A finite-volume lambda formulation for solving Euler equations and able to handle compressible as well as transonic flow computations is presented. The easy extension of the methodology to the solution of Navier-Stokes equations is indicated. The integration scheme is in nonconservative form in smooth flow regions in order to take advantage of its superior accuracy and computational efficiency. It automatically switches to conservative form in shock regions, in order to capture them correctly. Computations of two-and three-dimensional shockless source flows prove the superior accuracy and computational efficiency of the proposed technique in comparison with a classical conservative upwind methodology. Moreover, computed results referring to some two-and three-dimensional test cases are compared with numerical or experimental published ones, thus showing the capabilities of the proposed formulation to deal with inviscid subsonic as well as transonic flow cases.

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The viscous finite volume lambda formulation is presented. The suggested technique is apt to compute viscous flows with heat fluxes. The inviscid terms are evaluated by means of the non‐conservative, very accurate upwind methodology, known as the finite volume lambda formulation. The diffusive terms, on the contrary, are approximated by a central scheme. Both methods are characterized by a nominal second order accuracy in space. Efficiency is enhanced by means of a multigrid technique which directly combines each grid level with each stage of an explicit multistage time integration technique. A laminar viscous flow about a NACA 0012 airfoil and a turbulent one about a RAE 2822 airfoil have been computed as well as the two‐ and three‐dimensional turbulent flows inside the Stanitz elbow. The computed numerical results are in very good agreement with well assessed published numerical or experimental results. The suggested multigrid technique allows significant work reductions for laminar as well as for turbulent flow computations.