Anisotropic mesh adaptation for evolving triangulated surfaces

Dynamic surfaces arise in many applications, such as free surfaces in multiphase flows and moving interfaces in fluid-solid interaction. In many engineering applications, an explicit surface triangulation is often used to represent dynamic surfaces, posing significant challenges in adapting their meshes, especially if large curvatures and sharp features may dynamically emerge or vanish as the surfaces evolve. In this paper, we present an anisotropic mesh adaptation technique to meet these challenges. Our technique strives for optimal aspect ratios of the triangulation to reduce positional errors and to capture geometric features of dynamic surfaces based on a novel extension of the quadrics. Our adaptation algorithm combines the operations of vertex redistribution, edge flipping, edge contraction, and edge splitting. Experimental results demonstrate the effectiveness of our anisotropic adaptation technique for static and dynamic surfaces.