有限深两层流体内孤立波非线性数值模拟入口边界条件研究

Investigation on the inlet boundary conditions for the nonlinear numerical simulations of internal solitary waves in a two-layer fluid of finite depth

基于有限深两层流体KdV(Korteweg-de Vries)、eKdV(extended KdV)和MCC(Miyata-Choi-Camassa)理论,以内孤立波诱导上下层深度平均水平速度为入口边界条件,采用理想流体完全非线性欧拉方程,建立了两层流体中内孤立波生成的CFD(Computational Fluid Dynamics)数值模拟方法。以系列数值模拟结果为依据,结合内孤立波非线性和色散参数的组合条件,给出了选择合适内孤立波理论解作为CFD数值模拟入口边界条件的方法,从而实现了振幅与波形可控的内孤立波完全非线性数值模拟。

Based on KdV（ Korteweg-de Vries）, eKdV（extended KdV） and MCC（Miyata-Choi-Camassa） theories in a two-layer fluid of finite depth, a CFD （ computational fluid dynamics） numerical method based on the fully nonlinear Euler equation in an ideal fluid is presented to simulate the generation and propagation of the internal solitary wave in a two-layer fluid, where the velocity-inlet boundary is applied by use of the depth-averaged velocities in the upper-and lower-layer fluids induced by the internal solitary wave. On basis of a series of numerical experiments, a method based on the combination conditions for the nonlinear and dispersion parameters is presented to choose the appropriate internal solitary theory which is applied to the velocity-inlet boundary condition of the CFD numerical simulation. Results show that the presented method can accomplish the fully nonlinear numerical simulation for the internal solitary wave under the condition of giving its amplitude and wave form.