A Contribution to the Outflow Boundary Conditions for Navier-Stokes Time-Splitting Methods

Abstract

We present in this paper a numerical scheme for incompressible Navier-Stokes equations with open boundary conditions, in the framework of the pressure and velocity correction schemes. In Poux et al. (J Comput Phys 230:4011–4027, 2011), the authors presented an almost second-order accurate version of the open boundary condition with a pressure-correction scheme in finite volume framework. This paper proposes an extension of this method in spectral element method framework for both pressure- and velocity-correction schemes. A new way to enforce this type of boundary condition is proposed and provides a pressure and velocity convergence rate in space and time higher than with the present state of the art. We illustrate this result by computing some numerical tests.