Numerical treatment of singularity cells around the polar axis for finite volume method

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.