Numerical simulations of the severe squall line of 14 July 1987 are di
scussed within the context of semi-Lagrangian and semi-implicit integr
ations. The fully compressible non-hydrostatic Euler set of equations
constitutes the basic dynamical framework of the numerical model. With
elementary precipitation physics and with a generalized treatment of
lateral boundary conditions, nested integrations simulate the observed
structure of the squall line. The numerical solution and observations
show a well organized precipitation system including a mesoscale fast
-propagating prefrontal squall line and a slow-propagating system movi
ng with the synoptic wave. The prefrontal squall line is seen to be a
manifestation of the organization of an inertia-gravity wave and has c
haracteristics of a wave-CISK mechanism. Owing to the interaction betw
een the upper jet stream dynamics and moisture, the prefrontal perturb
ation is initiated locally and subsequently irradiates away from its p
oint source. The high computational efficiency and the accuracy of the
model emphasize its potential and demonstrate its value as an interes
ting tool for mesoscale modelling.