A FULLY IMPLICIT NAVIER-STOKES ALGORITHM USING AN UNSTRUCTURED GRID AND FLUX-DIFFERENCE SPLITTING

An implicit algorithm is developed for the two-dimensional, compressib le, laminar Navier-Stokes equations using an unstructured grid of tria ngles. A cell-centered data structure is employed with the flow variab les stored at the centroids of the triangles. The algorithm is based o n Roe's flux difference split method for the inviscid fluxes, and a di screte representation of the viscous fluxes and heat transfer using Ga uss' Theorem. Linear reconstruction of the flow variables to the cell faces, employed for the inviscid terms, provides second-order spatial accuracy. Interpolation of the flow variables to the nodes is achieved using a second-order accurate method. Temporal discretization employs Euler, trapezoidal or 3-point backward differencing. The complete, ex act Jacobian of the inviscid and viscous terms is derived. The algorit hm is applied to the Riemann Shock Tube problem, a supersonic laminar boundary layer on a flat plate, and subsonic viscous flow past an NACA 0012 airfoil. Results are in excellent agreement with theory and previ ous computations.