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Unstructured High-Order Accurate Finite-Volume Solutions of the Navier-Stokes Equations

2009; Linguagem: Inglês

10.2514/6.2009-954

Chris Michalak, Carl Ollivier‐Gooch,

Advanced Numerical Methods in Computational Mathematics

A nite-volume scheme utilizing a fourth-order reconstruction for convective and di usive uxes of the Navier-Stokes equations is presented. The reconstruction is obtained e ciently by precomputing the pseudo-inverse of the reconstruction matrix. Viscous boundary conditions are handled by introducing additional rows in the reconstruction matrices. Rapid convergence of steady-state problems is made possible by computing the exact ux Jacobian and the use of a Newton-GMRES algorithm. A grid convergence study of cylindrical Couette ow is used to demonstrate the order of accuracy of the scheme. Laminar ow over an airfoil on a sequence of anisotropic grids is also used to qualitatively demonstrate the superior accuracy of the fourth-order scheme.