. 8, No 1

41-49

EN

Both basic computational fluid dynamics methods: the finite element method (FEM) and the finite volume method (FVM) have been used to simulate flow fields in a cross-flow fan (CFF). A review of previous numerical simulations of flow in CFF's is presented. The theorethical foundations of the applied numerical algorithms and specifications of the computer programs are given. The procedure of computations is described in detail. Computational results are shown in the form of contour and vector velocity and contour pressure plots.

14

Numerical simulation of rapidly varied water flow in the "Wild River" type water slide

88%

Burzyński K. , Szydłowski M.

Archives of Hydro-Engineering and Environmental Mechanics

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2003

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tom Vol. 50, nr 1

37-57

EN

The numerical analysis of the water flow along the 'Wild River' type water slide is presented. As the mathematical model of the free surface flow shallow water equations are assumed. In order to solve the equations, when transient, rapidly varied flow is present, the numerical scheme based on finite volume method is applied. The numerical simulation of water slide flow is computed on unstructured, triangular mesh. The results of calculation are examined against flow parameters observed on the real object installed in water park in Sopot. Generally good agreement between measured and calculated results was observed. Moreover, the calculations are compared to experimental data available due to physical modelling. As the similarity between physical phenomena of flow within water slide and in the river valley after dam-break event is observed, the investigation was realized within the framework of the State Committee for Scientific Research 6P06S04121 project.

15

Finite Volume Method for the Combustion Reaction of Energetic Materials

88%

Yu Y. , Fu Q. , Ma J. , Chen W. , Yan H.

Central European Journal of Energetic Materials

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2023

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tom Vol. 20, no. 2

159--199

EN

In order to analyse the effects of launch on the internal structure due to launch and given the relative paucity of experimental tests in this regime numerical simulations are an important method of prediction. Viscoelastic statistical crack mechanics offer a solution to the dynamic damage problems of explosives involved in explosion, impact and collision. Most finite element software does not include a viscoelastic statistical crack constitutive model; the model can only be embedded in the finite element software. Therefore, a computer program based on the finite volume method combined with viscoelastic statistical crack mechanics is presented, aiming to analyze the explosion problems more precisely and conveniently. A combustion equation of state is proposed to study the combustion reaction of explosives; the trends of temperature and stress of explosive during the combustion process are studied; Hot spot zones formed inside explosives are analyzed. The results are in accordance with the reaction law of combustion. The results indicate that when the bottom of the explosive charge is heated to a certain temperature, the explosive charge have a combustion reaction occurs. This conclusion has important value for studying the effect of the base gap on the launch safety of explosive munitions.

16

A sixth-order finite volume method for the 1D biharmonic operator: Application to intramedullary nail simulation

88%

Costa R. , Machado G. , Clain S.

International Journal of Applied Mathematics and Computer Science

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2015

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tom 25

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nr 3

529-537

EN

A new very high-order finite volume method to solve problems with harmonic and biharmonic operators for onedimensional geometries is proposed. The main ingredient is polynomial reconstruction based on local interpolations of mean values providing accurate approximations of the solution up to the sixth-order accuracy. First developed with the harmonic operator, an extension for the biharmonic operator is obtained, which allows designing a very high-order finite volume scheme where the solution is obtained by solving a matrix-free problem. An application in elasticity coupling the two operators is presented. We consider a beam subject to a combination of tensile and bending loads, where the main goal is the stress critical point determination for an intramedullary nail.

17

Numerical analysis of turbulent flow around twodimensional bodies using non-orthogonal body-fitted mesh

75%

Tarafder M. S. , Mursaline M. A.

International Journal of Applied Mechanics and Engineering

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2019

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tom Vol. 24, no. 2

387--410

EN

This paper deals with the numerical simulation of a turbulent flow around two-dimensional bodies by the finite volume method with non-orthogonal body-fitted grid. The governing equations are expressed in Cartesian velocity components and solution is carried out using the SIMPLE algorithm for collocated arrangement of scalar and vector variables. Turbulence is modeled by the turbulence model and wall functions are used to bridge the solution variables at the near wall cells and the corresponding quantities on the wall. A simplified pressure correction equation is derived and proper under-relaxation factors are used so that computational cost is reduced without adversely affecting the convergence rate. The numerical procedure is validated by comparing the computed pressure distribution on the surface of NACA 0012 and NACA 4412 hydrofoils for different angles of attack with experimental data. The grid dependency of the solution is studied by varying the number of cells of the C-type structured mesh. The computed lift coefficients of NACA 4412 hydrofoil at different angles of attack are also compared with experimental results to further substantiate the validity of the proposed methodology.

18

The numerical solution of the Advection-Dispersion Equation: A review of some basic principles

75%

Wallis S.

Acta Geophysica

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2007

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tom Vol. 55, no. 1

85-94

EN

The simulation of solute transport in rivers is frequently based on numerical models of the Advection-Dispersion Equation. The construction of reliable computational schemes, however, is not necessarily easy. The paper reviews some of the most important issues in this regard, taking the finite volume method as the basis of the simulation, and compares the performance of several types of scheme for a simple case of the transport of a patch of solute along a uniform river. The results illustrate some typical (and well known) deficiencies of explicit schemes and compare the contrasting performance of implicit and semi-Lagrangian versions of the same schemes. It is concluded that the latter have several benefits over the other types of scheme.

19

The Basic Equations of Fluid Mechanics in form Characteristic of the Finite Volume Method

75%

Sobieski W.

Technical Sciences / University of Warmia and Mazury in Olsztyn

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2011

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tom nr 14(2)

299-313

EN

The article presents the derivation of the basic balance equations in form characteristic of the Finite Volume Method. In the following sections the origin of the balance equation of momentum, mass and energy is presented. Next, the conservation equations in vector form are described. The Finite Volume Method is used in Computational Fluid Mechanics for numerical modeling of fluid flows in wide range. The motivation for writing the article was the difficulty in finding short and concise articles on this subject in the literature. The current article is a first part of a cycle dedicated to the mathematical basis of the Finite Volume Method.

PL

W artykule przedstawiono wyprowadzenie podstawowych równań bilansowych w formie charakterystycznej dla metody objętości skończonych. Przedstawiono pochodzenie równania bilansu pędu, masy i energii, następnie równania zachowania w formie wektorowej. Metoda objętości skończonych jest stosowana w tzw. numerycznej mechanice płynów do numerycznego modelowania przepływów płynów w możliwie szerokim zakresie. Motywacją do napisania artykułu była trudność w znalezieniu podobnego rodzaju krótkich i zwięzłych opracowań na ten temat w literaturze. Artykuł jest pierwszą częścią cyklu poświęconego matematycznym podstawom metody objętości skończonych.

20

On convergence of explicit finite volume scheme for one-dimensional three-component two-phase flow model in porous media

75%

Mostefai M. L. , Choucha A. , Cherif B.

Demonstratio Mathematica

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2021

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tom Vol. 54, nr 1

510--526

EN

In this work, we develop and analyze an explicit finite volume scheme for a one-dimensional nonlinear, degenerate, convection–diffusion equation having application in petroleum reservoir. The main difficulty is that the solution typically lacks regularity due to the degenerate nonlinear diffusion term. We analyze a numerical scheme corresponding to explicit discretization of the diffusion term and a Godunov scheme for the advection term. L∞ stability under appropriate CFL conditions and BV estimates are obtained. It is shown that the scheme satisfies a discrete maximum principle. Then we prove convergence of the approximate solution to the weak solution of the problem, and we mount convergence results to a weak solution of the problem in L1 . Results of numerical experiments are presented to validate the theoretical analysis.