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The present work has the objective of demonstrating the capabilities of a spectral finite volume scheme implemented in a cell-centered finite volume context for unstructured meshes. The two-dimensional Euler equations are considered to represent the flows of interest. The spatial discretization scheme is developed to achieve high resolution for flow problems governed by hyperbolic conservation laws. Roe's flux difference splitting method is used as the numerical approximate Riemann solver. Several applications are performed in order to assess the method capability compared to data available in the literature and also compared to an weighted essentially nonoscillatory scheme. There is good agreement with the comparison data, and efficiency improvements over the weighted essentially nonoscillatory method are observed. The features of the present methodology include an implicit timemarching algorithm; second-, third-, and fourth-order spatial resolution; exact high-order domain boundary representation; and a hierarchical moment limiter to treat flow solution discontinuities.

An effort is underway to develop a chimera ow simulation code capable of handling the external aerodynamics of general launch vehicle con gurations. Aerodynamic results are presented referring to inviscid, laminar, and turbulent viscous simulations of the rst Brazilian satellite launch vehicle during its rst-stage ight. The nite difference method is applied to the governing equations, written in conservation-law form for general body conforming curvilinear coordinates. The spatial discretization is accomplished with a central difference scheme in which arti cial dissipation terms, based on a scalar, nonisotropic model, are added to the numerical scheme to maintain stability. The time-marching process is accomplished with a ve-stage, second-order accurate, RungeKutta scheme. Studies of mesh re nement are also presented as a part of the validation effort, with the objective of providing a certi ed ow simulation capability for actual engineering work. Nomenclatureand N G v = viscous ux vectors e = total energy per unit volume J = Jacobian of the transformation M = Mach number p = pressure N Q = vector of conserved variables Re = Reynolds number U; V , and W = contravariant velocity components u; v, and w = Cartesian velocity components ® = angle of attack°= ratio of speci c heats ± = standard three-point central difference operators N ± = midpoint central difference operators ½ = density Subscript 1 = freestream quantities

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The present work is primarily concerned with studying the effects of artificial dissipation and of certain diffusive terms in the turbulence model formulation on the capability of representing turbulent boundary layer flows. The flows of interest in the present case are assumed to be adequately represented by the compressible Reynolds-averaged Navier-Stokes equations, and the Spalart-Allmaras eddy viscosity model is used for turbulence closure. The equations are discretized in the context of a general purpose, density-based, unstructured grid finite volume method. Spatial discretization is based on the Steger-Warming flux vector splitting scheme and temporal discretization uses a backward Euler point-implicit integration. The work discusses in detail the theoretical and numerical formulations of the selected model. The computational studies consider the turbulent flow over a flat plate at 0.3 freestream Mach number. The paper demonstrates that the excessive artificial dissipation automatically generated by the original spatial discretization scheme can deteriorate boundary layer predictions. Moreover, the results also show that the inclusion of Spalart-Allmaras model cross-diffusion terms is primarily important in the viscous sublayer region of the boundary layer. Finally, the paper also demonstrates how the spatial discretization scheme can be selectively modified to correctly control the artificial dissipation such that the flow simulation tool remains robust for high-speed applications at the same time that it can accurately compute turbulent boundary layers.