Accuracy and Conservation Properties of a Three-Dimensional Unstructured Staggered Mesh Scheme for Fluid Dynamics

A three-dimensional unstructured mesh discretization of the rotational from of the incompressible Navier–Stokes is presented. The method uses novel and highly efficient algorithms for interpolating the velocity vector and constructing the convention term. The resulting discretization is shown to conserve mass, kinetic energy, and vorticity to machine precision both locally and globally. The spatial accuracy of the method is analyzed and found to be second order on regular meshes and first order on irregular meshes. The numerical efficiency, accuracy, and conservation properties of the method are tested on three-dimensional meshes and found to be in agreement with theory.