A Numerical Comparison of Outflow Boundary Conditions for Spectral Element Simulations of Incompressible Flows

Outflow boundary conditions(OBCs)are investigated for calculation of incompressible flows by spectral element methods.Several OBCs,including essentialtype,natural-type,periodic-type and advection-type,are compared by carrying out a series of numerical experiments.Especially,a simplified form of the so-called Orlanski’s OBCs is proposed in the context of spectral element methods,for which a new treatment technique is used.The purpose of this paper is to find stable low-reflective OBCs,suitable and flexible for use of spectral element methods in simulation of incompressible flows in complex geometries.The computation is firstly carried out for a 2D simulation of Poiseuille-B´enard channel flow with Re=10,Ri=150 and Pr=2/3.This flow serves as a useful example to demonstrate the applicability of the proposed OBCs because it exhibits a feature of vortex shedding propagating through the outflow boundary.Then a 3D flow around an obstacle is computed to show the efficiency in the case of more general geometries.Among the tested OBCs,the advection-type OBCs are proven to have better behavior as compared with the others.