Bin Xie, Peng Jin, Feng Xiao. 基于非结构网格的不可压N-S方程多矩有限体积法[J]. 空气动力学学报, 2016, 34(2): 252-266. DOI: 10.7638/kqdlxxb-2016.0013
引用本文: Bin Xie, Peng Jin, Feng Xiao. 基于非结构网格的不可压N-S方程多矩有限体积法[J]. 空气动力学学报, 2016, 34(2): 252-266. DOI: 10.7638/kqdlxxb-2016.0013
Bin Xie, Peng Jin, Feng Xiao. A Multi-Moment Finite Volume Method for Incompressible Navier-Stokes Equations on Unstructured Grids[J]. ACTA AERODYNAMICA SINICA, 2016, 34(2): 252-266. DOI: 10.7638/kqdlxxb-2016.0013
Citation: Bin Xie, Peng Jin, Feng Xiao. A Multi-Moment Finite Volume Method for Incompressible Navier-Stokes Equations on Unstructured Grids[J]. ACTA AERODYNAMICA SINICA, 2016, 34(2): 252-266. DOI: 10.7638/kqdlxxb-2016.0013

基于非结构网格的不可压N-S方程多矩有限体积法

A Multi-Moment Finite Volume Method for Incompressible Navier-Stokes Equations on Unstructured Grids

  • 摘要: 提出了一种基于三角形及四面体非结构网格的有限体积法(FVM),用以鲁棒且精确地求解不可压粘性流动问题。与传统的FVM方法仅将体积分平均值(VIA)作为计算变量的做法不同,本文提出的方法将VIA及点值(PV)同时作为计算变量并在每个迭代步进行计算更新。VIA以通量形式进行计算以确保数值守恒,PV可以通过控制方程的不同形式进行求解更新,无需守恒,因此可以采用非常高效的方法进行求解。将PV作为增加的变量使得紧致网格模板得以实现更高阶精度的重构,而且由此获得的数值模型对于非结构网格变得更鲁棒。本文针对二维/三维的三角形/四面体非结构网格提出了数值格式,给出了几个基准测试算例,验证了本文提出的数值方法在采用非结构网格求解不可压粘性流动问题时的精确性和鲁棒性。

     

    Abstract: A robust and accurate finite volume method (FVM) is proposed for incompressible viscous fluid dynamics on triangular and tetrahedral unstructured grids. Different from conventional FVM where the volume integrated average (VIA) value is the only computational variable, the present formulation treats both VIA and the point value (PV) as the computational variables which are updated at each time step. The VIA is computed from a finite volume scheme of flux form, and is thus numerically conservative. The PV is updated from the differential form of the governing equation that does not have to be conservative but can be solved in a very efficient way. Including PV as the additional variable enables us to make higher-order reconstructions over compact mesh stencil to improve the accuracy, and moreover, the resulting numerical model is more robust for unstructured grids. We present the numerical formulations in both two and three dimensions on triangular and tetrahedral mesh elements. Numerical results of several benchmark tests are also presented to verify the proposed numerical method as an accurate and robust solver for incompressible flows on unstructured grids.

     

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