紧致差分格式的分辨率与精度的实例比较与讨论

通过比较先前建立的4阶最优紧致差分格式,以及传统的6阶和8阶紧致差分格式,来研究精度和分辨率之间的关系,主要比较了空间离散格式的有效波数范围、实际数值计算精度、以及对小尺度波动的模拟能力.数值试验结果表明:(1)这3种格式的计算精度都可以达到理论精度,并且此时精度越高,误差越小;(2)对于小尺度波动,最优4阶紧致格式比6阶和8阶紧致格式具有更高的分辨率;(3)对于行波问题,最优4阶紧致格式能够更加准确地模拟波动的传播行为.理论分析和数值算例的比较结果均表明,数值格式的精度和分辨率并不能互相替代,而是要根据计算问题的需要选择具有合适的精度和分辨率的数值格式.

Comparison and Discussion on the Resolution and Accuracy of Compact Difference Schemes Based on Cases Study

Three compact finite difference schemes,which are the optimal fourth order compact scheme(OCS4) were developed by us recently,the classical sixth and eighth order compact schemes are employed to elucidate the concepts of accuracy and resolution of a numerical scheme.Our theoretical and numerical results show that:(1) the order of numerical accuracy of these schemes can reach their theoretical accuracy order.The errors of these schemes decrease with increasing order of accuracy;(2) the fourth order optimal compact finite difference scheme has highest resolution among the three schemes;(3) for the wave propagation problem,the advantages of OCS4 is more obviously in resolving the propagation of a wave packet.Our theoretical analysis and numerical examples also indicate that the accuracy and resolution of a numerical scheme can't be replaced with each other.Thus,we suggest that the accuracy and resolution should be considered separately for choosing a suitable numerical scheme in actual applications.