Minimization of undesired wave reflections at the boundaries of the computational domain in flow simulations with free surface based on the Navier-Stokes equations

精确模拟自由表面波的传播以及相应的流体-结构-流体相互作用是计算流体力学中的重要课题，特别是在海洋工业和研究方面。应用基于Ranse的模拟技术的主要困难是最小化计算域边界上的不需要的波反射，因为这种反射可能导致模拟结果中的相当大的不确定性。通过在区域边界附近的区域内的控制方程中引入源项，可以抑制出射波。另一种减少波浪反射的方法是将Ranse解算器与第二个流动解算器耦合。在这种情况下，可以将Ranse解混合到另一个流动解算器的解中。在目前的知识状态下，选择最佳源项是一个仍然没有得到充分研究的问题。因此，本研究项目的主要目的是开发自适应方法，以最大限度地减少不需要的波反射。在这种情况下，源项将相对于入射波进行调整，以便在模拟期间始终将其设置为最佳值。所开发的方法将最大限度地减少不需要的波反射，并能够在开始模拟之前预测相应的不确定性。在对二维和三维简化算例进行充分验证的基础上，将所提出的方法应用于典型的三维海流模拟问题。

The ability to accurately simulate the propagation of free surface waves and the corresponding fluid-structure-interactions are important topics in computational fluid mechanics, especially in regards to maritime industry and research. The main difficulty in applying RANSE-based simulation techniques is minimizing undesired wave reflections at the boundaries of the computational domain, since such reflections can lead to considerable uncertainties in the simulation results. By introducing source terms into the governing equations within a zone in the vicinity of the domain boundary, outgoing waves can be damped. Another way to reduce wave reflections is to couple the RANSE solver with a second flow solver. In this case, the RANSE solution can be blended to the solution of the other flow solver. Within the current state of knowledge, selecting the optimum source terms is a problem which remains insufficiently investigated. Hence, the main aim of this research project is to develop adaptive approaches for minimizing undesired wave reflections. In this case, the source terms will be adjusted with respect to incoming waves so that they are set to their optimum values at all times during the simulation. The developed approaches will minimize undesired wave reflections and enable prediction of the corresponding uncertainties before starting the simulation. After sufficient validation for 2D and 3D simplified cases, the applicability of the developed methods will be demonstrated for typical three-dimensional maritime flow simulation problems.