Gives an extension coefficient to maintain ellipticity of SSA where ice is thin. More...

#include <SSA.hh>

Public Member Functions
	SSAStrengthExtension (const NCConfigVariable &c)
virtual	~SSAStrengthExtension ()
virtual PetscErrorCode	set_notional_strength (PetscReal my_nuH)
	Set strength = (viscosity times thickness).
virtual PetscErrorCode	set_min_thickness (PetscReal my_min_thickness)
	Set minimum thickness to trigger use of extension.
virtual PetscReal	get_notional_strength () const
	Returns strength = (viscosity times thickness).
virtual PetscReal	get_min_thickness () const
	Returns minimum thickness to trigger use of extension.
Private Attributes
const NCConfigVariable &	config
PetscReal	min_thickness
PetscReal	constant_nu

Detailed Description

Gives an extension coefficient to maintain ellipticity of SSA where ice is thin.

The SSA is basically a nonlinear elliptic, but vector-valued, equation which determines the ice velocity field from the driving stress, the basal shear stress, the ice hardness, and some boundary conditions. The problem loses ellipticity (coercivity) if the thickness actually goes to zero. This class provides an extension coefficient to maintain ellipticity.

More specifically, the SSA equations are

$\def\ddx#1{\ensuremath{\frac{\partial #1}{\partial x}}} \def\ddy#1{\ensuremath{\frac{\partial #1}{\partial y}}} - 2 \ddx{}\left[\nu H \left(2 \ddx{u} + \ddy{v}\right)\right] - \ddy{}\left[\nu H \left(\ddy{u} + \ddx{v}\right)\right] + \tau_{(b)x} = - \rho g H \ddx{h},$

and another similar equation for the $y$ -component. Schoof SchoofStream shows that these PDEs are the variational equations for a coercive functional, thus (morally) elliptic.

The quantity $\nu H$ is the nonlinear coefficient, and conceptually it is a membrane strength. This class extends $\nu H$ to have a minimum value at all points. It is a class, and not just a configuration constant, because setting both the thickness $H$ and the value $\nu H$ are allowed, and setting each of these does not affect the value of the other.