GALES - GAlerkin LEast Squares

MODEL

Transient 2D dynamics of multicomponent multiphase homogeneous fluid mixtures in the compressible-to-incompressible flow regimes. GALES solves the mass conservation of components, and the momentum and energy equations of the multiphase mixture. Mixtures are made of gas, liquid and dispersed solid particles. Phase and mixture properties are computed as a function of local P-T-X conditions, with embedded advanced constitutive equations for melt-gas mixtures (e.g., SOLWCAD).

ALGORITHM

Weak form of the transport equations is discretized on ustructured grids with advanced stabilized space-time, time discontinuous, Finite Element Method using Langrangian space-time shape functions. Least squares and discontinuity capturing terms prevent spurious oscillations of the solution with minor smoothing of sharp gradients. The non-linear transport equations are linearized with a Taylor series expansion. Time marching algorithm is of predictor-multicorrector type.

IMPLEMENTATION

The code is implemented and organized as a C++ object oriented library, with an extensive use of design patterns and template meta programming paradigms. GALES is a parallel computation MPI-based software employing the Trilinos package (developed by the Sandia Laboratories). Trilinos provides high-level representation for distributed dense and sparse matrices and vectors, as well as efficient tools for parallel computation (matrix multiplication, GMRES linear system iterative solver, etc...).

Fig 1. Distribution of computed composition and vertical velocity for a magmatic plume rising  through a  gravitationally unstable magmatic system. Initially two different magmas are placed in contact at the connection between the bottom dike and the upper magma chamber. The lower magma is richer in volatiles components H2O and CO2, thus lighter than the upper magma, originating the gravitational instability

Fig. 2. Distribution of composition and density after 3000 s of simulation of a gravitationally unstable  magmatic system. Initially two different magmas are placed in contact at the connection between the bottom dike and the upper magma chamber. The lower magma is richer in volatiles components H2O and CO2, thus lighter than the upper magma, originating the gravitational instability. A series of light magma plumes develop and invade the magma chamber. Light magma progressively accumulates at the top of the chamber

RELEVANT REFERENCES

Numerical simulation of the dynamics of fluid oscillations in a gravitationally unstable, compositionally stratified fissure. Longo A., D. Barbato, P. Papale, G. Saccorotti and M. Barsanti. From: LANE, S. J. & GILBERT, J. S. (eds) Fluid Motions in Volcanic Conduits: A Source of Seismic and Acoustic Signals, Geological Society, London, Spe. Vol. 307, pp: 33-44, 2008

Numerical simulation of convection and mixing in magma chambers replenished with CO2-rich magma Longo A., Vassalli M. , Papale P. and M. Barsanti Geophys. Res. Lett. 33, 2006 doi: 10.1029/2006GL027760

Magma convention and mixing dynamics as a source of Ultra-Long-Period oscillations. Longo A., Papale P., Vassalli M., Saccorotti G., Montagna C.P., Cassioli A., Giudice D. and E. Boschi Bull. Volcanol.,2011 doi: 10.1007/s00445-011-0570-0