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11.
Narava, inženirji in numerične simulacije
Jure Ravnik, 2006, professional article

Keywords: numerične simulacije, računalniške simulacije, tehnika, narava
Published: 31.05.2012; Views: 1127; Downloads: 40
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12.
Two-dimensional velocity-vorticity based LES for the solution of natural convection in a differentially heated enclosure by wavelet transform based BEM and FEM
Jure 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: 1549; Downloads: 54
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13.
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: 31.05.2012; Views: 1267; Downloads: 18
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14.
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: 31.05.2012; Views: 1561; Downloads: 67
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15.
16.
Comparison between wavelet and fast multipole data sparse approximations for Poisson and kinematics boundary - domain integral equations
Jure Ravnik, Leopold Škerget, Zoran Žunič, 2009, original scientific article

Abstract: The boundary element method applied on non-homogenous partial differential equations requires calculation of a fully populated matrix of domain integrals. This paper compares two techniques: the fast multipole method and the fast wavelet transform, which are used to reduce the complexity of such domain matrices. The employed fast multipole method utilizes the expansion of integral kernels into series of spherical harmonics. The wavelet transform for vectors of arbitrary length, based on Haar wavelets and variable thresholding limit, is used. Both methods are tested and compared by solving the scalar Poisson equation and the velocity-vorticity vector kinematics equation. The results show comparable accuracy for both methods for a given data storage size. Wavelets are somewhat better for high and low compression ratios, and the fast multipole methods gives better results for moderate compressions. Considering implementation of the methods, the wavelet transform can easily be adapted for any problem, while the fast multipole method requires different expansion for each integral kernel.
Keywords: wavelets, fast multipole method, Poisson equation, BEM
Published: 31.05.2012; Views: 1436; Downloads: 66
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17.
BEM simulation of compressible fluid flow in an enclosure induced by thermoacoustic waves
Leopold 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: 1362; Downloads: 64
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18.
Fast single domain-subdomain BEM algorithm for 3D incompressible fluid flow and heat transfer
Jure 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: 1349; Downloads: 53
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19.
Sledenje delcem v toku viskozne tekočine
Jure Ravnik, Matjaž Hriberšek, Janez Lupše, 2009, published scientific conference contribution

Abstract: Predstavljena je numerična študija obnašanja delcev v gnani kotanji. Viskozen laminaren tok je simuliran s programskim paketom, ki temelji na metodi robnih elementov. Razvit je algoritem za Lagrangeovo sledenje delcev. Fizikalni model vključuje težnost, vzgon, upor in prispevke zaradi tlačnega gradienta ter dodane mase. Algoritem je bil uporabljen za simulacijo toka in obnašanja delcev v gnani kotanji. Raziskani so bili pogoji za vstop delcev različnih premerov in gostot v sekundarne vrtince v kotanji. Izvedena je bila parametrična študija. Ugotovljeno je bilo, da je velikost delca odločujoč faktor za vstop v sekundarne vrtince. Izvedena je bila primerjava z eksperimentalnimi podatki, ki je pokazala odlično ujemanje rezultatov numeričnih simulacij in eksperimentov.
Keywords: disperzni dvofazni tokovi, viskozni laminarni tok, Lagrangeovo sledenje delcev, gnana kotanja, velikost delcev
Published: 31.05.2012; Views: 1480; Downloads: 18
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20.
Paralelizacija algoritma za simulacijo toka viskozne tekočine
Janez Lupše, Leopold Škerget, Jure Ravnik, 2009, published scientific conference contribution

Abstract: V članku je predstavljen primer paralelizacije algoritma za izvajanje numeričnih simulacij. Algoritem temelji na metodi robnih elementov in je namenjen reševanju problemov iz dinamike tekočin. Za paralelno programiranjeje bil uporabljen MPI standard. Učinki paralelizacije na izračun kinematike ter tlaka so predstavljeni na primeru toka skozi kanal z valovito steno. Uporabili smo tri mreže različnih gostot z namenom primerjave pospešitve izvajanja programa.
Keywords: numerične simulacije, viskozne tekočine, dinamika tekočin, paralelizacija
Published: 31.05.2012; Views: 851; Downloads: 12
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