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本文提出了一种近期发展起来的数值解法,即彼得罗夫—伽辽金法或耗散型伽辽金方法,并应用有限元法以模拟由纳维埃—斯托克斯(Navier-Stokes)方程控制的水动力学现象。为了说明该计算格式对改善数值解的质量和收敛性的有效性,选用了两个不同水域的水动力学振动问题的实例。其结果清楚地表明了由经典伽辽金格式产生的伪波动几乎完全消失,从而加快了收敛的速度。尽管该计算格式由有意识地引入了若干人工阻尼,其对解的精度的影响是可以忽略的。
In this paper, we present a recently developed numerical solution, Petrov-Galerkin method or dissipative Galerkin method, and apply the finite element method to simulate the Navier-Stokes Equations Controlled Hydrodynamics. In order to illustrate the validity of this computational format to improve the quality and convergence of numerical solutions, two examples of hydrodynamic vibration problems for different waters are chosen. The results clearly show that the pseudo-fluctuations generated by the classical Galerkin scheme disappear almost completely, which speeds up the convergence. Although the computational format was consciously introduced by a number of artificial damping, its impact on the accuracy of the solution is negligible.