Abstract In this work we consider the approximation of the isentropic Navier–Stokes equations. The model we present is capable of taking into account acoustic and flow scales at once. After space and time discretizations have been chosen, it is very convenient from the computational point of view to design fractional step schemes in time so as to permit a segregated calculation of the problem unknowns. While these segregation schemes are well established for incompressible flows, much less is known in the case of isentropic flows. We discuss this issue in this article and, furthermore, we study the way to weakly impose Dirichlet boundary conditions via Nitsche’s method. In order to avoid spurious reflections of the acoustic waves, Nitsche’s method is combined with a non-reflecting boundary condition. Employing a purely algebraic approach to discuss the problem, some of the boundary contributions are treated explicitly and we explain how these are included in the different steps of the final algorithm. Numerical evidence shows that this explicit treatment does not have a significant impact on the convergence rate of the resulting time integration scheme. The equations of the formulation are solved using a subgrid scale technique based on a term-by-term stabilization.

中文翻译：

---

使用 Dirichlet 边界条件弱施加的计算气动声学的分数步法

摘要 在这项工作中，我们考虑了等熵 Navier-Stokes 方程的近似。我们展示的模型能够同时考虑声学和流量尺度。在选择了空间和时间离散化之后，从计算的角度来看，及时设计分步方案是非常方便的，以便允许对未知问题进行分离计算。虽然这些分离方案对于不可压缩流已经很好地建立，但在等熵流的情况下知之甚少。我们在本文中讨论了这个问题，此外，我们研究了通过 Nitsche 方法弱施加 Dirichlet 边界条件的方法。为了避免声波的虚假反射，Nitsche 的方法与非反射边界条件相结合。使用纯粹的代数方法来讨论这个问题，一些边界贡献被明确处理，我们解释了这些是如何包含在最终算法的不同步骤中的。数值证据表明，这种显式处理对所得时间积分方案的收敛速度没有显着影响。使用基于逐项稳定性的子网格尺度技术求解公式的方程。