Adaptive anisotropic unstructured mesh generation method based on fluid relaxation analogy

In this paper, we extend the method (Fu et al., [1]) to anisotropic meshes by introducing an adaptive SPH (ASPH) concept with ellipsoidal kernels. First, anisotropic target feature-size and density functions, taking into account the effects of singularities, are defined based on the level-set methodology. Second, ASPH is developed such that the particle distribution relaxes towards the target functions. In order to prevent SPH particles from escaping the mesh generation regions, a ghost surface particle method is proposed in combination with a tailored interaction strategy. Necessary adaptations of supporting numerical algorithms, such as fast neighbor search, for enforcing mesh anisotropy are addressed. Finally, unstructured meshes are generated by an anisotropic Delaunay triangulation conforming to the Riemannian metrics for the resulting particle configuration. The performance of the proposed method is demonstrated by a set of benchmark cases.