Time-accurate unstructured grid algorithms for the compressible Navier-Stokes equations

Unstructured grid algorithms for the solution of the finite volume form of the unsteady compressible Navier-Stokes equations have been developed. The algorithms employ triangular cells in two-dimensions and tetrahedral cells in three-dimensions. Cell-averaged values are stored at the centroid of each cell, in a cell-centered storage scheme. Inviscid flux computations are performed by applying a Riemann solver across each face, the values at the points on the faces being obtained by function reconstruction from the cell-averaged values. The viscous fluxes and heat transfer are obtained by application of Gauss' theorem.;The first unstructured grid algorithm is a two-dimensional implicit algorithm for laminar flows. Tests using flow into a supersonic compression comer showed that preconditioning in the iterative linear solver dramatically reduced the CPU time. Computations were then performed for a NACA0012 airfoil pitching about the quarter-chord at a freestream Mach number Minfinity=0.2 and Reynolds numbers Rec=104 and 2 x 104 at a dimensionless pitching rate W+o=0.2 . The results for Rec=104 are in excellent agreement with previous computations using an explicit unstructured Navier-Stokes algorithm. New results for Rec=2x104 indicate that the principal effect of increasing Reynolds number is to reduce the angle at which the primary recirculation region appears, and to cause it to form closer to the leading edge. This trend, confirmed by a grid refinement study, is consistent with previous results obtained at Minfinity=0.5 .;The second unstructured grid algorithm is a three-dimensional explicit algorithm for turbulent flows. Function reconstruction via a least squares method capable of second- or third-order accuracy was implemented. Tests on the nonlinear propagation of an acoustic wave showed improved accuracy using third-order schemes but a substantial CPU-time cost. However, the second-order least squares is more accurate than the previous second-order scheme. The second-order least squares algorithm was used for Large Eddy Simulations of the decay of isotropic turbulence and of low Mach number plane channel (Poiseuille) flow. These Large Eddy Simulations used the numerical dissipation and the constant-coefficient Smagorinsky model as the sub-grid scale models respectively. Agreement with experimental data and direct numerical simulations is good.