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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: 1560; Downloads: 67
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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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A multidomain boundary element method for unsteady laminar flow using stream function-vorticity equations
Matjaž Ramšak, Leopold Škerget, Matjaž Hriberšek, Zoran Žunič, 2005, original scientific article

Abstract: The paper deals with the Boundary Element Method (BEM) for modelling 2D unsteady laminar flow using stream function-vorticity formulation of the Navier-Stokes equations. The numerical algorithm for solving a general parabolic diffusion-convection equation is based on linear mixed elements and a multidomain model also known as subdomain technique. Robustness, accuracy and economy of the developed numerical algorithm is shown on a standard case of steady backward facing step flow and a periodic flow past a circular cylinder test case.
Keywords: fluid mechanics, viscous fluid, unsteady laminar flow, boundary element method, multidomain model, stream function, vorticity formulation, backward facing step flow, flow past a cylinder
Published: 01.06.2012; Views: 1378; Downloads: 67
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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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Mixed boundary elements for laminar flows
Matjaž 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: 1201; Downloads: 55
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