[en] In this paper an improved mathematical model of melt/water detonations is described. The model has been developed to study the escalation and propagation stages of a vapour explosion. The modelling presented in this paper represents a significant extension of an earlier version of the CULDESAC code also developed at Culham Laboratory. After describing the physics of this problem, a complete description of the conservation equations and constitutive relations which form the model is given. The solution procedure is then described and some results from example simulations are presented. These results demonstrate the improved performance of the new model and illustrate the effect of the initial mixture void fraction on propagation. The role played by various solution parameters and constitutive physics assumptions is also examined. Part II of this paper contains a detailed study of the escalation stage. (author)