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Boundary domain integral method for high Reynolds viscous fluid flows in complex planar geometries
Matjaž 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: 1253; Downloads: 57
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Boundary element method for natural convection in non-Newtonian fluid saturated square porous cavity
Renata 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 non-Newtonian 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 non-Darcy viscous effects. The governing equations are transformed by the velocity-vorticity variables formulation enabling the computation scheme to be partitioned into kinematic and kinetic parts. To analyse the effects of the available non-Newtonian 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 non-Newtonian 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 non-Newtonian 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, non-Newtonian fluid, porous medium, cavity flow, boundary element method, boundary domain integral method
Published: 01.06.2012; Views: 1051; Downloads: 64
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Computational fluid dynamics by boundary-domain integral method
Leopold Škerget, Matjaž Hriberšek, G. Kuhn, 1999, original scientific article

Abstract: A boundary-domain integral method for the solution of general transport phenomena incompressible fluid motion given by the Navier-Stokes equation set is presented. Velocity-vorticity formulation of the conservations is employed. Different integral representations for conservation field functions based on different fundamental solutions are developed. Special attention is given to the use of subdomain technique and Krylov subspace iterative solvers. The computed solutions of several benchmark problems agree well with available experimental and other computational results.
Keywords: fluid mechanics, fluid dynamics, numerical methods, boundary domain integral method, viscous fluid, heat transfer, diffusion-convective solution
Published: 01.06.2012; Views: 1293; Downloads: 51
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Double diffusive natural convection in a horizontal porous layer with the boundary domain integral method
Renata Jecl, Janja Kramer Stajnko, Leopold Škerget, 2009, original scientific article

Abstract: We present the boundary-domain integral method, one of the numerical methods for solving the transport phenomena in porous media. The results for the case of double diffusive natural convection in a porous horizontal layer, which is fully saturated with an incompressible fluid, are obtained. Modified Navier-Stokes equations were used to describe the fluid motion in porous media in the form of conservation laws for mass, momentum, energy and species. Several results for different cases of double diffusive natural convection in a porous horizontal layer are presented and compared with some published studies in which calculations with other numerical methods were performed.
Keywords: porous media, boundary domain integral method, double diffusive natural convection, Darcy-Brinkman equation
Published: 06.06.2018; Views: 210; Downloads: 34
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