Yildiran Ibrahim Nasuh, Beratlis Nikolaos, Capuano Francesco, Loke Yue-Hin, Squires Kyle, Balaras Elias
Department of Mechanical and Aerospace Engineering, The George Washington University, 800 22nd Street NW, Washington DC, 20052, USA.
School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ, 85287, USA.
J Comput Phys. 2024 Aug 1;510. doi: 10.1016/j.jcp.2024.113057. Epub 2024 May 6.
Immersed boundary methods have seen an enormous increase in popularity over the past two decades, especially for problems involving complex moving/deforming boundaries. In most cases, the boundary conditions on the immersed body are enforced via forcing functions in the momentum equations, which in the case of fractional step methods may be problematic due to: i) creation of slip-errors resulting from the lack of explicitly enforcing boundary conditions on the (pseudo-)pressure on the immersed body; ii) coupling of the solution in the fluid and solid domains via the Poisson equation. Examples of fractional-step formulations that simultaneously enforce velocity and pressure boundary conditions have also been developed, but in most cases the standard Poisson equation is replaced by a more complex system which requires expensive iterative solvers. In this work we propose a new formulation to enforce appropriate boundary conditions on the pseudo-pressure as part of a fractional-step approach. The overall treatment is inspired by the ghost-fluid method typically utilized in two-phase flows. The main advantage of the algorithm is that a standard Poisson equation is solved, with all the modifications needed to enforce the boundary conditions being incorporated within the right-hand side. As a result, fast solvers based on trigonometric transformations can be utilized. We demonstrate the accuracy and robustness of the formulation for a series of problems with increasing complexity.
在过去二十年中，浸入边界方法的应用越来越广泛，尤其适用于涉及复杂移动/变形边界的问题。在大多数情况下，浸入物体上的边界条件是通过动量方程中的强迫函数来施加的，而在分数步方法中，这可能会产生问题，原因如下：i）由于在浸入物体上缺乏对（伪）压力的边界条件进行显式施加，从而产生滑移误差；ii）通过泊松方程在流体域和固体域中的解耦合。同时施加速度和压力边界条件的分数步公式的例子也已被开发出来，但在大多数情况下，标准泊松方程被一个更复杂的系统所取代，该系统需要昂贵的迭代求解器。在这项工作中，我们提出了一种新的公式，作为分数步方法的一部分，对伪压力施加适当的边界条件。整体处理方法受到通常用于两相流的虚拟流体方法的启发。该算法的主要优点是求解标准泊松方程，将施加边界条件所需的所有修改纳入右侧。因此，可以使用基于三角变换的快速求解器。我们针对一系列复杂度不断增加的问题，展示了该公式的准确性和鲁棒性。
