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1.
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 in DKUM: 01.06.2012; Views: 2385; Downloads: 77
URL Link to full text

2.
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 in DKUM: 01.06.2012; Views: 2338; Downloads: 95
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3.
Combined single domain and subdomain BEM for 3D laminar viscous flow
Jure Ravnik, Leopold Škerget, Zoran Žunič, 2009, original scientific article

Abstract: A subdomain boundary element method (BEM) using a continuous quadratic interpolation of function and discontinuous linear interpolation of flux is presented for the solution of the vorticity transport equation and the kinematics equation in 3D. By employing compatibility conditions between subdomains an over-determined system of linear equations is obtained, which is solved in a least squares manner. The method, combined with the single domain BEM, is used to solve laminar viscous flows using the velocity vorticity formulation of Navier-Stokes equations. The versatility and accuracy of the method are proven using the 3D lid driven cavity test case.
Keywords: subdomain boundary element method, laminar viscous fluid flow, velocity-vorticity fomulation, lid driven cavity
Published in DKUM: 01.06.2012; Views: 2008; Downloads: 107
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4.
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 in DKUM: 01.06.2012; Views: 2246; Downloads: 105
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5.
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 in DKUM: 01.06.2012; Views: 1753; Downloads: 99
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6.
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 in DKUM: 01.06.2012; Views: 2218; Downloads: 100
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7.
Velocity-vorticity formulation for 3D natural convection in an inclined enclosure by BEM
Jure Ravnik, Leopold Škerget, Zoran Žunič, 2008, original scientific article

Abstract: A natural convection phenomenon is studied in cubic and parallelepipedal inclined enclosures. The simulation of coupled laminar viscous flow and heat transfer is performed using a novel algorithm based on a combination of singledomain Boundary element method (BEM) and subdomain BEM. The algorithm solves the velocity-vorticity formulation of the incompressible Navier-Stokes equations coupled with the energy equation using the Boussinesq approximation.The subdomain BEM is used to solve the kinematics equation, the vorticity transport equation and the energy equation. The boundary vorticity values, which are needed as boundary conditions for the vorticity transport equation, are calculated by singe domain BEM solution of the kinematics equation. Simulation results are compared with benchmark results for a cubic inclined enclosure for Rayleigh number values ▫$10^3Keywords: podobmočna metoda robnih elementov, hitrostno-vrtinčna formulacija, laminarni tok viskozne tekočine, naravna konvekcija, nagnjena kotanja, fluid mechanics, subdomain boundary element method, velocity-vorticity formulation, laminar viscous fluid flow, natural convection, inclined enclosure
Published in DKUM: 31.05.2012; Views: 2713; Downloads: 101
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8.
Velocity vorticity-based large eddy simulation with the bounadr element method
Jure Ravnik, Leopold Škerget, Matjaž Hriberšek, 2006, published scientific conference contribution (invited lecture)

Abstract: A large eddy simulation using the velocity-vorticity formulation of the incompressible Navier-Stokes equations in combination with the turbulent heat transfer equation is proposed for the solution of the turbulent natural convection drive flow in a 1:4 enclosure. The system of equations is closed by an enthropy-based subgrid scale model.The Prandtl turbulent number is used to estimate turbulent diffusion in the heat transfer equation. The boundary element method is used to solve the kinematics equation and estimate the boundary vorticity values. The vorticity transport equation is solved by FEM. The numerical example studied in this paper is the onset of a turbulent flow regime occuring at high Rayleigh number values ▫$(Ra=10^7-10^10)$▫. The formation of vortices in the boundary layer is observed, along with buoyancy driven diffusive convective transport. Quantitative comparison with the laminar flow model and the worh of other authors is also presented in terms of Nusselt number value oscillations.
Keywords: fluid mechanics, incompressible viscous fluid, turbulent flow, velocity vorticity formulation, finite element method, large eddy simulation
Published in DKUM: 31.05.2012; Views: 2312; Downloads: 40
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