A convective boundary condition for the Navier–Stokes equations

Abstract

A convective boundary condition (CBC) on an outflow boundary for flow problems governed by the Navier–Stokes equations is studied, and existence and uniqueness results of solutions are established. By illustrating other known outflow boundary conditions, such as “do-nothing”, “directional do-nothing” and “total pressure”, the difference of flows is observed numerically. The following are properties of CBC: (i) Natural from a mathematical viewpoint. (ii) Possible to discuss existence and uniqueness of solutions. (iii) Easy to implement the Newton method of the Navier–Stokes equations and an adjoint method arising in, e.g., shape optimization problems.