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. Simulation results are compared with benchmark results for a cubic inclined enclosure for Rayleigh number values ?10^3<Ra<10^5.
COBISS.SI-ID: 12278550
The boundary element method applied on non-homogenous partial differential equations requires calculation of a fully populated matrix of domain integrals. This paper compares two techniques: the fast multipole method and the fast wavelet transform, which are used to reduce the complexity of such domain matrices. The results show comparable accuracy for both methods for a given data storage size. Considering implementation of the methods, the wavelet transform can easily be adapted for any problem, while the fast multipole method requires different expansion for each integral kernel.
COBISS.SI-ID: 13062678
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 viscous flows. The versatility and accuracy of the method are proven using the 3D lid driven cavity test case.
COBISS.SI-ID: 12948502
In this paper acceleration and computer memory reduction of an algorithm for the simulation of laminar viscous flows and heat transfer is presented. The CPU time and storage requirements are reduced by implementing a fast multipole expansion method. The Laplace fundamental solution is expanded in terms of spherical harmonics. The paper presents results of exploring the effect of the multipole expansion algorithm on the accuracy of the solution. Two 3D benchmark numerical examples are used: the lid-driven cavity and the onset of natural convection in a differentially heated enclosure.
COBISS.SI-ID: 13066774
A wavelet transform based BEM and FEM numerical scheme was used to simulate laminar viscous flow. The flow simulation algorithm was coupled with a Lagrangian particle tracking scheme for dilute suspensions of particles. The algorithm was used to simulate flow and particle paths for two test cases: flow over a backward-facing step and flow past a circular cylinder. Particle distributions were investigated in unsteady wakes behind 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.
COBISS.SI-ID: 11868182