# Blatter-Pattyn Boundary Conditions

Boundary conditions + masking, one sided differences, basal BC (no-slip, viscous, and plastic behavior all through Beta^2 implementation)

NEED: sfc and basal BC description from HO model descrip. doc

TO DO: add links from previous pages discussing BP equations and BP numerical solution

## Sliding over a plastic bed

\begin{align} & x:\quad \left[ 2\tau _{xx}\left( b \right)+\tau _{yy}\left( b \right) \right]\frac{\partial b}{\partial x}+\tau _{xy}\left( b \right)\frac{\partial b}{\partial y}-\tau _{xz}\left( b \right)=-\tau _{bx} \\ & \quad \quad \quad \quad \quad \quad \quad \quad \quad \tau _{bx}\approx \tau _{0} \\ & x:\quad \quad \quad \quad \quad \quad \quad ...\quad \quad \quad \quad =-\tau _{0}\left( \frac{u}{\left| \mathbf{u} \right|} \right) \\ & x:\quad \quad \quad \quad \quad \quad \quad ...\quad \quad \quad \quad =-\tau _{0}\left( \frac{u}{\sqrt{u_{0}^{2}+v_{0}^{2}+\gamma }} \right) \\ \end{align}

figures here showing the results for simple ice stream setup ...