论文标题
一种用于求解不可压缩的Navier-Stokes方程的压力型HHO方法
A pressure-robust HHO method for the solution of the incompressible Navier-Stokes equations on general meshes
论文作者
论文摘要
在最近的一项工作[10]中，我们引入了一种压力型混合高阶方法，用于用于匹配简单网格的不可压缩Navier-Stokes方程的数值解。压力射击方法的特征是完全独立于压力的速度的误差估计值。在这项工作中，一个关键的问题是一个关键的问题，即是否可以将拟议的建筑扩展到一般的多面网格。在本文中，我们为这个问题提供了积极的答案。具体而言，我们介绍了一种新颖的脱离差异速度重建，该速度重建呈现在亚三角调节上的混合问题的每个元素内部的溶液上，然后将其用于设计体力的离散和对流术语，从而导致压力稳健性。对该速度重建的性质及其对该方案的回响的深入理论研究是针对多项式学度进行的，$ k \ geq 0 $ and由一般多型的网格进行。该方法的理论收敛估计值和压力鲁棒性通过广泛的数值示例确认。
In a recent work [10], we have introduced a pressure-robust Hybrid High-Order method for the numerical solution of the incompressible Navier-Stokes equations on matching simplicial meshes. Pressure-robust methods are characterized by error estimates for the velocity that are fully independent of the pressure. A crucial question was left open in that work, namely whether the proposed construction could be extended to general polytopal meshes. In this paper we provide a positive answer to this question. Specifically, we introduce a novel divergence-preserving velocity reconstruction that hinges on the solution inside each element of a mixed problem on a subtriangulation, then use it to design discretizations of the body force and convective terms that lead to pressure robustness. An in-depth theoretical study of the properties of this velocity reconstruction, and their reverberation on the scheme, is carried out for polynomial degrees $k \geq 0$ and meshes composed of general polytopes. The theoretical convergence estimates and the pressure robustness of the method are confirmed by an extensive panel of numerical examples.
