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首页> 外文会议>AIAA computational fluid dynamics conference;AIAA aviation forum >A Hybrid Reconstructed Discontinuous Galerkin and Continuous Galerkin Finite Element Method for Incompressible Flows on Unstructured Grids
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A Hybrid Reconstructed Discontinuous Galerkin and Continuous Galerkin Finite Element Method for Incompressible Flows on Unstructured Grids

机译：非结构网格上不可压缩流的混合重构不连续Galerkin和连续Galerkin有限元方法

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A hybrid reconstructed discontinuous Galerkin and continuous Galerkin method based on an incremental pressure projection formulation, termed rDG(P_nP_m)+CG(P_n) in this paper, is developed for solving the unsteady incompressible Navier-Stokes equations on unstructured grids. In this method, a reconstructed discontinuous Galerkin method (rDG(P_nP_m)) is used to discretize the velocity and a standard continuous Galerkin method (CG(P_n)) is used to approximate the pressure. The rDG(P_nP_m)-CG(P_n) method is designed to increase the accuracy of the hybrid DG(P_n)-CG(P_n) method and yet still satisfy Ladyzenskaja-Babuska-Brezzi (LBB) condition, thus avoiding the pressure checkerboard instability. An upwind method is used to discretize the nonlinear convective fluxes in the momentum equations in order to suppress spurious oscillations in the velocity field. A number of incompressible flow problems for a variety of flow conditions are computed to numerically assess the spatial order of convergence of the rDG(P_nP_m)+CG(P_m) method. The numerical experiments indicate that both rDG(P_0P_1)+CG(P_1) and rDG(P_1P_2)+CG(P_1) methods can attain the designed second order and third order accuracy in space for the velocity, respectively and the third order rDG(P_1P_2)+CG(P_1) method significantly outperforms its second order rDG(P_1P_1)+CG(P_1) and rDG(P_1P_1)+CG(P_1) counterparts: being able to not only increase the accuracy of the velocity by one order but also improve the accuracy of the pressure.
机译：提出了一种基于增量压力投影公式的混合重构不连续Galerkin和连续Galerkin方法，该方法称为rDG（P_nP_m）+ CG（P_n），用于求解非结构化网格上的非稳态不可压缩Navier-Stokes方程。在此方法中，使用重构的不连续Galerkin方法（rDG（P_nP_m））离散速度，并使用标准连续Galerkin方法（CG（P_n））近似压力。 rDG（P_nP_m）-CG（P_n）方法旨在提高DG（P_n）-CG（P_n）混合方法的精度，但仍满足Ladyzenskaja-Babuska-Brezzi（LBB）条件，从而避免了压力棋盘的不稳定性。为了抑制速度场中的虚假振荡，采用逆风方法离散动量方程中的非线性对流通量。计算了各种流动条件下的许多不可压缩流动问题，以数值评估rDG（P_nP_m）+ CG（P_m）方法收敛的空间顺序。数值实验表明，rDG（P_0P_1）+ CG（P_1）和rDG（P_1P_2）+ CG（P_1）方法均可分别获得设计的速度空间二阶和三阶精度，以及三阶rDG（P_1P_2） ）+ CG（P_1）方法明显优于其二阶rDG（P_1P_1）+ CG（P_1）和rDG（P_1P_1）+ CG（P_1）对应物：不仅可以将速度的精度提高一级，还可以提高压力的准确性。

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