Numerical Algorithm

The first kernel considered in this study is the software AERO developed at the University of Colorado with the collaboration of INRIA - see Dervieux [#!derv1!#], Konga and Guillard [#!BNkonga_HGuillard_1994!#], Farhat [#!farhat1!#], and Martin and Guillard [#!RMartin_HGuillard_1996!#] for details. AERO relies on an unsteady three-field model consisting of a structural model (AERO-S), a fluid model (AERO-F), and a pseudo-elasticity model (AERO-E) for the dynamical fluid mesh. It is useful for the sequel to give a few equations describing the coupled model:

$$\begin{array}{rl} \displaystyle{ \frac{\partial}{\partial t}... ...{\partial t} + \tilde{K} x }&=\displaystyle{ K_c q} \end{array}$$ (1)

where $t$ designates time, $x$ the position of a moving fluid grid point, $w$ is the fluid state vector, $V$ results from the finite-element/volume discretization of the fluid equations, $F^c$ is the vector of convective ALE fluxes. $R$ is the vector of diffusive fluxes, $q$ is the structural displacement vector, $f^{int}$ denotes the vector of internal forces in the structure, and $f^{ext}$ the vector of external forces. $M$ is the finite-element mass matrix of the structure, $\tilde{M}$, $\tilde{D}$ and $\tilde{K}$ are fictitious mass, damping and stiffness matrices associated with the moving fluid grid and $K_c$ is a transfer matrix that describes the action of the motion of the structural side of the fluid/structure interface on the fluid dynamic mesh. An implicit finite-element time scheme is used for the structural model and an implicit time-staggered scheme for the structure. A vertex-centered upwind finite-volume scheme is employed when AERO-F is used in the fluid-only mode. Numerical options address second-order accuracy both in space and time - see Dervieux [#!derv1!#], Konga and Guillard [#!BNkonga_HGuillard_1994!#], Farhat [#!farhat1!#], and Martin and Guillard [#!RMartin_HGuillard_1996!#].

The goals of this study were: 1) Creation of the MecaGrid, 2) Studing the efficiency of the one-phase AERO-F code using the MecaGRID, and 3) Developing and examining the efficiency of a three-dimensional two-phase version of the AERO-F code for Grid applications. The results of these experiments are reported in the sections that follow.