This paper presents the formulation of an implicit upwind finite volume method, reconstructed using a few very recent advance in the Euler and Navier-Stokes flows. It solves two-dimensional compressible inviscid and viscous flow on unstructured triangular grid. The inviscid fluxes are computed using an upwind algorithm based on Roe's flux difference splitting while the viscous flux terms are treated by central implicit differencing. The numerical solution is advanced in time using a backward-Euler implicit time-stepping scheme with convergence accelerated to the steady state by local time stepping. At each time step, the linear system of equations is approximately solved with the GMRES(Generalized Minimum RESidual) algorithm. The initial grid generation is used for Delaunay triangulation based on the Bowyer's algorithm.
Calculated results are compared with the existing experimental data and other numerical solutions. Five test problems are computed for the validation of this algorithm. For inviscid flow problem, supersonic flow over 4% arc bump, transonic flow around a NACA 0012 airfoil with 1.25 degree angle of attack and transonic flow around two-element airfoils are included. In addition, for viscous flow calculation, the laminar Navier-Stokes flow around a NACA 0012 airfoil and the same flow around two-element airfoils at various Reynolds numbers are included.
