Inviscid/Viscous Hypersonic Flow In Confined Ducts And Around Of Immersed Bodies Considering Anisotropic Shock Capturing And Adaptive Mesh Refinement Techniques.

Abstract

In this paper, we present a numerical study of the viscous/inviscid hypersonic flows in confined
ducts and around of immersed bodies. Nowadays the flow at high Mach numbers and its
interaction with deformable structures is considered a ‘challenge’ in the context of numerical
methods.
In hypersonic flow problems the non-linearities become high and any difficulty in the convergence
of the linear system may influence the nonlinear convergence and finally make the
solution to blow up. Then, global iteration result in a non suitable scheme (high cpu and
memory demands for preconditioned GMRes method, for instance) for this step. A new preconditioner
for domain decomposition methods (see References1, 2, 3) is used in order to obtain
physical solutions and to accelerate the convergence to a low tolerance in residuals.
In order to diminish the solution error near physical discontinuities (e.g. contact layers,
shock waves) or expansion shocks an adaptive mesh refinement technique is used. Besides, an
anisotropic shock capturing operator is added to the Galerkin/SUPG formulation.
Also in this work, we present results of a new methodology for imposing absorbing boundary
conditions for general advective-diffusive system of equations (e.g., the compressible Navier-
Stokes equations). Basically, two types of local absorbing boundary conditions (b.c.) are considered,
i.e. the linear absorbent b.c., based on the Jacobian of the flux function, assuming
small perturbations about a reference value, and the general non-linear absorbent b.c. based
on the Riemann invariants of the problem (see Reference4 for a more detailed description).