1. 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: 1599; Downloads: 55 Link to full text |
2. Boundary domain integral method for the study of double diffusive natural convection in porous mediaJanja Kramer Stajnko, Renata Jecl, Leopold Škerget, 2007, original scientific article Abstract: The main purpose of this paper is to present a boundary domain integral method(BDIM) for the solution of natural convection in porous media driven by combining thermal and solutal buoyancy forces. The Brinkman extension of the classical Darcy equation is used for the momentum conservation equation. The numerical scheme was tested on a natural convection problem within a square porous cavity, where different temperature and concentration values are applied on the vertical walls, while the horizontal walls are adiabatic and impermeable. The results for different governing parameters (Rayleigh number, Darcy number, buoyancy ratio and Lewis number) are presented and compared withpublished work. There is a good agreement between those results obtained using the presented numerical scheme and reported studies using other numerical methods. Keywords: double diffusive natural convection, porous medium, velocity-vorticity formulation, Brinkman extended Darcy formulation, boundary domain integrated method Published: 31.05.2012; Views: 1183; Downloads: 59 Link to full text |
3. Velocity vorticity-based large eddy simulation with the bounadr element methodJure 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: 1319; Downloads: 18 Link to full text |
4. 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: 1603; Downloads: 68 Link to full text |
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6. Boundary domain integral method for high Reynolds viscous fluid flows in complex planar geometriesMatjaž Hriberšek, Leopold Škerget, 2005, original scientific article Abstract: 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. Keywords: fluid mechanics, numerical methods, boundary domain integral method, algorithms, incompressible fluid flow, Navier-Stokes equations, velocity vorticity formulation, segmentation technique, driven cavity flow Published: 01.06.2012; Views: 1213; Downloads: 55 Link to full text |
7. Numerical simulation of dilute particle laden flows by wavelet BEM-FEMJure Ravnik, Leopold Škerget, Matjaž Hriberšek, Zoran Žunič, 2008, original scientific article Abstract: A wavelet transform based BEM and FEM numerical scheme was used to simulate laminar viscous flow. The velocity-vorticity formulation of the Navier-Stokes equations was used. The flow simulation algorithm was coupled with a Lagrangian particle tracking scheme for dilute suspensions of massless particles and particles without inertia. The proposed numerical approach was used to simulate flow and particle paths for two test cases: flow over a backward-facing step and flow past a circular cylinder. We present methods of calculating the pressure and stream function field at the end of each time step. The pressure field was used to calculate drag and lift coefficients, which enable qualitative comparison of our results with the benchmark. The stream function enabled the comparison of streamlines and massless particle paths in steady state low Reynolds number value flow fields, and thus provided an estimate on the accuracy of the particle tracking algorithm. Unsteady higher Reynolds number value flows were investigated in terms of particle distributions in vortex streets in the wake of the cylinder and behind the step. Sedimentation of particles without inertia was studied in the flow field behind a backward-facing step at Reynolds number value 5000. Keywords: boundary element method, velocity-vertocity formulation, discrete wavelet transform, Lagrangian particle tracking, backward-facing step, bluff body flow, dilute particle suspension Published: 01.06.2012; Views: 1126; Downloads: 63 Link to full text |
8. The wavelet transform for BEM computational fluid dynamicsJure 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: 1342; Downloads: 61 Link to full text |
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10. Mixed boundary elements for laminar flowsMatjaž 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: 1236; Downloads: 56 Link to full text |