Numerical Algorithm

The MecaGRID project was created specifically for MPI codes applied to fluid dynamics problems. Therefore a natural candidate for the MecaGRID was the AERO-F software developed at the University of Colorado with the collaboration of INRIA that executes on parallel computers using MPI. A second important reason for selecting the AERO code is the ease of integrating the recent two-phase advancements of the SMASH team (see Murrone and Guillard [#!murrone1!#], Murrone [#!murrone2!#]) into a three-dimensional code. The integration is facilitated by the fact that the origins of the two-dimensional code of Murrone and Guillard are an earlier version of the AERO code therefore the structure of the two codes is very similar.

Therefore in the context of the MecaGRID, the fluid part of the software AERO-F has been extended to the calculation of two-phase flows. The Euler equations for a unique perfect gas has been replaced by the following model:

Seven-equation quasi conservative reduced model

$$\begin{array}{lll} \displaystyle \frac {\partial } {\partial ... ...k=1}^2 \alpha_{k'}\rho_k a_k^2 }\mbox{div}{u}\ \\ \end{array}$$

with $e=\varepsilon+u^2/2$ and $\rho \varepsilon={\sum_{k=1}^2 \alpha_{k}\rho_k \varepsilon_k(p,\rho_k)}$.

where $\alpha_k$ are the mass fractions of the two fluids. To distinguish the different versions of the AERO codes, the two-phase version is named AEDIF, only the explicit solver is used. Details on the development of AEDIF are given in [#!wornom2!#]