加权型紧致格式与加权本质无波动格式的比较

线性紧致格式和加权本质无波动格式是两种典型的高阶精度数值格式,它们各有优缺点.线性紧致格式在具有高阶精度的同时,格式的分辨率也比较高,耗散低,是计算多尺度流场结构的较好格式,但是不能计算具有强激波的流场.加权本质无波动格式是一种高阶精度捕捉激波格式,鲁棒性好,但耗散比较高,分辨率也不理想.近年来,在莱勒的线性紧致格式基础上,采用加权本质无波动格式捕捉激波思想,发展了一系列加权型紧致格式.本文较全面地比较了加权型紧致格式和加权本质无波动格式,包括构造方法、鲁棒性、分辨率、耗散特性、收敛特性以及并行计算效率.结果表明,现有的加权型紧致格式基本保持了加权本质无波动格式的性质,对于气动力等宏观量的计算,比加权本质无波动格式没有明显的优势. 

THE COMPARISON OF WEIGHTED COMPACT SCHEMES AND WENO SCHEME

Linear compact scheme and weighted essentially non-oscillatory(WENO) scheme are two typical high order numerical schemes.They have their own merits and drawbacks.Linear compact scheme has high order accuracy order, high resolution and low dissipation, which is a nice numerical scheme for multi-scale flow.However, it can not compute the flow with strong shock wave.WENO scheme is a robust high order shock capturing scheme.But the dissipation is high.The resolution for short wave is not ideal.In recent years, a series of weighted compact schemes were developed by the combination of linear compact scheme and WENO scheme.In this paper, we systematically compare the properties of weighted compact schemes and WENO scheme including the construction, the capability to capture strong shock wave, the resolution, the convergence and paralleling efficiency.Our study shows that weighted compact schemes have no obvious superiority in the computation of aerodynamics to WENO scheme.