一种非静压的平面二维水动力学模型

Plane two-dimensional hydrodynamic model with non-hydrostatic pressure

将N-S方程中的压力分解为静压和动压并将水平动量方程沿水深积分,垂向动量方程则只考虑动压梯度项.求解过程分解为静压步和非静压步,采用有限差分法离散水平动量方程,基于Keller-box格式离散垂向动量方程,得到关于动压的泊松方程并采用稳定双共轭梯度法求解,最后根据动压更新流速和水位,建立了一种非静压的平面二维水动力学模型.利用孤波和规则波的算例验证了模型的有效性.

To improve the hydrodynamic model, the pressure terms in the Navier-Stokes （N-S） equa- tions were separated into hydrostatic and dynamic components. The horizontal momentum equations were integrated from bottom to free surface. The vertical momentum equation only retained the dy- namic pressure gradient term. The solution process was divided into hydrostatic and non-hydrostatic step. The horizontal equations were discretized with finite difference method and the vertical one was approximated using the Keller-box scheme. The Poisson-type equations of dynamic pressure were solved by Bi-CGSTAB method. Using the calculated dynamic pressure, the velocity and water surface elevation were updated finally. The solitary wave and regular waves were used to validate the model. And the results show their good agreements.