torm processes constitute prototype models for spatial extremes. They are classically simulated on a finite number of points within a given domain. We propose a new algorithm that allows to perform such a task in continuous domains like hyper-rectangles or balls, in arbitrary dimension. This consists in generating basic ingredients that can subsequently be used to assign a value at any point of the simulation field. Such an approach is particularly appropriate to investigate the geometrical properties of storm processes. Particular attention is paid to efficiency: by introducing and exploiting the notion of domain of influence of each storm, the running time is considerably reduced. Besides, most parts of the algorithm are designed to be parallelizable.