Journal of the Brazilian Society of Mechanical Sciences and Engineering
Print version ISSN 1678-5878
BREVIGLIERI, Carlos; AZEVEDO, João Luiz F. and BASSO, Edson. An unstructured grid implementation of high-order spectral finite volume schemes. J. Braz. Soc. Mech. Sci. & Eng. [online]. 2010, vol.32, n.spe, pp. 419-433. ISSN 1678-5878. http://dx.doi.org/10.1590/S1678-58782010000500001.
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.
Keywords : spectral finite volume; high-order discretization; 2-D euler equations; unstructured meshes.