Compressible Flow Simulations with an Spectral Difference Method and Using High-Order Boundary Treatment

Abstract

The present work addresses several aspects associated with an efficient use of the high-order Spectral Difference (SD) method for the simulation of compressible flows. Flows of interest are assumed to be adequately modeled by the two-dimensional (2-D) Euler or the 2-D Navier-Stokes equations. Issues associated with the use of curved boundaries are discussed. Namely, for special cases where highly stretched meshes are required, the problem of auto-intersecting elements is highlighted. Further developments on general order meshes with an attention to node positioning are also discussed. Motivated primarily by the needs of compressible viscous flows, the use of radial basis functions and mesh optimization will be discussed in order to accommodate the interior nodes. Furthermore, an important validation test for curved meshes is addressed, in order to demonstrate the capability implemented.