Abstract: The problem of preserving the spherical symmetry of fluid flow in twodimensional cylindrical geometry was detailed studied. This problem called for cautious analysis and design of the entire hydrodynamics algorithms, which led to various methods. A programs was created, which based on the following schemes: utilizing the staggered Lagrangian algorithms; evolving the momentum by using the modified pressure gradient operators introduced by Caramana; advancing the internal energy compatibly; utilizing the edge-centered artificial viscosity; including the effects of the subzonal pressure forces; and ensuring the secondorder time accuracy by combining the predictor and corrector steps. The conservation of total energy was also investigated, the necessity of maintaining constant nodal masses was discussed, and the dissipativity of edge-centered artificial viscosity based on the compatible hydrodynamics algorithms was proved. In the end, the comparisons between numerical results and the known solutions demonstrated the correctness and robustness of the programs.