A parallel adaptive numerical method with generalized curvilinear coordinate transformation for compressible Navier–Stokes equations
A parallel adaptive numerical method with generalized curvilinear coordinate transformation for compressible Navier–Stokes equations
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可压缩纳维-斯托克斯方程广义曲线坐标变换的并行自适应数值方法
DOI：
10.1002/fld.4235
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发表时间：
2016
影响因子：
1.8
通讯作者：
S. Guzik
中科院分区：
文献类型：
--
作者：
Xinfeng Gao;Landon D. Owen;S. Guzik
提出了一种四阶有限体积法，用于求解映射网格上的Navier-Stokes方程，该方法具有自适应网格细化，并用于非定常可压缩粘性流动的预测。该方法采用四阶正交规则来计算面平均通量。我们的方法是自由流保存，通过计算细胞表面度量项的平均值来保证。采用标准的龙格-库塔推进法进行时间离散。为了验证在映射网格上应用非线性粘性算子时，该方法在形式上是四阶精确的，得到了一个光滑流动的解。给出了一个激波管问题的解，证明了自适应网格细化在解决不连续性问题中的有效性。通过求解一个马赫反射问题，验证了该映射算法在非矩形物理域上的应用。仿真结果与实验结果进行了比较。未来的工作将考虑实际工程几何的映射多块网格。版权所有©2016 John Wiley & Sons， Ltd。
A fourth‐order finite‐volume method for solving the Navier–Stokes equations on a mapped grid with adaptive mesh refinement is proposed, implemented, and demonstrated for the prediction of unsteady compressible viscous flows. The method employs fourth‐order quadrature rules for evaluating face‐averaged fluxes. Our approach is freestream preserving, guaranteed by the way of computing the averages of the metric terms on the faces of cells. The standard Runge–Kutta marching method is used for time discretization. Solutions of a smooth flow are obtained in order to verify that the method is formally fourth‐order accurate when applying the nonlinear viscous operators on mapped grids. Solutions of a shock tube problem are obtained to demonstrate the effectiveness of adaptive mesh refinement in resolving discontinuities. A Mach reflection problem is solved to demonstrate the mapped algorithm on a non‐rectangular physical domain. The simulation is compared against experimental results. Future work will consider mapped multiblock grids for practical engineering geometries. Copyright © 2016 John Wiley & Sons, Ltd.