WIT Press

Boundary Element–finite Element Method For Velocity-vorticity Formulation Of Navier-Stokes Equations


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Z. ˇZuniˇc, L. ˇSkerget, M. Hriberˇsek & J. Ravnik


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