1. BEM simulation of compressible fluid flow in an enclosure induced by thermoacoustic wavesLeopold Škerget, Jure Ravnik, 2009, izvirni znanstveni članek Opis: 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. Ključne besede: compressible fluid flow, boundary element method, thermoacoustic waves, velocity-vorticity fomulation Objavljeno: 31.05.2012; Ogledov: 1296; Prenosov: 59 Povezava na celotno besedilo |
2. Fast single domain-subdomain BEM algorithm for 3D incompressible fluid flow and heat transferJure Ravnik, Leopold Škerget, Zoran Žunič, 2009, izvirni znanstveni članek Opis: 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. Ključne besede: boundary element method, fast multipole method, fluid flow, heat transfer, velocity-vorticity fomulation Objavljeno: 31.05.2012; Ogledov: 1307; Prenosov: 47 Povezava na celotno besedilo |
3. Velocity vorticity-based large eddy simulation with the bounadr element methodJure Ravnik, Leopold Škerget, Matjaž Hriberšek, 2006, objavljeni znanstveni prispevek na konferenci (vabljeno predavanje) Opis: 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. Ključne besede: fluid mechanics, incompressible viscous fluid, turbulent flow, velocity vorticity formulation, finite element method, large eddy simulation Objavljeno: 31.05.2012; Ogledov: 1227; Prenosov: 18 Povezava na celotno besedilo |
4. Velocity-vorticity formulation for 3D natural convection in an inclined enclosure by BEMJure Ravnik, Leopold Škerget, Zoran Žunič, 2008, izvirni znanstveni članek Opis: 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 ▫$10^3Ključne besede: 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 Objavljeno: 31.05.2012; Ogledov: 1519; Prenosov: 61 Povezava na celotno besedilo |
5. Boundary domain integral method for high Reynolds viscous fluid flows in complex planar geometriesMatjaž Hriberšek, Leopold Škerget, 2005, izvirni znanstveni članek Opis: The article presents new developments in boundary domain integral method (BDIM) for computation of viscous fluid flows, governed by the Navier-Stokes equations. The BDIM algorithm uses velocity-vorticity formulation and is basedon Poisson velocity equation for flow kinematics. This results in accurate determination of boundary vorticity values, a crucial step in constructing an accurate numerical algorithm for computation of flows in complex geometries, i.e. geometries with sharp corners. The domain velocity computations are done by the segmentation technique using large segments. After solving the kinematics equation the vorticity transport equation is solved using macro-element approach. This enables the use of macro-element based diffusion-convection fundamental solution, a key factor in assuring accuracy of computations for high Reynolds value laminar flows. The versatility and accuracy of the proposed numerical algorithm is shown for several test problems, including the standard driven cavity together with the driven cavity flow in an L shaped cavity and flow in a Z shaped channel. The values of Reynolds number reach 10,000 for driven cavity and 7500 for L shapeddriven cavity, whereas the Z shaped channel flow is computed up to Re = 400. The comparison of computational results shows that the developed algorithm is capable of accurate resolution of flow fields in complex geometries. Ključne besede: fluid mechanics, numerical methods, boundary domain integral method, algorithms, incompressible fluid flow, Navier-Stokes equations, velocity vorticity formulation, segmentation technique, driven cavity flow Objavljeno: 01.06.2012; Ogledov: 1118; Prenosov: 46 Povezava na celotno besedilo |
6. Combined single domain and subdomain BEM for 3D laminar viscous flowJure Ravnik, Leopold Škerget, Zoran Žunič, 2009, izvirni znanstveni članek Opis: 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. Ključne besede: subdomain boundary element method, laminar viscous fluid flow, velocity-vorticity fomulation, lid driven cavity Objavljeno: 01.06.2012; Ogledov: 993; Prenosov: 53 Povezava na celotno besedilo |
7. The wavelet transform for BEM computational fluid dynamicsJure Ravnik, Leopold Škerget, Matjaž Hriberšek, 2004, izvirni znanstveni članek Opis: 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. Ključne besede: fluid mechanics, computational fluid dynamics, boundary element method, wavelet transform, linear systems of equations, velocity vorticity formulation, driven cavity, natural convection, system matrix compression Objavljeno: 01.06.2012; Ogledov: 1262; Prenosov: 55 Povezava na celotno besedilo |
8. On new approach to rheological modeling of an electrostatic ash and water - quadratic lawPrimož Ternik, 2002, objavljeni znanstveni prispevek na konferenci Opis: 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. Ključne besede: 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 Objavljeno: 01.06.2012; Ogledov: 1408; Prenosov: 15 Povezava na celotno besedilo |
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10. Mixed boundary elements for laminar flowsMatjaž Ramšak, Leopold Škerget, 1999, izvirni znanstveni članek Opis: 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. Ključne besede: fluid mechanics, incompressible fluid, laminar flow, velocity vorticity formulation, boundary element method, mixed boundary elements Objavljeno: 01.06.2012; Ogledov: 1170; Prenosov: 50 Povezava na celotno besedilo |