A novel dynamic adaptive unstructured mesh algorithm for simulating multi-object relative motion in incompressible fluid

A novel dynamic adaptive unstructured mesh (DAUM) algorithm is proposed to solve incompressible multi-object relative motion (MORM). The DAUM algorithm, consisting of exponential function deformation, adaptive edge swapping, and area Laplace smoothing, can greatly improve dynamic mesh robustness and perfectly overcome mesh skewness. The core of DAUM is the adaptive edge swapping inspired by Delaunay triangulation, which is distinguished from traditional edge swapping. The adaptive edge swapping can fully consider the relationship of neighbor elements only using Delaunay triangulation. Meanwhile, the implementation and reliability of adaptive edge swapping are better than the traditional edge swapping method due to eliminating the interference of the non-convex polygon, so more code remedies can be avoided. Using the DAUM, none of the vertices is inserted or deleted so that the manipulation of the dynamic mesh is easily implemented and maintains computational efficiency in the process of mesh motion. Three representative geometries are used to assess the performance of the DAUM in MORM. To systematically analyze the advantages of DAUM, two relatively moving cylinders have been numerically investigated in incompressible flow. The inline force and lift force profiles on two cylinders are obtained and analyzed by using the flow field information. Three interaction stages are divided based on the parameter G and the interactional intensity of two inner anticlockwise vortices is considered as the division criteria. At the running process of the DAUM algorithm, the dynamic mesh quality is well controlled and remains in the high-quality range based on the aspect ratio (AR) criterion. The results indicate that the proposed DAUM algorithm can properly solve the difficulties caused by MORM, especially for period oscillation motion.