# Solving the equation for thickness evolution

From Interactive System for Ice sheet Simulation

## A generic conservation equation

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

Notes on mass continuity equation here and how it can be solved for HO models ...

Advection schemes, simplest of which is 1st-order upwinding. Notes on why we call it "upwinding"

Problems w/ upwinding schemes, especially 1st order ones (too diffusive, false diffusion, etc.)

Discuss some "higher-order" upwinding schemes (e.g. incremental remapping, PPM), how/why they are better, and not that they are/will be implemented in future release of Glimmer/CISM.