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本文应用具有四阶频散特征的新型Boussinesq方程,采用空间差分为交错Shuman格式,时间层为ADI的有限差分格式,对非线性Stem波进行了数值模拟研究.其结果表明,这种组合式差分格式能有效地模拟非线性Stem波的演变规律.同时由计算结果也发现当人射波系的角大于某临界值时,Stem波动场向Genus-2波系转化并呈现出较稳定的六角形波型双周期结构.在入射波系的人射用小于某一临界值时,沿墙发展的Stem波呈现着半波周期型地稳定发展和推进,形成了较为典型的Mach茎效应.
In this paper, a new type of Boussinesq equation with fourth-order dispersion characteristics is applied, and the nonlinear differential equation is used to study the nonlinear Stem wave by using the finite difference scheme in which the spatial difference is the staggered Shuman scheme and the time horizon is ADI. The results show that this combined differential Format can effectively simulate the evolution of nonlinear Stem waves.At the same time, the results also show that when the angle of the human input is greater than a critical value, the Stem wave field transforms into the Genus-2 wave system and presents a stable hexagonal Wave-type bi-periodic structure. When the incidence of the incident wave is less than a certain threshold, the development of Stem wave along the wall showed a half-wave periodic stable development and advance, forming a typical Mach stem effect.