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首页> 外文期刊>Journal of Computational Physics >A high-order solver for unsteady incompressible Navier-Stokes equations using the flux reconstruction method on unstructured grids with implicit dual time stepping
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A high-order solver for unsteady incompressible Navier-Stokes equations using the flux reconstruction method on unstructured grids with implicit dual time stepping

机译：含隐式双重时间步长的非结构化网格上通量重构方法的非定常不可压缩Navier-Stokes方程的高阶求解器

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摘要

We report development of a high-order compact flux reconstruction method for solving unsteady incompressible flow on unstructured grids with implicit dual time stepping. The method falls under the class of methods now referred to as flux reconstruction/correction procedure via reconstruction. The governing equations employ Chorin's classic artificial compressibility formulation with dual time stepping to solve unsteady flow problems. An implicit non-linear 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 verify and validate implementation of the high-order method coupled with our implicit time stepping scheme using both steady and unsteady incompressible flow problems. The current implicit time stepping scheme is proven effective in satisfying the divergence-free constraint on the velocity field in the artificial compressibility formulation within the context of the highorder flux reconstruction method. This compact high-order method is very suitable for parallel computing and can easily be extended to moving and deforming grids. (C) 2016 Elsevier Inc. All rights reserved.
机译：我们报告了一种高阶紧凑通量重构方法的开发，该方法可通过隐式双重时间步长解决非结构化网格上的非稳态不可压缩流。该方法属于现在称为通过重建的通量重建/校正过程的方法类别。控制方程采用了Chorin的经典人工可压缩性公式和双重时间步长来解决非稳态流动问题。使用具有反向欧拉离散化的隐式非线性下-上对称高斯-赛德尔格式，可以有效地在伪时间内进行解，而使用二阶反向欧拉离散化则可以在物理时间进行。我们使用稳定和不稳定的不可压缩流问题，验证并验证了高阶方法的实现以及我们的隐式时间步进方案。在高阶通量重构方法的背景下，目前的隐式时间步进方案被证明可有效地满足人工可压缩性公式中对速度场的无散度约束。这种紧凑的高阶方法非常适合于并行计算，并且可以轻松扩展到移动和变形的网格。 （C）2016 Elsevier Inc.保留所有权利。

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