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A stabilized finite element method based on SGS models for compressible flows

机译：基于SGS模型的可压缩流稳定有限元方法。

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摘要

We present an appropriate extension of the stabilized finite element formulation, introduced in [A. Corsini, F. Rispoli, A. Santoriello, A variational multiscale high-order finite element formulation for turbomachinery flow computations, Comput. Methods Appl. Mech. Engrg. 194 (2005) 4797-4823] for the prediction of incompressible flows, aimed at compressible flows. The stabilized formulation is the so-called variable subgrid scale method (V-SGS) based on an approximation of the class of subgrid scale models (SGS) derived from the Hughes variational multiscale method (Hughes-VMS) introduced in [T.J.R. Hughes, Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods, Comput. Methods Appl. Mech. Engrg. 127 (1995) 387-401]. It is characterized by a variable stabilization parameter within the domain of element. We also propose an innovative procedure for computing the stabilization parameter by using the one-dimensional element Green's functions corresponding to an advective-diffusive differential operator. The stabilization parameter is defined as the sum of two components, the first providing its mean value and the second its element-wise space dependency. On this basis the present work proposes the stabilization matrix for the multidimensional advective-diffusive system of equations governing compressible flows. The procedure developed for computing the stabilization parameter can be applied to other differential operators as it has been shown in [A. Corsini, F. Rispoli, A. Santoriello, A variational multiscale high-order finite element formulation for turbomachinery flow computations, Comput. Methods Appl. Mech. Engrg. 194 (2005) 4797-4823]. The proposed stabilization device is validated by simulation of inviscid and viscous supersonic flow configurations.
机译：我们提出了在[A. Corsini，F.Rispoli，A.Santoriello，一种用于涡轮机械流量计算的变分多尺度高阶有限元公式，计算机。方法应用。机甲gr 194（2005）4797-4823]针对不可压缩流的预测，针对可压缩流。稳定的公式是所谓的可变子网格规模方法（V-SGS），它基于从[T.J.R.引入的休斯多尺度多尺度方法（Hughes-VMS）派生的子网格规模模型（SGS）的类别的近似值。休斯，多尺度现象：格林函数，Dirichlet-to-Neumann公式，子网格尺度模型，气泡和稳定方法的起源，计算机。方法应用。机甲gr 127（1995）387-401]。它的特征在于元素域内的可变稳定参数。我们还提出了一种创新方法，通过使用与对流扩散微分算子相对应的一维元素格林函数来计算稳定参数。稳定参数定义为两个分量的总和，第一个提供其平均值，第二个提供其元素空间依赖性。在此基础上，本工作为支配可压缩流的多维对流扩散方程组提出了稳定矩阵。如[A.A.B]中所示，可以将用于计算稳定参数的过程应用于其他微分算子。 Corsini，F.Rispoli，A.Santoriello，一种用于涡轮机械流量计算的变分多尺度高阶有限元公式，计算机。方法应用。机甲gr 194（2005）4797-4823]。拟议的稳定装置通过对粘性和超音速流动配置的仿真进行了验证。

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