自由液面水流与固体构筑物作用的高精度数值模拟

采用界面保持水平集法捕捉自由液面，结合浸入边界法处理固液交界面的方式，开展自由液面水流经过固定障碍物的复杂流场模拟.在计算过程中，将障碍物对水流的影响用虚拟力的形式加入到流场求解中.求解水平集函数时，使用迎风紧致差分格式，以得到高精度的解.为了确保界面始终处于一个非常薄的厚度，在每个计算步长中对水平集函数进行重距离化处理，利用投影法求解Navier-Stokes方程中的压力项.通过将模型应用于计算带障碍物的典型溃坝问题，包括底床上的矩形和工程中常见的悬空支撑圆形障碍物，得到的数值结果与实验数据吻合较好，验证了该算法的准确性和稳定性.
Abstract: A sharp interface capturing method was presented to simulate free surface flow over a stationary obstacle. The efficient interface preserving level set method was used and immersed boundary method was interpolated to handle the air-water and solid-fluid interface. The artificial momentum forcing term was applied at computational nodes where the solid obstacle presented to solve the velocity field, accounting for the impact of the obstacle. The upwinding combined compact difference scheme was adapted to approximate spatial derivative terms in level set function in order to accurately predict the air-water interface. The re-initialization equation for distance function was used to ensure interface front with a very thin thickness. The pressure field of Navier-Stokes equations was effectively solved by the projection method. Two typical cases of the flow propagating over different obstacles, including rectangular and circular cross-sections, were simulated by the method. The numerical results accorded well with the experimental results. The method can accurately simulate the complicated free surface flow with good stability.