Absorbing boundary conditions for nonlinear Euler and Navier-Stokes equations based on the perfectly matched layer technique

作者：Hu, Fang Q.^*; Li, X. D.; Lin, D. K.

来源：Journal of Computational Physics, 2008, 227(9): 4398-4424.

DOI：10.1016/j.jcp.2008.01.010

• non-reflecting boundary condition
• perfectly matched layer
• Navier-Stokes equations
• Euler equations
• computational fluid dynamics
• computational aeroacoustics

Absorbing boundary conditions for the nonlinear Euler and Navier-Stokes equations in three space dimensions are presented based on the perfectly matched layer (PML) technique. The derivation of equations follows a three-step method recently developed for the PML of linearized Euler equations. To increase the efficiency of the PML, a pseudo mean flow is introduced in the formulation of absorption equations. The proposed PML equations will absorb exponentially the difference between the nonlinear fluctuation and the prescribed pseudo mean flow. With the nonlinearity in flux vectors, the proposed nonlinear absorbing equations are not formally perfectly matched to the governing equations as their linear counter-parts are. However, numerical examples show satisfactory results. Furthermore, the nonlinear PML reduces automatically to the linear PML upon linearization about the pseudo mean flow. The validity and efficiency of proposed equations as absorbing boundary conditions for nonlinear Euler and Navier-Stokes equations are demonstrated by numerical examples.

• 出版日期2008-4-20
• 单位北京航空航天大学