Adapted unstructured LBM for flow simulation on curved surfaces

Flow motion on curved surfaces of arbitrary topology is an interesting visual effect but a complex dynamics to simulate. In this paper, we introduce a novel and effective way to model such dynamics. We propose a technique that adapts a recently emerged computational fluid dynamics (CFD) model, unstructured lattice Boltzmann model (Unstructured LBM), from the 2D unstructured meshes to the 3D surface meshes. Unlike previous methods in modeling flows on surfaces, which start from the macroscopic point of view and modify the Navier Stokes solvers for the curved surfaces, our method is based on the microscopic kinetic equations for discrete particle distribution functions. All computations on the surface mesh only involve the information within local neighborhoods. This model lends itself the following advantages: (i) simplicity and explicit parallelism in computation, (ii) great capability in handling complex interactions, such as the interactions between flow and boundaries and the interactions of multiple-component fluids; (iii) no need of global surface parameterization which may cause strong distortions; (iv) capability of being applied to meshes with arbitrary connectivity.