Hyperbolic cell-centered finite volume method for steady incompressible Navier-Stokes equations on unstructured grids

Abstract

A hyperbolic method for incompressible Navier-Stokes equations is presented in a cell-centered finite volume framework on unstructured meshes. Solution algorithms were introduced on triangular meshes in 2D and on tetrahedral meshes in 3D. Justification of the absolute Jacobian approximation is discussed, and a solution reconstruction algorithm utilizing the robust and effective wrapping stencil is illustrated. The effectiveness of the unconditionally stable implicit solution strategy was demonstrated by comparison to an explicit scheme. A series of test cases are presented in order of study accuracy and as a comparison with other reference computational and experimental results, namely Kovasznay flow, driven cavity flow, and flow past a circular cylinder in 2D and a sphere in 3D. The equal order of accuracy feature of the hyperbolic method, namely the second order accuracy in solution and the gradient variables, was verified. The superior accuracy of the current hyperbolic scheme in terms of predicting the velocity gradient on a solid surface was emphasized by comparison with standard second order finite volume results.