1. Natural convection of micropolar fluid in an enclosure with boundary element methodMatej Zadravec, Matjaž Hriberšek, Leopold Škerget, 2009, original scientific article Abstract: The contribution deals with numerical simulation of natural convection in micropolar fluids, describing flow of suspensions with rigid and underformable particles with own rotation. The micropolar fluid flow theory is incorporated into the framework of a velocity-vorticity formulation of Navier-Stokes equations. The governing equations are derived in differential and integral form, resulting from the application of a boundary element method (BEM). In integral transformations, the diffusion-convection fundamental solution for flow kinetics, including vorticity transport, heat transport and microrotation transport, is implemented. The natural convection test case is the benchmark case of natural convection in a square cavity, and computations are performed for Rayleigh number values up to 107. The results show, which microrotation of particles in suspension in general decreases overall heat transfer from the heated wall and should not therefore be neglected when computing heat and fluid flow of micropolar fluids. Keywords: natural convection, micropolar fluid, boundary element method Published: 31.05.2012; Views: 1520; Downloads: 75 Link to full text |
2. BEM simulation of compressible fluid flow in an enclosure induced by thermoacoustic wavesLeopold Škerget, Jure Ravnik, 2009, original scientific article Abstract: The problem of unsteady compressible fluid flow in an enclosure induced by thermoacoustic waves is studied numerically. Full compressible set of Navier-Stokes equations are considered and numerically solved by boundary-domain integral equations approach coupled with wavelet compression and domain decomposition to achieve numerical efficiency. The thermal energy equation is written in its most general form including the Rayleigh and reversible expansion rate terms. Both, the classical Fourier heat flux model and wave heat conduction model are investigated. The velocity-vorticity formulation of the governing Navier-Stokes equations is employed, while the pressure field is evaluated from the corresponding pressure Poisson equation. Material properties are taken to be for the perfect gas, and assumed to be pressure and temperature dependent. Keywords: compressible fluid flow, boundary element method, thermoacoustic waves, velocity-vorticity fomulation Published: 31.05.2012; Views: 1482; Downloads: 67 Link to full text |
3. 3D multidomain BEM for a Poisson equationMatjaž Ramšak, Leopold Škerget, 2009, original scientific article Abstract: This paper deals with the efficient 3D multidomain boundary element method (BEM) for solving a Poisson equation. The integral boundary equation is discretized using linear mixed boundary elements. Sparse system matrices similar to the finite element method are obtained, using a multidomain approach, also known as the ćsubdomain techniqueć. Interface boundary conditions between subdomains lead to an overdetermined system matrix, which is solved using a fast iterative linear least square solver. The accuracy, efficiency and robustness of the developed numerical algorithm are presented using cube and sphere geometry, where the comparison with the competitive BEM is performed. The efficiency is demonstrated using a mesh with over 200,000 hexahedral volume elements on a personal computer with 1 GB memory. Keywords: fluid mechanics, Poisson equation, multidomain boundary element method, boundary element method, mixed boundary elements, multidomain method Published: 31.05.2012; Views: 1701; Downloads: 67 Link to full text |
4. Fast single domain-subdomain BEM algorithm for 3D incompressible fluid flow and heat transferJure Ravnik, Leopold Škerget, Zoran Žunič, 2009, original scientific article Abstract: In this paper acceleration and computer memory reduction of an algorithm for the simulation of laminar viscous flows and heat transfer is presented. The algorithm solves the velocity-vorticity formulation of the incompressible Navier-Stokes equations in 3D. It is based on a combination of a subdomain boundary element method (BEM) and single domain BEM. The CPU time and storage requirements of the single domain BEM are reduced by implementing a fast multipole expansion method. The Laplace fundamental solution, which is used as a special weighting function in BEM, is expanded in terms of spherical harmonics. The computational domain and its boundary are recursively cut up forming a tree of clusters of boundary elements and domain cells. Data sparse representation is used in parts of the matrix, which correspond to boundary-domain clusters pairs that are admissible for expansion. Significant reduction of the complexity is achieved. The paper presents results of testing of the multipole expansion algorithm by exploring its effect on the accuracy of the solution and its influence on the non-linear convergence properties of the solver. Two 3D benchmark numerical examples are used: the lid-driven cavity and the onset of natural convection in a differentially heated enclosure. Keywords: boundary element method, fast multipole method, fluid flow, heat transfer, velocity-vorticity fomulation Published: 31.05.2012; Views: 1416; Downloads: 66 Link to full text |
5. Two-dimensional velocity-vorticity based LES for the solution of natural convection in a differentially heated enclosure by wavelet transform based BEM and FEMJure Ravnik, Leopold Škerget, Matjaž Hriberšek, 2006, original scientific article Abstract: A wavelet transform based boundary element method (BEM) numerical scheme is proposed for the solution of the kinematics equation of the velocity-vorticityformulation of Navier-Stokes equations. FEM is used to solve the kinetics equations. The proposed numerical approach is used to perform two-dimensional vorticity transfer based large eddy simulation on grids with 105 nodes. Turbulent natural convection in a differentially heated enclosure of aspect ratio 4 for Rayleigh number values Ra=107-109 is simulated. Unstable boundary layer leads to the formation of eddies in the downstream parts of both vertical walls. At the lowest Rayleigh number value an oscillatory flow regime is observed, while the flow becomes increasingly irregular, non-repeating, unsymmetric and chaotic at higher Rayleigh number values. The transition to turbulence is studied with time series plots, temperature-vorticity phase diagrams and with power spectra. The enclosure is found to be only partially turbulent, what is qualitatively shown with second order statistics-Reynolds stresses, turbulent kinetic energy, turbulent heat fluxes and temperature variance. Heat transfer is studied via the average Nusselt number value, its time series and its relationship to the Rayleigh number value. Keywords: numerical modelling, boundary element method, discrete wavelet transform, large eddy simulation, velocity-vertocity formulation, natural convection Published: 31.05.2012; Views: 1632; Downloads: 58 Link to full text |
6. 3D multidomain BEM for solving the Laplace equationMatjaž Ramšak, Leopold Škerget, 2007, original scientific article Abstract: An efficient 3D multidomain BEM for solving problems governed by the Laplace equation is presented. Integral boundary equations are discretized using mixed boundary elements. The field function is interpolated using a continuous linear function while its derivative in a normal direction is interpolated using a discontiuous constant function over surface boundaey elements. Using amultidomain approach, also known as the subdomain technique, sparse system matrices similar to FEM are obtained. Interface boundary conditions between subdomains leads to an over-determined system matrix which is solved using a fast iterative linear least square solver. The accuracy and the robustness of the developed algorithm is presented on a scalar diffusion problem using simple cube geometry and various types of meshes. The efficiency is demonstrated with potential flow around a complex geometry of a fighter airplane using a tetrahedral mesh with over 100.000 subdomains on a personal computer. Keywords: fluid mechanics, aerodynamics, multidomain boundary element method, Laplace equation, mixed boundary elements, potential flow Published: 31.05.2012; Views: 1474; Downloads: 67 Link to full text |
7. Velocity-vorticity formulation for 3D natural convection in an inclined enclosure by BEMJure 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 ▫$10^3Keywords: podobmočna metoda robnih elementov, hitrostno-vrtinčna formulacija, laminarni tok viskozne tekočine, naravna konvekcija, nagnjena kotanja, fluid mechanics, subdomain boundary element method, velocity-vorticity formulation, laminar viscous fluid flow, natural convection, inclined enclosure Published: 31.05.2012; Views: 1647; Downloads: 73 Link to full text |
8. Boundary element method for thermal flows using k-[epsilon] turbulence modelsMatjaž Ramšak, Leopold Škerget, 2008, published scientific conference contribution Abstract: Purpose - This paper aims to develop a multidomain boundary element method (BEM) for modeling 2D complex turbulent thermal flow using low Reynolds two-equation turbulence models. Design/methodology/approach - The integral boundary domain equations are discretised using mixed boundary elements and a multidomain method also known as a subdomain technique. The resulting system matrix is an overdetermined, sparse block banded and solved using a fast iterative linear least squares solver. Findings - The simulation of a turbulent flow over a backward step is in excellent agreement with the finite volume method using the same turbulent model. A grid consisting of over 100,000 elements could be solved in the order of a few minutes using a 3.0 GhzP4 and 1 GB memory indicating good efficiency. Originality/value - The paper shows, for the first time, that the BEM is applicable to thermal flows using k-▫$epsilon$▫. Keywords: thermal flow, heat exchange, turbulence, boundary element method, simulation Published: 31.05.2012; Views: 952; Downloads: 23 Link to full text |
9. Magnetic particle separation in viscous flows by BEMMatjaž Hriberšek, Jure Ravnik, Primož Kocutar, 2011, published scientific conference contribution Abstract: A boundary element method based solver for particle motion simulation in dilute suspensions under the influence of hydrodynamic and magnetic forces was applied. The Euler-Lagrangian formulation for simulation of dilute two-phase flow was applied. The algorithm solves the incompressible Navier-Stokes equations written in velocity-vorticity formulation. The non uniform magnetic field was defined analytically for the case of a set of long thin wires. The particle trajectories were computed by applying the 4th order Runge-Kutta method. The computed test case consisted of a narrow channel under the influence of a nonuniform magnetic field, where magnetite and aluminium particles were suspended in water. The results of computations show the distributions of particles along the channel and confirms the suitability of the proposed configuration as a separation device under ideal conditions. Keywords: boundary element method, laminar flow, magnetic particles, viscous fluids Published: 01.06.2012; Views: 1776; Downloads: 28 Link to full text |
10. Simulation of unsteady fluid flow and heat transfer by BEMJure Ravnik, Leopold Škerget, 2011, published scientific conference contribution Abstract: A boundary element method based solver for simulation of unsteady laminar viscous flow and heat transfer in three-dimensions has been developed. The algorithm solves the incompressible Navier- Stokes equations written in velocity-vorticity form and coupled with energy equation. Buoyancy is modelled within the Boussinesq approximation. The solver has recently been adapted for simulation of unsteady phenomena. The governing set of equations consists of the kinematics equation and transport equations for vorticity and temperature. Velocity and temperature boundary conditions are known, vorticity boundary conditions are calculated during the simulation by single domain BEM applied on the kinematics equation. The transport equations are solved by a domaindecomposition BEM approach, which yields sparse integral matrices and enables simulation using large computational grids. Rayleigh-Benard convection is used for a test case. In this case fluid is heated flow below, thus making it highly unstable. Already at low driving temperature of the bottom wall, the fluid becomes unstable. Vortices are formed above the hot bottom wall and travel up by buoyancy forces. Flow exhibits oscillatory behaviour, which at higher temperatures leads to chaotic and turbulent flow. The phenomenon was simulated using different driving temperatures of the bottom wall, observing the change of flow characteristics for steady to unsteady oscillatory regime and at even higher temperature to chaotic behaviour. Time series of heat flux and field functions were examined by phase portraits to determine the flow regime. A grid independence study and time step analysis was performed to asses the algorithms capability of simulation of unsteady behaviour. Keywords: boundary element method, heat transfer, unsteady fluid flow, transport equations Published: 01.06.2012; Views: 1112; Downloads: 16 Link to full text |