一维拉氏计算中交错格式与单元中心格式的数值研究

Comparison of Staggered and Cell-centered Lagrangian Schemes for One-dimensional Compressible Flow

在拉氏计算中,根据流体速度未知量离散在网格位置的不同将计算格式分为交错格式和单元中心格式两大类.这两类格式各自在计算中取得显著的成果,但少有人关注这两种格式的对比.本文通过大量一维算例进行数值试验,系统研究了这两种格式的特点,并详细比较了两种格式的计算精度.结果表明:两种格式总体上均能较精确地刻画流场并捕捉激波和接触间断.交错格式由于引入了人工粘性导致在间断处的精度降低,且人工粘性的形式,参数会较大影响其计算结果;而单元中心格式能在间断处能保持一致精度,但其在计算中需要根据不同问题选择合适的数据重构方法和Riemann问题合适的近似解法.

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.