# Higher order velocity schemes

From Interactive System for Ice sheet Simulation

## Higher-Order model basics

The main distinction between so-called "higher-order" models and "0-order" (or "shallow ice") models is that higher-order models attempt a closer approximation to solving the non-linear, full Stokes system of equations. In general, this usually means incorporating some approximation of horizontal-stress gradients; along-flow stretching or compression and across-flow shearing.

shallow

- HO model; what distinguishes it from a LO model, why is it useful.

- Available HO schemes (e.g. Full Stokes, Blatter-Pattyn, Bueler & Pollard Hybrids)
- Architecture (transport, and non-linear iteration on diffusivity) of Glimmer an how it differs from a HO model architecture
- Introduce HO CISM (Blatter-Pattyn 1st-order scheme)
- Discretization and solution (elliptic solve, operator splitting approach, etc)
- Boundary conditions + masking, one sided differences, basal BC (no-slip, viscous, and plastic behavior all through Beta^2 implementation)
- Run verification suites; ISMIP-HOM, Ross IS
- Apply HO velocity fields to 1st-order upwind transport (dH/dt) scheme (see Adding a module to Glimmer I)