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Risks and damages related to effusive eruptions (e.g., the most recent Etna eruptions) require satisfactory models to reliably forecast lava flow paths. An overview of the principal approaches used to forecast lava flow invasion is presented: from the simple probabilistic methods to the more complex computational fluid dynamics (CFD) models. Lava flow simulations can be used for planning the evacuation or organizing countermeasures for risk mitigation during an effusive eruption. In this case, a deterministic approach can be very useful to forecast lava flow paths, flow front velocity, and possibly to simulate the effects of the human intervention such as...

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