Developing physical-mathematical models able to describe the evolution of eruptive phenomena is a key point in volcanology. In the case of high-risk phenomena, such as lava flows or ash dispersal, predicting their spatial and temporal evolution and determining the potentially affected areas is fundamental in supporting every action directed at mitigating the risk as well as effective land use planning. This session aims to address unresolved challenging questions related to complex geophysical flow modeling and simulation, gathering physical-mathematical models, numerical methods and field and satellite data analysis in order to: (i) expand knowledge of complex volcanic processes and their space-time dynamics; (ii) monitor and model volcanic phenomena; (iii) quantify model robustness and simulation performances through validation against real case studies, analytical solutions and laboratory experiments; (iv) conduct sensitivity analysis and optimization/calibration of input parameters in all components of volcanic hazard modelling in response to eruptive crisis.