ABSTRACT
John A. Ekaterinaris, School of Mechanical and Aerospace Engineering, University of Patras, Greece and Foundation for Research and Technology-Hellas, Institute of Applied and Computational Mathematics, 71110 Heraklion, Greece, ekaterin@iacm.forth.gr
In the following chapters we present high-order methods for high-order accurate in space discretizations of the compressible flow governing equations. These are the full Navier-Stokes (N-S) equations which govern non-linear fluid dynamics and aeroacoustics. For the majority of compressible flow simulations, these equations are cast in the strong conservation form [8]. Numerical solutions based on the Galerkin/least-square method, use different sets of variables [84]. This is not, however, true for finite difference and finite volume numerical methods traditionally used in aerodynamics. These methods use the conservative flow variables to ensure conservation and discontinuity capturing. The primitive variable formulation was used rarely in aerodynamics either with shock fitting schemes [31], or for the computation of subsonic compressible flows without discontinuities [147]. The transformation from conservative to primitive variables or other sets of variables is obtained by multiplying the conservative variables vector with the appropriate flux Jacobian. For example, primitive variables are obtained by multiplying with M = ∂U/∂V , U = [ρ, ρu, ρv,ET ], V = [ρ, u, v, p] see [87] for more details.
