无自由参数型混合格式

针对紧致-加权本质无振荡混合格式中子格式的权重,设计了新的算子.该算子利用模板的光滑因子求解权重,避免引入自由参数,提高了格式的易用性和鲁棒性.利用新的权重算子,分别将两种五阶迎风紧致格式与WENO-Z(Weighted Essentially Non-Oscillatory Scheme)耦合.新权重算子使子格式之间的切换较为光滑.WENO-Z能够保持格式在极点附近的精度,紧致格式在光滑区域耗散低,混合格式因此能够保持高分辨率、高精度特性以及对间断的捕捉能力.数值试验针对若干双曲型方程算例展开,比较了两种混合格式在采用新权重算子与采用其他典型算子时的数值特性.结果表明无自由参数型权重算子性能良好. 

Hybrid finite difference schemes without free parameters

A new algorithm was proposed to calculate the weights of sub-schemes in hybrid compact-WENO (weighted essentially non-oscillatory) schemes. It used smoothness indicators of the stencils of hybrid schemes as variables to work globally. The new weight algorithm employed none freely user-defined parameter, making the hybrid schemes more robust and applicable. Two different 5th order upwind compact schemes were coupled with a 5th order WENO-Z scheme respectively. The new algorithm maked the transition between two sub-schemes more smoothly. Generally, WENO-Z could preserve the accuracy at critical points while compact schemes were less dissipative in smooth area. Thus, these hybrid schemes with new algorithm maintained high resolution and high order of accuracy qualities and shock-capturing abilities. Numerical tests were taken upon benchmarks of hyperbolic equations to test performances of these two hybrid schemes between the new weight algorithm and a typical one. Numerical results demonstrate that the new parameter-free weight algorithm performs well.