INVESTIGADORES
STORTI Mario Alberto
artículos
Título:
A General algorithm for Compressible and Incompressible flow. Stability analysis and explicit time integration
Autor/es:
STORTI MARIO; NIGRO NORBERTO; IDELSOHN, SERGIO
Revista:
International Journal for Numerical Methods in Heat and Fluid Flow
Editorial:
Emerald Group Publishing Limited
Referencias:
Lugar: Bingley, United Kingdom; Año: 1996 vol. 73 p. 50 - 77
ISSN:
0961-5539
Resumen:
This paper presents several numerical results using a
vectorized version of a 3D finite element compressible and nearly
incompressible Euler and Navier-Stokes code. The assumptions were set
on laminar flows and Newtonian fluids.
The goal of
this research is to show the capabilities of the present code to treat
a wide range of problems appearing in laminar fluid dynamics towards
the unification from incompressible to compressible and from inviscid
to viscous flow codes.
Several authors with different
approaches have tried to attain this target in CFD with relative
success. At the beginning the methods based on operator splitting and
perturbation were preferred, but lately, with the wide usage of
time-marching algorithms, the preconditioning mass matrix (PMM) has
become very popular. With this kind of relaxation scheme it is possible
to accelerate the rate of convergence to steady state solutions with
the modification of the mass matrix under certain restrictions. The
selection of the mass matrix is not an easy task, but we have certain
freedom to define it in order to improve the condition number of the
system. In this paper we have used a physics-based preconditioner for
the GMRES implicit solver developed previously by us and an SUPG
formulation for the semidiscretization of the spatial operator.
In
sections 2 and 3 we present some theoretical aspects related to the
physical problem and the mathematical model, showing the inviscid and
viscous flow equations to be solved and the variational formulation
involved in the finite element analysis. Section 4 deals with the
numerical solution of non-linear systems of equations, with some
emphasis on the preconditioned matrix-free GMRES solver. Section 5
shows how boundary conditions were treated for both Euler and
Navier-Stokes problems. Section 6 contains some aspects about
vectorization on the Cray C90. The performance reached by this
implementation is close to 1 Gflop using multitasking. Section 7
presents several numerical examples for both models covering a wide
range of interesting problems, such as inviscid low subsonic, transonic
and supersonic regimes and viscous problems with interaction between
boundary layers and shock waves in either attached or separated flows.