论文标题
可压缩流的移动边界多项式校正：使用线性网格在弯曲域上的高阶
Shifted boundary polynomial corrections for compressible flows: high order on curved domains using linear meshes
论文作者
论文摘要
在这项工作中，我们提出了一种简单但有效的高阶多项式校正，可以在2D和3D中增强Euler方程（dirichlet，dirichlet，dirichlet，特征性远场和滑动壁）的各种边界条件的一致性，可在2D和3D中保持高度的准确性，而无需弯曲的网眼。提出的方法是对移位边界方法（SBM）的简化重新印象，并依赖于基于细胞多项式对真实几何形状的外推值的校正，因此不需要对高阶泰勒系列的明确评估。此外，该策略可以轻松地将其实施到任何已经存在的有限元和有限卷代码中。提出了几项验证测试，以证明与具有弯曲边界的2D和3D模拟订单的收敛属性，并有效地扩展了具有冲击的流量。
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.
