Abstract: In calculating one-dimensional cylindrical flow problems,famous Wilkins finite difference scheme under Cartesian coordinate system can get exact symmetry with peripheral grids zoned by equal angle,and get severe non-symmetry with peripheral grids zoned by unequal angle.By analyzing the reason that the Wilkins scheme may damage symmetry under the condition of peripheral grids zoned by unequal angle in computing 1-dimensional cylindrical problems,it is pointed out that the unequal angle zoning of peripheral grids results in peripheral pressure component,accordingly, peripheral acceleration and velocity components.On the basis of the analysis,a modified scheme is brought forward,which operates an arithmetic average on the peripheral pressure component at each point in order to eliminate the peripheral pressure component and automatically to maintain only the radial component.So the modified scheme can preserve exact symmetry under the condition of peripheral grids zoned by arbitrary angle.The conclusion is shown by several representative examples,and the modified method has very consistent results with the primary method for the symmetry flows and very little differences from the primary method for the unsymmetry flows.The representative examples demonstrate that the modified scheme is reasonable.

Key words: two-dimensional Lagrangian hydrodynamics equations, preserved symmetry, Wilkins finite difference scheme