Boundary Element–finite Element Method For
Velocity-vorticity Formulation Of Navier-Stokes Equations
Author(s)
Z. ˇZuniˇc, L. ˇSkerget, M. Hriberˇsek & J. Ravnik
Abstract
A numerical method for the solution of the Navier-Stokes equations is developed
using an integral representation of the conservation equations. The velocityvorticity
formulation is employed, where the kinematics is given with the Poisson
equation for a velocity vector, while the kinetics is represented with the vorticity
transport equation. The corresponding boundary-domain integral equations are
presented along with discussions of the kinematics and kinetics of the fluid flow
problem. Kinematics is solved using the boundary element method (BEM), while
kinetics is solved using the finite element method (FEM). Quadratic continuous
interpolation functions are used for both BEM and FEM. Two benchmark problems
are considered to show the robustness and versatility of this formulation including
lid driven flow in a square cavity and flow over a backward facing step.
1 Introduction
Research in the field of numerical algorithms for computation of viscous fluid flow
was mainly concerned with development of approximation methods for the solution
of Navier-Stokes equations. The majority of approaches were focused on the
use of a single type of approximation method, like Finite difference, Finite Volume
or Finite Element methods (FEM). As each of the methods has some favourable,
but also unfavourable properties, a lot of research was also done in the development
of mixed approximation methods.
In the context of Boundary Element methods (BEM), several researchers
worked on combination of Boundary Element and Finite Element methods. In the
Keywords
Related Book
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