ABSTRACT: The work is a study of conservation on linearization techniques of time-marching schemes for the unstructured finite volume Reynolds-averaged Navier-Stokes formulation. The solver used in this work calculates the numerical flux applying an upwind discretization based on the flux vector splitting scheme. This numerical treatment results in a very large sparse linear system. The direct solution of this full implicit linear system is very expensive and, in most cases, impractical. There are several numerical approaches which are commonly used by the scientific community to treat sparse linear systems, and the point-implicit integration was selected in the present case. However, numerical approaches to solve implicit linear systems can be non-conservative in time, even for formulations which are conservative by construction, as the finite volume techniques. Moreover, there are physical problems which strongly demand conservative schemes in order to achieve the correct numerical solution. The work presents results of numerical simulations to evaluate the conservation of implicit and explicit time-marching methods and discusses numerical requirements that can help avoiding such non-conservation issues.

ABSTRACT: 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.

Abstract: Aerodynamic flow simulations over a typical sounding rocket are presented in this paper. The work is inserted in the effort of developing computational tools necessary to simulate aerodynamic flows over configurations of interest for Instituto de Aeronáutica e Espaço of Departamento de Ciência e Tecnologia Aeroespacial. Sounding rocket configurations usually require fairly large fins and, quite frequently, have more than one set of fins. In order to be able to handle such configurations, the present paper presents a novel methodology which combines both Chimera and patched multiblock grids in the discretization of the computational domain. The flows of interest are modeled using the 3-D Euler equations and the work describes the details of discretization procedure, which uses a finite difference approach for structure, body-conforming, multiblock grids. The method is used to calculate the aerodynamics of a sounding rocket vehicle. The results indicate that the present approach can be a powerful aerodynamic analysis and design tool.

The present work implements the spectral finite volume scheme in a cell centered finite volume context for unstructured meshes. The 2-D Euler equations are considered to represent the flows of interest. The spatial discretization scheme is developed to achieve high resolution and computational efficiency for flow problems governed by hyperbolic conservation laws, including flow discontinuities. Such discontinuities are mainly shock waves in the aerodynamic studies of interest in the present paper. The entire reconstruction process is described in detail for the 2nd to 4th order schemes. Roe's flux difference splitting method is used as the numerical Riemann solver. Several applications are performed in order to assess the method capability compared to data available in the literature. The results obtained with the present method are also compared to those of essentially nonoscillatory and weighted essentially non-oscillatory high-order schemes. There is a good agreement with the comparison data and efficiency improvements have been observed.