双曲守恒律标量方程的高分辨率激波追踪方法  

A HIGH RESOLUTION ALGORITHM FOR TRACKING SHOCK IN HYPERBOLIC CONSERVATION LAWS FOR SCALAR EQUATION

作　　者：封建湖[1] 蔡力[2] 谢文贤[3] 王振海[3] 佘红伟[3] 

机构地区：[1]长安大学理学院,西安710064 [2]西北工业大学航天学院,西安710072 [3]西北工业大学理学院,西安710072

出　　处：《数值计算与计算机应用》2005年第2期153-160,共8页Journal on Numerical Methods and Computer Applications

摘　　要：本文将四阶CWENO(中心加权基本无振荡)格式、LevelSet方法以及四阶NCE—RK(自然连续外推的Runge—Kutta)方法结合起来,追踪了一维双曲守恒律方程的激波解.利用NSFD(非标准有限差分)格式来扩展CWENO重构的范围同时提高格式的精度.上述方法也能成功追踪二维双曲守恒律方程的激波解.还将本方法与标准的激波捕捉方法相比较,由此可知基于LevelSet方法的格式的有效性和逐点收敛性.To track shock waves effectively in hyperbolic conservation law in one-dimension cases, the fourth-order accurate CWENO (Central Weighted Essentially Non-Oscillatory) scheme is applied with the Level Set algorithm and the fourth-order accurate NCE-RK (Natural Continuous Extensions of Runge-Kutta) method. To magnify the range of CWENO reconstructions and improve the accuracy of the scheme, the NSFD (Nonstandard Finite Differences) scheme is used. Using the same methods, two-dimension cases are solved successfully. The solutions are compared with standard high order shock capturing schemes. It is clear that Level Set based schemes are very effective and have high order pointwise convergence quality.

关 键 词：追踪 高分辨率 双曲守恒律方程 Level SET方法 标量 中心加权 捕捉方法 有限差分 激波解 格式 无振荡 非标准 收敛性 四阶 外推 一维 

分 类 号：O354.5[理学—流体力学]