1. Lagrangian particle tracking in velocityvorticity resolved viscous flows by subdomain BEMJure Ravnik, Matjaž Hriberšek, Janez Lupše, 2016, original scientific article Abstract: A numerical study of particle motion in a cubic lid driven cavity is presented. As a computational tool, a boundary element based flow solver with a Lagrangian particle tracking algorithm is derived. Flow simulations were performed using an inhouse boundary element based 3D viscous flow solver. The Lagrangian particle tracking algorithm is capable of simulation of dilute suspensions of particles in viscous flows taking into account gravity, buoyancy, drag, pressure gradient and added mass. The derived algorithm is used to simulate particle behaviour in a cellular flow field and in a lid driven cavity flow. Simulations of particle movement in a cellular flow field were used to validate the algorithm. The main goal of the paper was to numerically simulate the flow behaviour of spheres of different densities and different diameters, as experimentally observed in work of Tsorng et al.The study of slightly buoyant and nonbuoyant particles in a lid driven cavity was aimed at discovering cases when particles leave the primary vortex and enter into secondary vortices, a phenomenon described in the work of Tsorng et al. A parametric study of this phenomenon was preformed. The presented computational results show excellent agreement with experiments, confirming the accuracy of the developed computational method. Keywords: dispersed two phase flow, Lagrangian particle tracking, cellular flow, lid driven cavity, boundary element method Published: 04.08.2017; Views: 570; Downloads: 311 Full text (13,57 MB) This document has many files! More...

2. Heat diffusion in fractal geometry cooling surfaceMatjaž Ramšak, Leopold Škerget, 2012, original scientific article Abstract: In the paper the numerical simulation of heat diffusion in the fractal geometry of och snowflake is presented using multidomain mixed Boundary Element Method. he idea and motivation of work is to improve the cooling of small electronic devices sing fractal geometry of surface similar to cooling ribs. The heat diffusion is ssumed as the only principle of heat transfer. The results are compared to the heat lux of a flat surface. The limiting case of infinite small fractal element is computed sing Richardson extrapolation. Keywords: heat transfer, cooling of electronic devices, boundary element method, fractals Published: 10.07.2015; Views: 1051; Downloads: 257 Full text (313,63 KB) This document has many files! More...

3. 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 diffusionconvective 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: 1494; Downloads: 70 Link to full text 
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5. Boundary element method for natural convection in nonNewtonian fluid saturated square porous cavityRenata Jecl, Leopold Škerget, 2003, original scientific article Abstract: The main purpose of this work is to present the use of the Boundary Element Method (BEM) in the analysis of the natural convection in the square porous cavity saturated by the nonNewtonian fluid. The results of hydrodynamic and heat transfer evaluations are reported for the configuration in which the enclosure is heated from a side wall while the horizontal walls are insulated.The flow in the porous medium is modelled using the modified Brinkman extended Darcy model taking into account the nonDarcy viscous effects. The governing equations are transformed by the velocityvorticity variables formulation enabling the computation scheme to be partitioned into kinematic and kinetic parts. To analyse the effects of the available nonNewtonian viscosity and to evaluate the presented approach, the power law model for shear thinning fluids (n<1), for shear thickening fluids (n>1) and in the limit for the Newtonian fluids (n=1) is considered. Numerical model is tested also for the Carreau model adequate for many nonNewtonian fluids. Solutions for the flow and temperature fields and Nusselt numbers are obtainedin terms of a modified Rayleigh number Ra*, Darcy number Da, and the nonNewtonian model parameters. The agreement between the results obtained with finite difference method is very good indicating that BEM can be efficiently used for solving transport phenomena in saturated porous medium. Keywords: natural convection, nonNewtonian fluid, porous medium, cavity flow, boundary element method, boundary domain integral method Published: 01.06.2012; Views: 1246; Downloads: 76 Link to full text 
6. Natural convection flows in complex cavities by BEMLeopold Škerget, Matjaž Hriberšek, Zoran Žunič, 2003, original scientific article Abstract: A numerical method for the solution of NavierStokes equations is developed using an integral representation of the conservation equations. The velocity vorticity formulation is employed, where the kinematics is given with the Poisson equation for a velocity vector, while the kinetics is represented with the vorticity transport equation. The corresponding boundarydomain integral equations are presented along with discussions of the kinetics and kinematics of the fluid flow problem. THE BEM formulation is developed and tested for natural convection flows in closed cavities with complex geometries. Keywords: fluid dynamics, natural convection, boundary element method, differential equations, closed cavity Published: 01.06.2012; Views: 1466; Downloads: 69 Link to full text 
7. 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 velocityvorticity 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 nonlinear. The results also showed that the increasing nonlinearity (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: 1546; Downloads: 74 Link to full text 
8. Integral formulation of a diffusiveconvective transport equation for reacting flowsNiko Samec, Leopold Škerget, 2004, original scientific article Abstract: This peper deals with a numerical solution of a diffusiveconvective transport equation for reacting flows based on boundary domain integral formulation for diffusiveconvective fundamental solution. A great part of attention has been dedicated to the numerical treatment of the diffusiveconvective transport equation for high Pe number and reaction term values as the convective or reaction term becomes dominant compared to the diffusion one. In this case, the hyperbolic character predominates the ellipticity or parabolicity of the governing transport equation, and stability problems arise in the numerical solution. Numerical efficiency of the developed numerical implementation is tested against analytical and numerical results for the typical test cases of diffusiveconvective transport problems (i.e. multicomponent reacting flows). Keywords: fluid mechanics, boundary element method, diffusion, convection, transport problems, reacting flow Published: 01.06.2012; Views: 1138; Downloads: 79 Link to full text 
9. Solving exterior problems of wave propagation based on an iterative variation of local DtN operatorsMiroslav Premrov, Igor Špacapan, 2004, original scientific article Abstract: This paper discusses the problem of wave reflection from the fictitious boundary, with particular regard to the higher harmonic modes. This problem occurs when solving the wave equation in exterior domains using an asymptotic local loworder DirichlettoNeumann (DtN) map for computational procedures applied to a finite domain. We demonstrate that the amplitudes of the reflected fictitious harmonics depend on the wave number, the location of the fictitious boundary, as well as on the local DtN operator used in the computations. Moreover, we show that a constant value of the asymptotic local loworder operator cannot sufficiently eliminate the amplitudes of all reflected waves, and that the results are poor especially for higher harmonics. We propose therefore an iterative method, which varies the tangential dependence of the local operator in each computational step. We only discuss some logical and interesting choices for the operators although this method permits several possibilities on how to vary the operator. The method is simple to apply and the presented examples demonstrate that the accuracy is considerably improved by iterations. Keywords: wave motion, infinite domains, fictitious boundary, radiation condition, finite element method, DirichlettoNeumann map Published: 01.06.2012; Views: 1255; Downloads: 65 Link to full text 
10. Numerical simulation of dilute particle laden flows by wavelet BEMFEMJure 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 velocityvorticity formulation of the NavierStokes 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 backwardfacing 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 backwardfacing step at Reynolds number value 5000. Keywords: boundary element method, velocityvertocity formulation, discrete wavelet transform, Lagrangian particle tracking, backwardfacing step, bluff body flow, dilute particle suspension Published: 01.06.2012; Views: 1342; Downloads: 78 Link to full text 