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Finite-element multigrid scheme for the Navier-Stokes solutions, part II: Formulation and validation

机译:Navier-Stokes解决方案的有限元多重网格方案,第二部分:公式化和验证

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This article develops a finite-element-based methodology for the numerical stimulation of the compressible Navier-Stokes equations on unstructured triangular meshes [1]. The flow solver uses a Galerkin finite-element discretization in space and an explicit Runge-Kutta multistage integration in time. Element-based and edged-based finite-element approximations for the discretization of the viscous terms in these equations are presented. Acceleration techniques, such as multigrid, local time-stepping, and residual smoothing are used for the computation of the steady-state solutions. The modeling of turbulent flow is accomplished by using the Reynolds-averaged form of the Navier-Stokes equation and an eddy viscosity model for the turbulent stresses. Two of such models, the algebraic model of Baldwin and Lomax and the one-equation model of Baldwin and Earth, are implemented and validated. The performance and accuracy of the proposed numerical technique is demonstrated for a variety of external-flow test cases. [References: 25]
机译:本文开发了一种基于有限元的方法,用于非结构化三角形网格上可压缩Navier-Stokes方程的数值激励[1]。流动求解器在空间中使用Galerkin有限元离散化,并在时间上使用显式的Runge-Kutta多级积分。给出了这些方程中粘性项离散化的基于元素和基于边的有限元逼近。诸如多重网格,局部时间步长和残差平滑之类的加速技术用于稳态解的计算。湍流的建模是通过使用Navier-Stokes方程的雷诺平均形式和湍流应力的涡流粘度模型完成的。实现并验证了其中两个模型,即Baldwin和Lomax的代数模型以及Baldwin和Earth的单方程模型。所提出的数值技术的性能和准确性已在各种外部测试案例中得到了证明。 [参考:25]

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