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中文摘要：
利用黎曼精确解和行波法相结合,在一维浅水方程中实现大时间步长（Large Time Step,LTS）格式,并采用多波近似解决稀疏波断裂的问题,采用随机选取法（Random Choice Method,RCM）解决非线性方程使用LTS格式出现的震荡问题.一系列数值试验发现,通过多波近似和随机选取法对大时间步长格式的改进,提高了计算效率,减小了震荡,取得了很好的计算效果.
英文摘要：
Exact Riemann solver and wave propagation method are combined to achieve large time-step scheme （LTS） in shallow water flow. Multi-wave approximation is adapted to solve discontinuity of rarefaction, and a random choice method （RCM） is used to eliminate oscillation in nonlinear hyperbolic systems. Efficiency is increased in LTS scheme with multi-wave approximation and random choice method as large Courant-Fridrichs-Lewy （CFL） number is imposed.
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