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首页> 外文期刊>Journal of Computational Physics >A multi-block ADI finite-volume method for incompressible Navier-Stokes equations in complex geometries
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A multi-block ADI finite-volume method for incompressible Navier-Stokes equations in complex geometries

机译：复杂几何中不可压缩的Navier-Stokes方程的多块ADI有限体积方法

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摘要

An efficient second-order accurate finite-volume method is developed for a solution of the incompressible Navier-Stokes equations on complex multi-block structured curvilinear grids. Unlike in the finite-volume or finite-difference-based alternating-direction-implicit (ADI) methods, where factorization of the coordinate transformed governing equations is performed along generalized coordinate directions, in the proposed method, the discretized Cartesian form Navier-Stokes equations are factored along curvilinear grid lines. The new ADI finite-volume method is also extended for simulations on multi-block structured curvilinear grids with which complex geometries can be efficiently resolved. The numerical method is first developed for an unsteady convection-diffusion equation, then is extended for the incompressible Navier-Stokes equations. The order of accuracy and stability characteristics of the present method are analyzed in simulations of an unsteady convection-diffusion problem, decaying vortices, flow in a lid-driven cavity, flow over a circular cylinder, and turbulent flow through a planar channel. Numerical solutions predicted by the proposed ADI finite-volume method are found to be in good agreement with experimental and other numerical data, while the solutions are obtained at much lower computational cost than those required by other iterative methods without factorization. For a simulation on a grid with O(10~5) cells, the computational time required by the present ADI-based method for a solution of momentum equations is found to be less than 20% of that required by a method employing a biconjugate-gradient-stabilized scheme.
机译：针对复杂的多块结构曲线网格上不可压缩的Navier-Stokes方程的求解，开发了一种有效的二阶精确有限体积方法。不同于在有限体积或基于有限差分的交替方向隐式（ADI）方法中，坐标变换的控制方程是沿着广义坐标方向进行因式分解的，在该方法中，离散笛卡尔形式的Navier-Stokes方程沿曲线网格线分解。新的ADI有限体积方法也扩展了用于多块结构曲线网格的仿真，可以有效地解决复杂的几何形状。首先为非稳态对流扩散方程开发了数值方法，然后将其扩展为不可压缩的Navier-Stokes方程。在模拟非稳态对流扩散问题，涡旋衰减，盖驱动腔中的流动，圆柱体上的流动以及通过平面通道的湍流的模拟中，分析了本方法的精度和稳定性特征。发现通过拟议的ADI有限体积法预测的数值解与实验数据和其他数值数据非常吻合，而获得的解的计算成本比其他没有因式分解的迭代方法所需的计算成本低得多。对于在具有O（10〜5）个像元的网格上进行的仿真，发现本基于ADI的方法求解动量方程所需的计算时间少于采用双共轭方法的方法所需的计算时间的20％。梯度稳定方案。

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