Pressure boundary conditions for the vorticity-velocity formulation of Navier-Stokes equations

The pressure boundary conditions (BC) for the vorticity-velocity formulation of the NS equations are considered. The aim of the paper is to formulate the BC problem on the strict basis of the theory of potential. Two aspects of the pressure BC are discussed. The first one is pressure BC at open boundaries (for example, at the inlet and outlet of the pipe). The problem is reduced finally to the system of Fredholm equations of the second type relative to unknown vorticity and sources (sinks) distributions over the boundaries. The second aspect is the determination of the pressure field on the basis of the known velocity field. The approach alternative to the pressure Poisson equation is proposed. It is based on the Helmholz decomposition of the vector field, and it is free from the ambiguities inherent to the previous considerations. (C) 1998 Elsevier Science Ltd. All rights reserved.