Towards A Fast Single Domain – Subdomain
BEM Algorithm For 3D Incompressible Fluid Flow
Author(s)
J. Ravnik, L. Skerget & Z. Zunic
Abstract
Work towards acceleration and computer memory reduction of an algorithm for
the simulation of laminar viscous flows by solving of 3D velocity-vorticity formulation
of the Navier–Stokes equations is presented. The algorithm employs a combination
of a subdomain boundary element method (BEM) and fast single domain
BEM. The single domain BEM on a Poisson type equation is employed to calculate
boundary vorticity values. After discretization, the single domain BEM algorithm
yields a fully populated system of linear equations. The non-homogenous part of
the Poisson equation yields a fully populated matrix of domain integrals. In order
to lower the computational demand, a fast multipole expansion algorithm is used
on the domain matrix. The fundamental solution 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. Compression
is achieved in parts of the matrix, which correspond to boundary-domain cluster
pairs that are admissible for expansion. Significant reduction of the complexity is
achieved. The paper presents results of initial testing of the FMM algorithm.
Keywords: fast multipole method, boundary element method, Poisson equation.
1 Introduction
Our research group works on the application of the Boundary Element Method to
fluid flow problems. Recently Ravnik et al. [1] developed a 3D subdomain - single
domain BEM numerical scheme for solving incompressible velocity-vorticity
formulation of Navier–Stokes equations. A crucial part of this algorithm is the
calculation of boundary vorticity values. They are obtained by solving a Poisson
type partial differential equation using single domain BEM. The domain integral,
which arises from the non-homogenous part of the Poisson equation, requires the
Keywords
fast multipole method, boundary element method, Poisson equation.
Related Book
Other papers in this volume
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