A note on the imposition of traction boundary conditions when using the FEM for solving incompressible flow problems

Abstract

Abstract A traction boundary condition is particularly useful when analysing flow governed by the Navier–Stokes equation. For a large range of flow situations, such as fully developed laminar flow in a pipe or far field flow, the values of boundary traction can be evaluated explicitly. The former can be readily determined from the local values of the primitive variables, while the latter corresponds to zero traction. A general approach is advocated where traction boundary conditions can be evaluated as part of the solution procedure and its value is not required, a priori , before the solution can proceed. An iterative procedure for the evaluation and imposition of non‐zero tractions on boundaries, where advection is appreciable, is demonstrated by utilizing the finite element method (FEM) to simulate laminar flow, both steady state and transient, rearward of a downstream‐facing step within a bounded domain.