In this work we propose a simple but effective high order polynomial correction allowing to enhance the consistency of all kind of boundary conditions for the Euler equations (Dirichlet, characteristic far-field and slip-wall), both in 2D and 3D, preserving a high order of accuracy without the need of curved meshes. The method proposed is a simplified reformulation of the Shifted Boundary Method (SBM) and relies on a correction based on the extrapolated value of the in cell polynomial to the true geometry, thus not requiring the explicit evaluation of high order Taylor series. Moreover, this strategy could be easily implemented into any already existing finite element and finite volume code. Several validation tests are presented to prove the convergence properties up to order four for 2D and 3D simulations with curved boundaries, as well as an effective extension to flows with shocks.

翻译：在这项工作中,我们提出了一个简单而有效的高顺序多式校正方案,以便提高Euler方程式(Drichlet、特质远方和滑墙)在2D和3D中各种边界条件(Drichlet、特质远方和防滑墙)的一致性,保持高度的精度,而不需要弯曲的网片。建议的方法是简化改写改变的边界方法(SBM),并依靠基于细胞多面体外推值的校正,从而不需要对高序泰勒系列进行明确的评估。此外,这一战略可以很容易地适用于任何已经存在的有限元素和有限体积代码。提出若干验证测试,以证明在2D和3D之间进行有弯曲边界的模拟时最多需要4个和3D的趋同特性,以及有效扩展到冲击波流。