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Primerjava valčne transformacije in metode mnogokratnih polov za reševanje integralskih enačb Poissonovega tipa
Jure Ravnik, Leopold Škerget, Matjaž Hriberšek, 2009, published scientific conference contribution

Abstract: Če metodo robnih elementov uporabimo za rešitev nehomogene parcialne diferencialne enačbe, moramo po diskretizaciji izračunati polno matriko območnih integralov. V prispevku primerjamo dve metodi: metodo mnogokratnih polov in valčno transformacijo, ki omogočata izdelavo razpršene aproksimacije območnih matrik. Pri metodi mnogokratnih polov uporabljamo razvoj integralskega jedra po sferičnih harmonikih. Uporabljena valčna transformacija temelji na diskretni Haarovi transformaciji za vektorje poljubnih dolžin. Metodi smo testirali na skalarni Poissonovi enačbi in vektorski hitrostno vrtinčni enačbi kinematike. Rezultati kažejo, da metoda večkratnih polov daje natančnejše rezultate pri enaki stopnji razpršenosti območne matrike. Po drugi strani pa valčno transformacijo lahko uporabljamo nespremenjeno za katerokoli matriko, medtem ko je metoda večkratnih polov odvisna od razvoja integralskega jedra v vrsto.
Keywords: metoda robnih elementov, nehomogene parcialne diferencialne enačbe, diskretizacija, metoda mnogokratnih polov, valčna transformacija
Published: 31.05.2012; Views: 1095; Downloads: 20
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Magnetic particle separation in viscous flows by BEM
Matjaž 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: 1721; Downloads: 27
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Simulation of unsteady fluid flow and heat transfer by BEM
Jure 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: 1023; Downloads: 16
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Turbulent RANS simulations by BEM
Leopold Škerget, Jure Ravnik, 2011, published scientific conference contribution abstract

Keywords: boundary element method, turbulent flow, velocity-vorticity formulation
Published: 01.06.2012; Views: 970; Downloads: 27
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Fast BEM based methods for heat transfer simulation
Jure Ravnik, Leopold Škerget, 2011, independent scientific component part or a chapter in a monograph

Published: 01.06.2012; Views: 1016; Downloads: 58
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Combined single domain and subdomain BEM for 3D laminar viscous flow
Jure Ravnik, Leopold Škerget, Zoran Žunič, 2009, original scientific article

Abstract: 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.
Keywords: subdomain boundary element method, laminar viscous fluid flow, velocity-vorticity fomulation, lid driven cavity
Published: 01.06.2012; Views: 1028; Downloads: 57
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Numerical simulation of dilute particle laden flows by wavelet BEM-FEM
Jure 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: 1083; Downloads: 60
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