摘要
大时间步长格式(LTS)作为一种高效的计算格式,在将其应用于求解双曲型偏微分方程时,能显著提高其计算效率。从其被提出至今已有40多a,仍然是研究的热点。从线性标量方程出发,引出了LTS的基本思想和方法,通过单波在一个时间步长内穿过多个单元,突破了CFL定理的限制。在将其扩展到非线性双曲守恒律时,出现了非线性波叠加、稀疏波断裂、振荡等一系列问题。这些问题有的通过巧妙的方法得到了解决,有的仍然悬而未决,这也是LTS将来研究的方向。
Large Time Step (LTS) is high efficiency scheme which can speed the computation when it is applied to hyperbolic equations. It isstill a hotspot even over four decades passed since it was proposed. The basic methods were introduced from linear hyperbolic equation in thisarticle. In LTS, simple wave could pass through more than one element which broke through the limitation of CFL theorem. When it was ex⁃panded to non⁃linear hyperbolic system, there were several problems including the non⁃linear property, discontinuity of rarefaction and oscil⁃lation. Some of them had been resolved while others were still unresolved which was the direction of development of LTS.
作者
许仁义
赵磊
王远见
徐波
XU Renyi;ZHAO Lei;WANG Yuanjian;XU Bo(College of Hydraulic Science and Engineering,Yangzhou University,Yangzhou 225009,China;Yellow River Institute of Hydraulic Research,Zhengzhou 450003,China)
出处
《人民黄河》
CAS
北大核心
2023年第1期41-46,共6页
Yellow River
基金
国家自然科学基金资助项目(51509216,52079120)。
关键词
浅水方程
数值模拟
大时间步长格式
底坡源项-
shallow water equations
numerical simulation
large time step scheme
bed slope source term
