# Difference between revisions of "Solving the equation for thickness evolution"

From Interactive System for Ice sheet Simulation

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<math>\frac{\partial \varphi }{\partial t}=-\nabla \cdot Q+S_{\varphi }</math> | <math>\frac{\partial \varphi }{\partial t}=-\nabla \cdot Q+S_{\varphi }</math> | ||

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+ | On the left-hand side we have the change in ''φ'' per unit time, which is given by the negative of the divergence (the | ||

+ | <math>\nabla \cdot </math> operation) of the flux, ''Q'', plus any contribution from sources, <math>S_{\varphi }</math>. |

## Revision as of 10:18, 5 August 2009

## A generic conservation equation

Evolution of the ice sheet geometry is simply the result of mass conservation. Consider a generic conservation equation for some scalar value *φ*

On the left-hand side we have the change in *φ* per unit time, which is given by the negative of the divergence (the
operation) of the flux, *Q*, plus any contribution from sources, .