INVESTIGADORES
STORTI Mario Alberto
artículos
Título:
A preconditioning mass matrix to accelerate the convergence to the steady Euler solutions using explicit schemes
Autor/es:
STORTI MARIO; BAUMANN, CARLOS; 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. 519 - 541
ISSN:
0029-5981
Resumen:
When explicit time marching algorithms are used to reach the
steady state of problems governed by the Euler equations, the rate of
convergence is strongly impaired both in the zones with low Mach number
and in the zones with transonic flow, e.g. Mach and | Mach - 1| , with 0·2. The rate of convergence becomes slower as diminishes.
We
show in this paper, with analytical and numerical results, how the use
of a preconditioning mass matrix accelerates the convergence in the
aforementioned ranges of Mach numbers.
The
preconditioning mass matrix (PMM) we advocate in this paper can be
applied to any FEM/FVM that uses an explicit time marching scheme to
find the steady state. The method's rate of convergence to the steady
state is studied, and results for the one- and two-dimiensional cases
are presented.
In Sections 1-3, using the
one-dimensional Euler equations, we first explain why there exists a
slow rate of convergence when the plain lumping of mass is used. Then
the convergence rate to steady solutions is analysed from its two
constituents, that is, convergence by absorption at the boundaries and
by damping in the domain. Next we give the natural solution to this
problem, and with several examples we show the effectiveness of the
proposed mass matrix when compared with the plain scheme.
In
Sections 4-8 we give the multidimensional version of the
preconditioning mass matrix. We make a stability analysis and compare
the group velocities and damping with and without the new mass matrix.
To finish, we show the velocity of convergence for a common test
problem.