Products developed at industries, institutes and research centers are expected to have high level of quality and performance, having a minimum waste, which require efficient and robust tools to numerically simulate stringent project conditions with great reliability. In this context, Computational Fluid Dynamics (CFD) plays an important role and the present work shows two numerical algorithms that are used in the CFD community to solve the Euler and Navier-Stokes equations applied to typical aerospace and aeronautical problems. Particularly, unstructured discretization of the spatial domain has gained special attention by the international community due to its ease in discretizing complex spatial domains. This work has the main objective of illustrating some advantages and disadvantages of numerical algorithms using structured and unstructured spatial discretization of the flow governing equations. Numerical methods include a finite volume formulation and the Euler and Navier-Stokes equations are applied to solve a transonic nozzle problem, a low supersonic airfoil problem and a hypersonic inlet problem. In a structured context, these problems are solved using MacCormack’s implicit algorithm with Steger and Warming’s flux vector splitting technique, while, in an unstructured context, Jameson and Mavriplis’ explicit algorithm is used. Convergence acceleration is obtained using a spatially variable time stepping procedure

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Products developed at industries, institutes and research centers are expected to have high level of quality and performance, having a minimum waste, which require efficient and robust tools to numerically simulate stringent project conditions with great reliability. In this context, Computational Fluid Dynamics (CFD) plays an important role and the present work shows two numerical algorithms that are used in the CFD community to solve the Euler equations applied to typical aerospace and aeronautical problems. Particularly, unstructured discretization of the spatial domain has gained special attention by the international community due to its ease in discretizing complex spatial domains. This work has the main objective of illustrating some advantages and disadvantages of a centered algorithm and an upwind one using an unstructured spatial discretization of the flow governing equations. Numerical methods include a finite volume formulation and the Euler equations are applied to solve a supersonic flow over a ramp problem, a hypersonic flow over a blunt body problem, a hypersonic flow over a double ellipsoid problem and a supersonic flow over a simplified configuration of VLS problem. Convergence acceleration is obtained using a spatially variable time stepping procedure

In the present work, the Jameson and Mavriplis and the Liou and Steffen unstructured algorithms are applied to solve the Euler and the Navier-Stokes equations in three-dimensions. The governing equations in conservative form are solved, employing a finite volume formulation and an unstructured spatial discretization. The Jameson and Mavriplis algorithm is a symmetrical second-order one, while the Liou and Steffen algorithm is a flux vector splitting first-order upwind one. Both schemes use a second-order Runge-Kutta method to perform time integration. The steady state problems of the supersonic flow along a ramp and of the "cold gas" hypersonic flow along a diffuser are studied. The results have demonstrated that both schemes predict appropriately the shock angles at the ramp and at the lower and upper walls of the diffuser, in the inviscid case. In the viscous study, only the Liou and Steffen scheme yielded converged results, obtaining good ramp shock angles.

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