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1.
Mixed boundary elements for laminar flows
Matjaž Ramšak, Leopold Škerget, 1999, original scientific article

Abstract: This paper presents a mixed boundary element formulation of the boundary domain integral method (BDIM) for solving diffusion-convective transport problems. The basic idea of mixed elements is the use of a continuos interpolation polynomial for conservative field function approximation and a discontinuous interpolation polynomial for its normal derivative along the boundary element. In this way, the advantages of continuous field function approximation are retained and its conservation is preserved while the normal flux values are approximated by interpolation nodal points with a uniquely defined normal direction. Due to the use of mixed boundary elements, the final discretized matrix system is overdetermined and a special solver based on the least squares method is applied. Driven cavity, natural and forced convection in a closed cavity are studied. Driven caviaty results at Re=100, 400 and 1000 agree better with the benchmark solution than Finite Element Method of Finite Volume Method results for the same grid density with 21 x 21 degrees of freedom. The average Nusselt number values for natural convection ▫$10^3$▫▫$le$▫Ra▫$le$▫▫$10^6$▫ agree better than 0.1% with benchmark solutions for maximal calculated grid desities 61 x 61 degrees for freedom.
Keywords: fluid mechanics, incompressible fluid, laminar flow, velocity vorticity formulation, boundary element method, mixed boundary elements
Published: 01.06.2012; Views: 1495; Downloads: 70
URL Link to full text

2.
Computational fluid dynamics by boundary-domain integral method
Leopold Škerget, Matjaž Hriberšek, G. Kuhn, 1999, original scientific article

Abstract: A boundary-domain integral method for the solution of general transport phenomena incompressible fluid motion given by the Navier-Stokes equation set is presented. Velocity-vorticity formulation of the conservations is employed. Different integral representations for conservation field functions based on different fundamental solutions are developed. Special attention is given to the use of subdomain technique and Krylov subspace iterative solvers. The computed solutions of several benchmark problems agree well with available experimental and other computational results.
Keywords: fluid mechanics, fluid dynamics, numerical methods, boundary domain integral method, viscous fluid, heat transfer, diffusion-convective solution
Published: 01.06.2012; Views: 1599; Downloads: 60
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3.
BEM for non-Newtonian fluid flow
Leopold Škerget, Niko Samec, 1999, original scientific article

Abstract: The main purpose of this work is to present the use of the boundary-domain integral method (BDIM) to analyse the flow behaviour of non-Newtoninan fluids. A few available parametric viscosity models are applied representing a non-linear dependence on shear strain rate and shear stress. To evaluate the presented approach the Rayleigh-Bernard natural convection was solved at different Rayleigh number values.
Keywords: fluid mechanics, non-Newtonian fluids, viscous fluids, velocity-vorticity formulation, boundary domian integral method
Published: 01.06.2012; Views: 1656; Downloads: 76
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4.
On new approach to rheological modeling of an electrostatic ash and water - quadratic law
Primož Ternik, 2002, published scientific conference contribution

Abstract: In the paper a new rheological model for an electrostatic ash and water mixture is proposed. The fundamental equation of the rheological model was used to determine the relationship between the shear stress and the shear rate as well as the equation of a velocity profile for the flow through a straight pipe. Experimental results obtained from a capillary viscometer were used as the basis to determine the parameters for the proposed model by the non-linear regression analysis. With the Quadratic law a numerical analysis of a mixture flow through a capillary pipe with the finite volume method was performed. The derived equations for the velocity profile, shear stress and shear rate were validated through a comparison of numerically obtained and theoretical results. Finally, the compariosn between the Quadratic and the Power law is presented.
Keywords: fluid mechanics, non-Newtonian fluids, mixture of electrofilter ash and water, flow in pipes, capillary pipes, rheological model, velocity profile, shear stress, finite volume method, numerical analysis, quadratic law, power law, mehanika fluidov
Published: 01.06.2012; Views: 1717; Downloads: 28
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5.
Weakly coupled analysis of a blade in multiphase mixing vessel
Matej Vesenjak, Zoran Ren, Matjaž Hriberšek, 2004, short scientific article

Abstract: Two or more physical systems frequently interact with each other, where the independent solution of one system is impossible without a simultaneous solution of the others. An obvious coupled system is that of a dynamic fluid-structure interaction. š8đ In this paper a computational analysis of thefluid-structure interaction in a mixing vessel is presented. In mixing vessels the fluid can have a significant influence on the deformation of blades during mixing, depending on speed of mixing blades and fluid viscosity.For this purpose a computational weakly coupled analysis has been performed to determine the multiphase fluid influences on the mixing vessel structure. The multiphase fluid field in the mixing vessel was first analyzed with the computational fluid dynamics (CFD) code CFX. The results in the form of pressure were then applied to the blade model, which was the analysed with the structural code MSC.visualNastran forWindows, which is based on the finiteelement method (FEM).
Keywords: fluid mechanics, solid mechanics, coupled problems, computational analysis, two-phase fluid, mixing blade, pressure distribution, finite volume method, finite element method
Published: 01.06.2012; Views: 1154; Downloads: 73
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6.
The wavelet transform for BEM computational fluid dynamics
Jure Ravnik, Leopold Škerget, Matjaž Hriberšek, 2004, original scientific article

Abstract: A wavelet matrix compression technique was used to solve systems of linear equations resulting from BEM applied to fluid dynamics. The governing equations were written in velocity-vorticity formulation and solutions of the resulting systems of equations were obtained with and without wavelet matrix compression. A modification of the Haar wavelet transform, which can transformvectors of any size, is proposed. The threshold, used for making fully populated matrices sparse, was written as a product of a user defined factor and the average value of absolute matrix elements values. Numerical tests were performed to assert, that the error caused by wavelet compression depends linearly on the factor , while the dependence of the error on the share of thresholded elements in the system matrix is highly non-linear. The results also showed that the increasing non-linearity (higher Ra and Re numbervalues) limits the extent of compression. On the other hand, higher meshdensity enables higher compression ratios.
Keywords: fluid mechanics, computational fluid dynamics, boundary element method, wavelet transform, linear systems of equations, velocity vorticity formulation, driven cavity, natural convection, system matrix compression
Published: 01.06.2012; Views: 1546; Downloads: 74
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7.
Integral formulation of a diffusive-convective transport equation for reacting flows
Niko Samec, Leopold Škerget, 2004, original scientific article

Abstract: This peper deals with a numerical solution of a diffusive-convective transport equation for reacting flows based on boundary domain integral formulation for diffusive-convective fundamental solution. A great part of attention has been dedicated to the numerical treatment of the diffusive-convective transport equation for high Pe number and reaction term values as the convective or reaction term becomes dominant compared to the diffusion one. In this case, the hyperbolic character predominates the ellipticity or parabolicity of the governing transport equation, and stability problems arise in the numerical solution. Numerical efficiency of the developed numerical implementation is tested against analytical and numerical results for the typical test cases of diffusive-convective transport problems (i.e. multicomponent reacting flows).
Keywords: fluid mechanics, boundary element method, diffusion, convection, transport problems, reacting flow
Published: 01.06.2012; Views: 1138; Downloads: 79
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8.
A multidomain boundary element method for unsteady laminar flow using stream function-vorticity equations
Matjaž Ramšak, Leopold Škerget, Matjaž Hriberšek, Zoran Žunič, 2005, original scientific article

Abstract: The paper deals with the Boundary Element Method (BEM) for modelling 2D unsteady laminar flow using stream function-vorticity formulation of the Navier-Stokes equations. The numerical algorithm for solving a general parabolic diffusion-convection equation is based on linear mixed elements and a multidomain model also known as subdomain technique. Robustness, accuracy and economy of the developed numerical algorithm is shown on a standard case of steady backward facing step flow and a periodic flow past a circular cylinder test case.
Keywords: fluid mechanics, viscous fluid, unsteady laminar flow, boundary element method, multidomain model, stream function, vorticity formulation, backward facing step flow, flow past a cylinder
Published: 01.06.2012; Views: 1646; Downloads: 84
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9.
BEM for the two-dimensional plane compressible fluid dynamics
Leopold Škerget, Niko Samec, 2005, original scientific article

Abstract: In this study, the boundary element method, which has been established for theviscous incompressible fluid motion, is modified and extended to capture the compressible fluid state. The velocity-vorticity formulation of the time dependent set of equations is employed, where the kinematics is given with thePoisson velocity vector equation, while the kinetics is represented with the vorticity transport equation, and the pressure field function is governed by the Poisson pressure scalar equation. The method is applied to consider buoyancy driven flow in closed cavity, differentially heated under large temperature gradients. The ideal gas law is used and viscosity is given by Sutherland law.
Keywords: fluid mechanics, compressible viscous fluid, natural convection, boundary element method, fluid dynamics
Published: 01.06.2012; Views: 1167; Downloads: 78
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10.
A multidomain boundary element method for two equation turbulence models
Matjaž Ramšak, Leopold Škerget, 2005, original scientific article

Abstract: The paper deals with the multidomain Boundary Element Method (BEM) for modelling 2D complex turbulent flow using low Reynolds two equation turbulence models. While the BEM is widely accepted for laminar flow this is the first case, where this method is applied for complex flow problems using ▫$k-epsilon$▫ turbulence model. The integral boundary domain equations are discretised using mixed boundary elements and a multidomain method also known as subdomain technique. The resulting system matrix is overdetermined, sparse, block banded and solved using fast iterative linear least squares solver. The simulation of turbulent flow over a backward step is in excellent agreement with the finite volume method using the same turbulent model.
Keywords: fluid mechanics, turbulent flow, boundary element method, incompressible viscous fluid, stream function-vorticity formulation, two equation turbulence model, backward facing step flow
Published: 01.06.2012; Views: 1437; Downloads: 77
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