This study on overset meshes for incompressible-flow simulations is motivated by accurate prediction of wind farm aerodynamics involving large motions and deformations of components with complex geometry. Using first-order hyperbolic and elliptic equation proxies for the incompressible Navier-Stokes (NS) equations, we investigate the influence of information exchange between overset meshes on numerical performance where the underlying discretization is second-order accurate. The first aspect of information exchange surrounds interpolation of solution where we examine Lagrange and point-cloud-based interpolation for creating constraint equations between overset meshes. To maintain overall second-order accuracy, higher-order interpolation is required for elliptic problems, but linear interpolation is sufficient for hyperbolic problems in first-order form. Higher-order point-cloud-based interpolation provides a pathway to maintaining accuracy in unstructured meshes, but at higher complexity. The second aspect of information exchange focuses on comparing the approaches of overset single system (OSS) and overset Additive Schwarz (OAS) for coupling the linear systems of the overlapping meshes. While the former involves a single linear system, in the latter the discrete linear systems are solved separately, and solving the global system is accomplished through outer iterations and sequential information exchange in a Jacobi fashion. For the test cases studied, accuracy for hyperbolic problems is maintained by performing two outer iterations, whereas many outer iterations are required for elliptic systems. The order-of-accuracy studies explored here are critical for verifying the overset-mesh coupling algorithms used in engineering simulations. Accuracy of these simulations themselves is, however, quantified using engineering quantities of interest such as drag, power, etc. Consequently, we conclude with numerical experiments using NS equations for incompressible flows where we show that linear interpolation and few outer iterations are sufficient for achieving asymptotic convergence of engineering quantities of interest.

这项针对不可压缩流模拟的过剩网格的研究是基于对风电场空气动力学的准确预测，其中涉及大运动和复杂几何形状的部件的变形。使用不可压缩的Navier-Stokes（NS）方程的一阶双曲和椭圆方程代理，我们研究了基数离散化为二阶精确的情况下，过剩网格之间的信息交换对数值性能的影响。信息交换的第一个方面是解决方案的插值，其中我们检查了拉格朗日插值法和基于点云的插值法，用于在过盈网格之间创建约束方程。为了维持整体的二阶精度，椭圆问题需要高阶插值，但是线性插值对于一阶形式的双曲问题就足够了。基于高阶点云的插值为维护非结构化网格中的精度提供了一条途径，但复杂度更高。信息交换的第二个方面着重于比较用于耦合重叠网格的线性系统的过高单一系统（OSS）和过高加性施瓦茨（OAS）的方法。前者涉及单个线性系统，而后者涉及离散线性系统，分别解决，而全局系统的求解则通过外部迭代和Jacobi方式的顺序信息交换来完成。对于所研究的测试用例，通过执行两次外部迭代来保持双曲型问题的准确性，而椭圆系统需要进行多次外部迭代。此处探索的精确度顺序研究对于验证工程仿真中使用的过啮合耦合算法至关重要。然而，这些仿真本身的精度是使用感兴趣的工程量（例如阻力，功率等）进行量化的。因此，我们使用不可压缩流的NS方程进行数值实验得出结论，其中表明线性插值和很少的外部迭代足以实现感兴趣的工程量的渐近收敛。