No abstract

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.

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 2 nd to 4 th 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.

Static aeroelastic deformations are nowadays considered as early as in the preliminary aircraft design stage, where low-fidelity linear aerodynamic modeling is favored because of its low computational cost. However, transonic flows are essentially nonlinear. The present work aims at assessing the impact of the aerodynamic level of fidelity used in preliminary aircraft design. Several fluid models ranging from the linear potential to the Navier–Stokes formulations were used to solve transonic flows for steady rigid aerodynamic and static aeroelastic computations on two benchmark wings: the Onera M6 and a generic airliner wing. The lift and moment loading distributions, as well as the bending and twisting deformations predicted by the different models, were examined, along with the computational costs of the various solutions. The results illustrate that a nonlinear method is required to reliably perform steady aerodynamic computations on rigid wings. For such computations, the best tradeoff between accuracy and computational cost is achieved by the full potential formulation. On the other hand, static aeroelastic computations are usually performed on optimized wings for which transonic effects are weak. In such cases, linear potential methods were found to yield sufficiently reliable results. If the linear method of choice is the doublet lattice approach, it must be corrected using a nonlinear solution.

The spectral difference (SD) method is applied to the spatial discretization of the 2-D Euler equations on several compressible flow simulations. An order of accuracy study is performed for schemes from 2nd to 6th order. The work also evaluates a high order hierarchical limiting technique for the SD method. The numerical method results are compared with other high-order methods, such as spectral finite volume and weighted essentially non-oscillatory schemes. Unsteady flow problems with strong shock waves and other discontinuities typical of compressible flows are also analyzed in order to allow for an assessment of the resolution capability and computational cost of the SD scheme along with the applied nonlinear stability technique.