A numerical scheme and method deducing "wall heating errors" in computing problems of radially symmetric flow using Lagrangian cell-centered schemes is investigated.Relation between "wall heating error" and modified equations of difference schemes is introduced.With comparision of sound wave approximate Riemann solver and HLL Riemann solver,a new adaptive heat conduction viscosity is introduced to ameliorate "wall heating errors".Numerical experiments show that this viscosity in current scheme provides satisfactory results.