In this work we address the compressible Navier-Stokes equations written in the so-called primitive formulation. The proposed methodology is a finite-element solver based on a fractional step scheme in time, which allows to uncouple the calculation of the problem unknowns providing important savings in computational cost. In addition, we include a stabilization technique within the Variational Multi-Scale framework and, in particular, we consider orthogonal and dynamic definitions for the subscales. In order to overcome any wave reflections which may arise in aeroacoustic simulations at the low compressibility regime, we present a method for enforcing boundary conditions based on a combination of a zero order non-reflecting condition plus the weak imposition of Dirichlet boundary conditions over the external contours. Several representative benchmark flow simulations are performed, which demonstrate the suitability of the proposed algorithm for the subsonic regime.

在这项工作中，我们解决了以所谓的原始公式编写的可压缩Navier-Stokes方程。所提出的方法是一种基于分数步法的有限元求解器，它可以解开未知问题的计算，从而大大节省了计算成本。此外，我们在“变分多尺度”框架内包含了一种稳定技术，尤其是考虑了子尺度的正交和动态定义。为了克服在低压缩率状态下在航空声学模拟中可能出现的任何波反射，我们提出了一种基于零阶非反射条件加上Dirichlet边界条件对外部的弱势的组合来实施边界条件的方法轮廓。