Santa Fe Preparatory School
Fire on the Mountain
The objective of this project is to simulate pyroclastic flows. These deadly cascades of rock, ash, and gas devastate whatever lies in their wake. This program will be able to predict the areas in danger and what the magnitude of the devastation will be at any point around a given volcano.
We will write a program using the laws of conservation of momentum, mass, and energy to do this. The program will be based on a three-dimensional matrix of finite difference objects encapsulating these variables. We will also graphically represent the topography of a virtual volcano, possibly derived from actual geological sites. Developing the means employed for graphical representation will also be an objective in the project.
When considering actual sites we need to take in to account the viscosity of the flow, climate, slope, topography, vegetation, and the wind. These variables become important in predicting the behavior of the flow. The dynamics of the explosion have to be considered also. Such things as velocity, temperature and the location of the eruption on the mountain are important in the prediction of the flow down the volcano'’ side.
This can all be achieved computationally by iterating a process in which every element is altered by interacting with its adjacent cells in accordance with proven techniques of numerical analysis. The iterations will represent the behavior of the flow in brief intervals of time. When repeated by a super-computer the simulation will be a mathematically accurate approximation.