Opis: 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. Ključne besede:subdomain boundary element method, laminar viscous fluid flow, velocity-vorticity fomulation, lid driven cavity Objavljeno v DKUM: 01.06.2012; Ogledov: 1943; Prenosov: 105 Povezava na celotno besedilo

Opis: In this paper acceleration and computer memory reduction of an algorithm for the simulation of laminar viscous flows and heat transfer is presented. The algorithm solves the velocity-vorticity formulation of the incompressible Navier-Stokes equations in 3D. It is based on a combination of a subdomain boundary element method (BEM) and single domain BEM. The CPU time and storage requirements of the single domain BEM are reduced by implementing a fast multipole expansion method. The Laplace fundamental solution, which is used as a special weighting function in BEM, is expanded in terms of spherical harmonics. The computational domain and its boundary are recursively cut up forming a tree of clusters of boundary elements and domain cells. Data sparse representation is used in parts of the matrix, which correspond to boundary-domain clusters pairs that are admissible for expansion. Significant reduction of the complexity is achieved. The paper presents results of testing of the multipole expansion algorithm by exploring its effect on the accuracy of the solution and its influence on the non-linear convergence properties of the solver. Two 3D benchmark numerical examples are used: the lid-driven cavity and the onset of natural convection in a differentially heated enclosure. Ključne besede:boundary element method, fast multipole method, fluid flow, heat transfer, velocity-vorticity fomulation Objavljeno v DKUM: 31.05.2012; Ogledov: 2168; Prenosov: 96 Povezava na celotno besedilo

Opis: The problem of unsteady compressible fluid flow in an enclosure induced by thermoacoustic waves is studied numerically. Full compressible set of Navier-Stokes equations are considered and numerically solved by boundary-domain integral equations approach coupled with wavelet compression and domain decomposition to achieve numerical efficiency. The thermal energy equation is written in its most general form including the Rayleigh and reversible expansion rate terms. Both, the classical Fourier heat flux model and wave heat conduction model are investigated. The velocity-vorticity formulation of the governing Navier-Stokes equations is employed, while the pressure field is evaluated from the corresponding pressure Poisson equation. Material properties are taken to be for the perfect gas, and assumed to be pressure and temperature dependent. Ključne besede:compressible fluid flow, boundary element method, thermoacoustic waves, velocity-vorticity fomulation Objavljeno v DKUM: 31.05.2012; Ogledov: 2409; Prenosov: 93 Povezava na celotno besedilo