求解Euler方程的高精度熵相容格式  

High Accuracy Entropy-consistent Schemes for Euler Equations

作　　者：龚承启 封建湖[1] 程晓晗[1] 郑素佩[1] GONG Cheng-qi, FENG Jian-hu, CHENG Xiao-han, ZHENG Su-pei(School of Sciences, Chang＇an University, Xi＇an 710064, Chin)

机构地区：[1]长安大学理学院

出　　处：《数学的实践与认识》2018年第6期211-221,共11页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11171043,11601037,11401045)

摘　　要：熵相容格式相比于一般的熵稳定格式进一步控制了激波处的熵增量，一维情况下能有效消除膨胀激波及间断处的伪振荡等现象．对于Euler方程，可以通过对特征变量进行WENO重构以获得高阶熵相容格式的数值粘性项，然后与高阶熵守恒格式结合得到高精度熵相容格式．在WENO重构过程中的权重关于特征变量是非线性的，这导致了大量的向量内积运算．通过用压强和熵代替特征变量来计算权重，可以显著减少重构的计算量，并且数值算例表明这种权重的计算方式能很好地保持数值格式的高阶精度和基本无振荡的效果．Entropy-Consistent schemes control entropy production more exactly than general entropy-stable schemes. It can eliminate rarefaction shock and spurious oscillations effectively in one-dimension case. For Euler Equations, high order entropy-consistent numerical viscosity can be obtained by reconstructing the characteristic variables, and such numerical viscosity can be added to high order entropy-conservative schemes to get high accuracy entropy-consistent schemes. In WENO reconstruction, the weights are nonlinear about characteristic variables, so it leads to too many inner product operations between vectors. The characteristic variables used in the weights computations can be replaced by pressure and entropy so that many inner product operations can be reduced. Numerical results have shown that the new method can retain the high accuracy and essential non- oscillations properties very well.

关 键 词：EULER方程 熵相容格式 WENO 高精度 

分 类 号：O241.8[理学—计算数学]