INVESTIGADORES
STORTI Mario Alberto
artículos
Título:
Improving the convergence rate of the Petrov-Galerkin techniques for the solution of transonic and supersonic flows
Autor/es:
BAUMANN, CARLOS; STORTI MARIO; IDELSOHN, SERGIO
Revista:
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Editorial:
John Wiley and sons
Referencias:
Lugar: Hoboken, New Jersey; Año: 1992 vol. 34 p. 543 - 568
ISSN:
0029-5981
Resumen:
This paper report
progress on a technique to accelerate the convergence to steady
solutions when the streamline-upwind/Petrov-Galerkin (SUPG) technique
is used. Both the description of a SUPG formulation and the
documentation of the development of a code for the finite element
solution of transonic and supersonic flows are reported. The aim of
this work is to present a formulation to be able to treat domains of
any configuration and to use the appropriate physical boundary
conditions, which are the major stumbling blocks of the finite
difference schemes, together with an appropriate convergence rate to
the steady solution.
The implemented code has the
following features: the Hughes' SUPG-type formulation with an
oscillation-free shock-capturing operator, adaptive refinement,
explicit integration with local time-step and hourglassing control. An
automatic scheme for dealing with slip boundary conditions and a
boundary-augmented lumped mass matrix for speeding up convergence.
It
is shown that the velocities at which the error is absorbed in and
ejected from the domain (that is damping and group velocities
respectively) are strongly affected by the time step used, and that
damping gives an O(N2) algorithm contrasting with the O(N)
one given by absorption at the boundaries. Nonetheless, the absorbing
effect is very low when very different eigenvalues are present, such as
in the transonic case, because the stability condition imposes a too
slow group velocity for the smaller eigenvalues. To overcome this
drawback we present a new mass matrix that provides us with a scheme having the highest group velocity attainable in all the components.
In
Section 1 we will describe briefly the theoretical background of the
SUPG formulation. In Section 2 it is described how the foregoing
formulation was used in the finite element code and which are the
appropriate boundary conditions to be used. Finally in Section 3 we
will show some results obtained with this code.