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Large stencil viscous flux linearization for the simulation of 3D compressible turbulent flows with backward-Euler schemes

机译：大型模板黏性通量线性化，用于使用反向欧拉法模拟3D可压缩湍流

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摘要

The purpose of this article is to study different approximate linearizations of the RANS equations viscous fluxes, for numerical simulations of compressible turbulent flows with backward-Euler schemes. The explicit convective flux under consideration is centred with artificial dissipation. The discrete viscous flux, calculated from cell-centred evaluation of the gradients, needs less computations and memory storage than other discretizations. But, in other respects, the balance of this numerical flux has a large stencil, which is not coherent with the 3-point per mesh direction stencil of classical implicit stages. Therefore 3-point and 5-point per mesh direction approximate linearizations are built from the thin layer flux formula. The stability condition of the corresponding backward-Euler schemes is given for a scalar linear equation (for the basic non-factored version of scheme and with LU-relaxation). Multigrid and monogrid computations of turbulent flow around two external configurations are performed with Wilcox's k-ω turbulence model. The 5-point per mesh direction linearizations, coherent with the differential of the fluxes balance of thin layer approximation of explicit viscous fluxes, leads to the most efficient implicit stages.
机译：本文的目的是研究RANS方程粘性通量的不同近似线性化，以便使用后向Euler方案对可压缩湍流进行数值模拟。考虑中的显式对流通量以人工耗散为中心。通过对梯度进行以单元为中心的评估计算得出的离散粘性通量，与其他离散化方法相比，所需的计算量和存储量更少。但是，在其他方面，该数值通量的平衡具有较大的模具，这与经典隐式阶段的每网格方向3点模具不相干。因此，从薄层通量公式可以建立每网格方向3点和5点的近似线性化。对于标量线性方程，给出了相应的反向欧拉方案的稳定性条件（对于该方案的基本非因式版本，并且具有LU松弛）。使用Wilcox的k-ω湍流模型对围绕两个外部配置的湍流进行多网格和单网格计算。每网格5点方向的线性化与显式粘性通量的薄层近似的通量平衡的微分一致，导致最有效的隐式阶段。

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