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首页> 外文会议>AIAA SciTech forum;AIAA Aerospace Sciences Meeting >A High-Order Method for Solving Unsteady Incompressible Navier-Stokes Equations with Implicit Time Stepping on Unstructured Grids
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A High-Order Method for Solving Unsteady Incompressible Navier-Stokes Equations with Implicit Time Stepping on Unstructured Grids

机译：非结构网格上具有隐式时间步长的非定常不可压缩Navier-Stokes方程的高阶方法

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This paper reports development of an unstructured high-order compact method for solving two-dimensional incompressible flow. This method employs the gGA correction from Huynh, and falls under the class of methods now referred to as Flux Reconstruction/Correction Procedure via Reconstruction. The artificial compressibility method and a dual time stepping scheme are used to simulate unsteady incompressible flow. A lower-upper symmetric Gauss-Seidel scheme with backward Euler discretization is used to efficiently march the solution in pseudo time, while a second order backward Euler discretization is used to march in physical time. We demonstrate order of accuracy with steady Taylor-Couette flow. We further validate the solver with steady flow past a NACA-0012 airfoil at zero angle of attack and unsteady flow past a circle. The implicit time stepping scheme is proven efficient and effective for driving the pseudo time derivative term toward zero in the classical artificial compressibility formulation. As a result, this scheme is capable of quickly establishing the divergence-free velocity condition of the continuity equation when compared to an explicit scheme.
机译：本文报道了解决二维不可压缩流的非结构化高阶紧致方法的发展。该方法采用了Huynh的gGA校正方法，属于现在称为“通过重建的磁通重建/校正过程”的方法类别。使用人工压缩方法和双重时间步长方案来模拟不稳定的不可压缩流动。具有后向欧拉离散化的较低上对称高斯-赛德尔算法用于在伪时间内有效地求解，而在物理时间中则采用二阶向后欧拉离散化进行。我们用稳定的Taylor-Couette流展示了精度的顺序。我们进一步验证了求解器是否以零迎角通过了NACA-0012机翼的稳定流以及通过圆的不稳定流。隐式时间步进方案被证明是有效的，并且在经典的人工可压缩性公式中，可以将伪时间导数项推向零。结果，与显式方案相比，该方案能够快速建立连续方程的无散度速度条件。

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