一种有限容积法中极点奇异单元的处理方法

Numerical Treatment of Singularity Cells Around the Polar Axis for Finite Volume Method

针对采用极坐标系结构化网格计算非轴对称流动会出现的奇异性问题,以圆形腔顶部驱动流为例分析奇异性问题产生的原因,并通过局部坐标系下压力梯度项的分解,提出了一种极坐标系统结构化网格中心奇异单元离散格式中压力梯度项的处理方法.圆形腔顶部驱动流的数值结果表明:经过压力修正的极坐标系结构化网格算法与单元数高于其数十倍的非结构化网格算法具有一致的计算精度.与同类处理方法相比,该算法不需要对极点处的网格进行特殊处理,在局部坐标系下,仅对极点处网格奇异单元的离散格式压力梯度项进行正交分解处理,极大地降低了有限容积法的实施难度,且保证了算法的准确有效性.

The reason of non-physical profiles of the lid driven flow in a closed circular cavity was analyzed to avoid singularity in solving a non-axisymmetrical fluid flow problem using a polar cylindrical grid.A new numerical method was proposed to treat these singularity elements by decomposing the pressure gradient term.The present method can obviously avoid the singularity without increasing the calculation amount.Compared with the unstructured grid,the same level of accuracy can be obtained using the present method with much fewer cells in a Cartesian coordinate system.Unlike the conventional methods,this method does not need special treatment of the cells.Our results indicate that the present method will reduce the difficulty of adopting the finite volume method and ensure its feasibility by orthogonal decomposition treatment of the pressure gradient term in the discretization scheme at the singularity cells.