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Accuracy and conservation properties of a three-dimensional unstructured staggered mesh scheme for fluid dynamics. (English) Zbl 1018.76036
Summary: We present a three-dimensional unstructured mesh discretization of the rotational form of incompressible Navier-Stokes equations. The method uses novel and highly efficient algorithms for interpolating velocity vector and constructing the convection 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 are found to be in agreement with the theory.

MSC:
76M99 Basic methods in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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