Existing volcanic eruption models need to be superceded by a more adequate modelling, since many observations of eruption columns, blasts and related phenomena still lack theoretical explanation. Careful theoretical analyses are essential to provide explanations against which field observations may be tested, and to provide the stimulus for new, insightful approaches to field investigation. Accurate modelling is now feasible due to availability of advanced numerical techniques and supercomputers. We therefore propose to develop a rigorous unified computational model for volcanic eruptions involving: three-dimensional, unsteady, turbulent, compressible, thermoviscous, multiphase radiating flow, with interaction from extraneous water, arbitrary cross-wind profiles, stratified humid atmosphere, and realistic ground topography. Vent orientation and shape will be arbitrary. This grant will partially support a graduate student who will participate in the development of this model under the supervision of the two PIs.