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An approximate method for solving incompressible Navier-Stokes problems with flow rate conditions

机译:一种求解带流量条件的不可压缩Navier-Stokes问题的近似方法

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We consider the incompressible Navier-Stokes problem with flow rate boundary conditions. This problem has been investigated in [J. Heywood, R. Rannacher, S. Turek, Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations, Int. J. Numer. Methods Fluids 22 (1996) 325-352; L. Formaggia, J. F. Gerbeau, F. Nobile, A. Quarteroni, Numerical treatment of defective boundary conditions for the Navier-Stokes equation, SIAM J. Numer. Anal. 40(1) (2002) 376-401; A. Veneziani, C. Vergara, Flow rate defective boundary conditions in haemodynamics simulations, Int. J. Numer. Methods Fluids 47 (2005) 803-816]. In the latter two papers, a feasible numerical formulation of this problem, based on a Lagrange multiplier approach has been investigated. This approach has the drawback of high computational costs. In this paper, we propose an approximate formulation of this problem, yielding a strong reduction of the computational costs. The error analysis shows that the error introduced by this approximate formulation is confined in a small region of the boundary. This is confirmed by the numerical simulations.
机译:我们考虑了带有流动边界条件的不可压缩的Navier-Stokes问题。这个问题已经在[J. Heywood,R。Rannacher,S。Turek,不可压缩的Navier-Stokes方程的人工边界以及通量和压力条件,国际。 J.纽默方法流体(Fluids)22(1996)325-352。 L. Formaggia,J。F. Gerbeau,F。Nobile,A。Quarteroni,Navier-Stokes方程缺陷边界条件的数值处理,SIAM J. Numer。肛门40(1)(2002)376-401; A. Veneziani,C。Vergara,血流动力学模拟中的流速缺陷边界条件,诠释。 J.纽默方法流体47(2005)803-816]。在后两篇论文中,研究了基于拉格朗日乘数法的一个可行的数值表示方法。该方法具有高计算成本的缺点。在本文中,我们提出了这个问题的近似公式,从而大大降低了计算成本。误差分析表明,由这种近似公式引入的误差被限制在边界的一小部分内。数值模拟证实了这一点。

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