A numerical wave tank equipped with a piston type wave-maker is presented for long-duration simulations of long waves in shallow water. Both wave maker and tank are modelled using the nonlinear shallow water equations, with motions of the numerical piston paddle accomplished via a linear mapping technique. Three approaches are used to increase computational efficiency and accuracy. First, the model satisfies the exact conservation property (C-property), a stepping stone towards properly balancing each term in the governing equation. Second, a high-order weighted essentially non-oscillatory (WENO) method is used to reduce accumulation of truncation error. Third, a cut-off algorithm is implemented to handle contaminated digits arising from round-off error. If not treated, such errors could prevent a numerical scheme from satisfying the exact C-property in long-duration simulations. Extensive numerical tests are performed to examine the well-balanced property, high order accuracy, and shock-capturing ability of the present scheme. Correct implementation of the wave paddle generator is verified by comparing numerical predictions against analytical solutions of sinusoidal, solitary, and cnoidal waves. In all cases, the model gives satisfactory results for small-amplitude, low frequency waves. Error analysis is used to investigate model limitations and derive a user criterion for long wave generation by the model.

提出了一种配备有活塞式造波器的数值波箱，用于在浅水中对长波进行长时间模拟。造波器和油箱都使用非线性浅水方程建模，数字活塞桨的运动通过线性映射技术完成。使用三种方法来提高计算效率和准确性。首先，该模型满足精确的守恒性质（C属性），这是正确平衡控制方程中每个项的垫脚石。其次，使用高阶加权基本非振荡（WENO）方法来减少截断误差的累积。第三，采用截断算法来处理舍入误差引起的污染数字。如果不治疗，这样的误差可能会阻止数值方案满足长时间模拟中的精确C属性。进行了广泛的数值测试，以检验本方案的平衡性能，高阶精度和捕捉震动的能力。通过将数值预测与正弦波，孤波和正弦波的解析解进行比较，验证了波桨发生器的正确实现。在所有情况下，该模型对于小振幅，低频波都能给出令人满意的结果。误差分析用于调查模型的局限性，并为模型推导长波产生的用户准则。通过将数值预测与正弦波，孤波和正弦波的解析解进行比较，验证了波桨发生器的正确实现。在所有情况下，该模型对于小振幅，低频波都能给出令人满意的结果。误差分析用于调查模型的局限性，并为模型推导长波产生的用户准则。通过将数值预测与正弦波，孤波和正弦波的解析解进行比较，可以验证波桨发生器的正确实现。在所有情况下，该模型对于小振幅，低频波都能给出令人满意的结果。误差分析用于调查模型的局限性，并为模型生成长波生成用户准则。