Abstract: According to different discrete locations of the kinematic variables on grids, the Lagrangian algorithm is divided into staggered schemes and cell-centered schemes. Both kinds of schemes achieve remarkable results in computational fluid dynamics, but few attentions are payed to their comparison. In this paper, various one dimensional numerical tests are conducted to study the characteristics of the staggered and cell-centered Lagrangian schemes, and the accuracy of this two type of schemes is compared in detail. The results show that both kinds of schemes can describe the flow field and capture the shock waves and contact discontinuities accurately. Due to the artificial viscosity, the accuracy at the discontinuities decreases in the staggered schemes, both the form and the parameters of the artificial viscosity term have much effect on the results. On the other hand, the cell-centered schemes can keep consistent accuracy at the discontinuities, but suitable reconstruction method and approximate Riemann solver need to be chosen for different problems.

Key words: Lagrangian algorithm, staggered schemes, cell-centered schemes