中文摘要：

提出了Lagrange中心型守恒气体动力学格式.引入了当前时刻子网格密度与当前时刻网格声速产生的网格分片常数压力.初始网格密度乘以初始子网格体积得到子网格质量,这些子网格质量除以当前时刻子网格体积得到当前时刻子网格密度.应用网格分片常数压力,构造了满足动量守恒、总能量守恒的Lagrange中心型守恒气体动力学格式,格点速度以与网格面的数值通量相容的方式计算.对Saltzman活塞问题等进行了数值模拟,数值结果显示Lagrange中心型守恒气体动力学格式的有效性和精确性.

英文摘要：

A Lagrangian cell-centered conservative gas dynamics scheme was presented.It introduced the piecewise constant pressures of cell,which arose from the current time sub cell densities and the current time isentropic speed of sound of cell.The sub cell Lagrangian masses which the initial cell density multiplied by the initial sub cell volumes,divided by the current time sub cell volumes,the current time sub cell densities were obtained.Using the current time piecewise constant pressures of cell,the scheme which conserved momentum,total energy was constructed.The vertex velocities and the numerical fluxes through the cell interfaces were computed in a consistent manner due to an original solver located at the nodes.Many numerical tests were presented.They are representative test cases for compressible flows and demonstrate the robustness and the accuracy of Lagrangian cell-centered conservative scheme.