  Context: We integrate the 2D MHD ideal equations of a straight slab to
simulate observational results associated with fundamental sausage trapped
modes. Aims: Starting from a non-equilibrium state with a dense chromospheric
layer, we analyse the evolution of the internal plasma dynamics of magnetic
loops, subject to line-tying boundary conditions, and with the coronal
parameters described in Asai et al. (2001) and Melnikov et al. (2002) to
investigate the onset and damping of sausage modes. Methods: To integrate the
equations we used a high resolution shock-capturing (HRSC) method specially
designed to deal appropriately with flow discontinuities. Results: Due to
non-linearities and inhomogeneities, pure modes are difficult to sustain and
always occur coupled among them so as to satisfy, e.g., the line-tying
constraint. We found that, in one case, the resonant coupling of the sausage
fundamental mode with a slow one results in a non-dissipative damping of the
former. Conclusions: In scenarios of thick and dense loops, where the
analytical theory predicts the existence of fundamental trapped sausage modes,
the coupling of fast and slow quasi-periodic modes -with a node at the center
of the longitudinal speed- occur contributing to the damping of the fast mode.
If a discontinuity in the total pressure between the loop and the corona is
assumed, a fundamental fast sausage transitory leaky regime is spontaneously
produced and an external compressional Alfv\'en wave takes away the magnetic
energy.
