This paper reviews some critical issues for the popular cell-centered numerical algorithms written in cylindrical geometry for compressible fluid.These issues include the spherical symmetry,conservation,singularity in the geometrical source and the compatibility between the numerical flux and nodal motion manner.Based on the understanding to above issues,some new cell-centered arbitrary Lagrangian Eulerian(ALE)methods on unstructured meshes are proposed.The main new feature of these algorithms is to establish a multi-dimensional Riemann solver based on HLLC method(denoted by ALE HLLC-2D).