Complex systems have been widely investigated using formal techniques for testing and verifying critical aspects of their reactive behaviour. Such behaviours are usually captured by the notion of data flow and by interactions with the environment. Other aspects require models to describe the systems' continuous evolution in time. In this work, we propose a timed contextual formalism able to model the combination of time evolution and contextual transformations. Further, we derive a manageable strategy to discretise such models and prove correctness of the discretised model against the original one. The flexibility to find suitable granularities both for the evolution of time and for the value of the contextual variables opens the possibility for constructing more compact grid automata. Based on this discretising approach we present a testing framework to automatically generate test suites from the resulting automata. The test suites can then be used to verify properties of candidate implementations with the aid of test purposes.542121137