波浪与大孔隙多孔介质相互作用的耦合数学模型

Coupling numerical model of interaction between wave and porous medium with large porosity

建立了波浪与大孔隙多孔介质相互作用的耦合数学模型,波浪域的控制方程为雷诺时均方程和k-ε紊流模型。对于计算域的入射波采用推板式造波,它可以是线性波、椭圆余弦波和孤立波。采用PLIC-VOF法追踪波浪自由表面。对于多孔介质内的孔隙流场采用非线性Forchheimer方程,两区域共享连续方程,最后导出的波浪域与孔隙流域的压力修正方程具有完全相同的形式,利用这个方程能够同时而不是分别求解波浪场和孔隙流场,避免了在内部边界上给定匹配条件,实现了波浪场与孔隙流场的同步耦合。波浪与粗颗粒海床、平底床面上抛石潜堤及斜坡上抛石潜堤相互作用的验证计算结果表明该模型可用于研究波浪与大孔隙多孔介质相互作用的问题。

A coupling model of interaction of wave with porous medium with large porosity is established. The wave field solver is based on the two-dimensional Reynolds averaged Navier-Stokes （RANS） equations with a k-ε closure. A piston-type wave maker is set up in the computational domain to produce incident waves and the free surface is traced through the piecewise linear interface construction-volume of fluid. The incident waves can be the linear wave, the cnoidal waves and the solitary waves. Forchheimer equations are adopted in porous flow within the porous media. By introducing a velocity-pressure correction equation for the waves and the porous flow, highly efficient coupling between the two flows is realized. The two flows can be solved simultaneously and no boundary condition is needed on the interface between them. It was found that the proposed model is effective for studying interaction of wave with scree seabed and is able to handle the water waves and the submerged porous breakwater on flat and slope beds. The verified numerical model can be used to study the interaction between waves and porous medium with large porosity.