守恒律方程组的大时间步长叠波格式  

Large Time Step Wave Adding Scheme for Hyperbolic Conservation Laws

作　　者：董海涛[1] 刘福军 DONG Hai-tao;LIU Fu-jun(National Laboratory of Computational Fluid Dynamics, School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China;School of Mathematical Sciences, Beihang University, Beijing 100191, China)

机构地区：[1]北京航空航天大学航空科学与工程学院,国家计算流体力学实验室,北京100191 [2]北京航空航天大学数学与系统科学学院,北京100191

出　　处：《气体物理》2020年第3期30-58,共29页Physics of Gases

摘　　要：大时间步长叠波格式最初思想为LeVeque提出的大时间步长Godunov格式,通过叠加间断分解发出的强波来构造数值格式.原方法只给出了间断强波的穿越叠加方法,文章对其进行了完善,并推广到多维.针对膨胀波提出了一种网格单元分解法可以自动满足熵条件,避免出现非物理解.给出了格式的具体计算公式,并用单个守恒律方程、一维/多维Euler方程组进行了数值计算.计算结果表明,新格式除了可以采用大时间步长的优点外,在一定范围内随CFL数增加其耗散反而更低,因而对激波接触间断膨胀波的分辨率更高.A large time step wave adding scheme originated from LeVeque′s large time step Godunov scheme was presented,i.e.constructing numerical schemes via adding strong waves of discontinuity decomposition.Compared with the original scheme,a different strategy for wave adding was presented and extended to multi-dimensional cases.For rarefaction waves,a grid cell decomposition method which can automatically satisfy the entropy condition and avoid nonphysical solutions was proposed.The detailed formulae of the scheme were given,and numerical experiments using scalar equations and Euler equations in one and multi-dimensional cases were carried out.Numerical results show that,besides the advantage of large time step,the new scheme has a lower numerical dissipation and a higher resolution of shocks and contact discontinuities with the increase of CFL number in a certain range.

关 键 词：叠波法 大时间步长 双曲型守恒律 EULER方程 RIEMANN问题 

分 类 号：V242[航空宇航科学与技术—飞行器设计] O35[理学—流体力学]