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Variational finite element methods for waves in a Hele-Shaw tank

机译：Hele-Shaw储罐中波浪的变分有限元方法

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The damped motion of driven water waves in a Hele-Shaw tank is investigated varia-tionally and numerically. The equations governing the hydrodynamics of the problem are derived from a variational principle for shallow water. The variational principle includes the effects of surface tension, linear momentum damping due to the proximity of the tank walls and incoming volume flux through one of the boundaries representing the generation of waves by a wave pump. The model equations are solved numerically using (dis)continuous Gaierkin finite element methods and are compared to exact linear wave sloshing and driven wave sloshing results. Numerical solutions of the nonlinear shallow water-wave equations are also validated against laboratory experiments of artificially driven waves in the Hele-Shaw tank.
机译：对Hele-Shaw储罐中驱动水波的阻尼运动进行了变化和数值研究。从浅水的变分原理推导了控制问题流体动力学的方程式。变化原理包括表面张力，由于储罐壁的接近而引起的线性动量阻尼以及通过代表波浪泵的波浪产生的边界之一的进入体积通量的影响。使用（不连续）Gaierkin有限元方法对模型方程进行数值求解，并将其与精确的线性波动和驱动波动进行比较。非线性浅水波方程的数值解也通过在Hele-Shaw坦克中人工驱动波的实验室实验得到了验证。

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