Finite volume scheme for the lattice Boltzmann method on curved surfaces in 3D

The fluid flows on the surface widely exist in the natural world, such as the atmospherical circulation on a planet. In this study, we present a finite volume lattice Boltzmann method (LBM) for simulating fluid flows on curved surfaces in three-dimensional (3D) space. The curved surfaces are discretized using unstructured triangular meshes. We choose the D3Q19 lattice and the triangular meshes for the velocity and spatial discretizations, respectively. In one time iteration, we only need to compute the distribution functions on each vertex in a fully explicit form. Therefore, our proposed method is highly efficient for solving fluid flows on curved surfaces using LBM. To keep the velocity field tangential to the surfaces, a practical velocity correction technique is adopted. We perform a series of computational experiments on various curved surfaces such as sphere, torus, and bunny to demonstrate the performance of the proposed method.