A FULLY-IMPLICIT 2-D NAVIER-STOKES ALGORITHM FOR UNSTRUCTURED GRIDS

A fully-implicit algorithm is developed for the two-dimensional, compr essible, Favre-averaged Navier Stokes equations. It incorporates the s tandard k-epsilon turbulence model of Launder and Spalding and the low Reynolds number correction of Chien. The equations are solved using a n unstructured grid of triangles with the dow variables stored at the centroids of the cells. A generalization of wall functions including p ressure gradient effects is implemented to solve the near-wall region for turbulent flows using a separate algorithm and a hybrid grid. The inviscid fluxes are obtained from Roe's flux difference split method. Linear reconstruction of the flow variables to the cell faces provides second-order spatial accuracy. Turbulent and viscous stresses as well as heat transfer are obtained from a discrete representation of Gauss 's theorem. Interpolation of the flow variables to the nodes is achiev ed using a second-order accurate method. Temporal discretization emplo ys Euler, Trapezoidal or 3-Point Backward differencing. An incomplete LU factorization of the Jacobian matrix is implemented as a preconditi oning method. The accuracy of the code and the efficiency of the solut ion strategy are presented for three test cases: a supersonic turbulen t mixing layer, a supersonic laminar compression corner and a superson ic turbulent compression corner.