PISM's SSA solver. More...

#include <SSA.hh>

Inheritance diagram for pism::stressbalance::SSA:

Public Member Functions
	SSA (std::shared_ptr< const Grid > g)

virtual	~SSA ()

virtual void	update (const Inputs &inputs, bool full_update)
	Update the SSA solution.

virtual std::string	stdout_report () const
	Produce a report string for the standard output.

Public Member Functions inherited from pism::stressbalance::ShallowStressBalance
	ShallowStressBalance (std::shared_ptr< const Grid > g)

virtual	~ShallowStressBalance ()

void	init ()

const array::Vector1 &	velocity () const
	Get the thickness-advective 2D velocity.

const array::Scalar &	basal_frictional_heating ()
	Get the basal frictional heating (for the adaptive energy time-stepping).

void	compute_basal_frictional_heating (const array::Vector &velocity, const array::Scalar &tauc, const array::CellType &mask, array::Scalar &result) const
	Compute the basal frictional heating.

std::shared_ptr< const rheology::FlowLaw >	flow_law () const

EnthalpyConverter::Ptr	enthalpy_converter () const

const IceBasalResistancePlasticLaw *	sliding_law () const

double	flow_enhancement_factor () const

Public Member Functions inherited from pism::Component
	Component (std::shared_ptr< const Grid > grid)

virtual	~Component ()=default

DiagnosticList	diagnostics () const

TSDiagnosticList	ts_diagnostics () const

std::shared_ptr< const Grid >	grid () const

const Time &	time () const

const Profiling &	profiling () const

void	define_model_state (const File &output) const
	Define model state variables in an output file.

void	write_model_state (const File &output) const
	Write model state variables to an output file.

MaxTimestep	max_timestep (double t) const
	Reports the maximum time-step the model can take at time t.

Public Attributes
SSAStrengthExtension *	strength_extension

Protected Member Functions
virtual void	define_model_state_impl (const File &output) const
	The default (empty implementation).

virtual void	write_model_state_impl (const File &output) const
	The default (empty implementation).

virtual void	init_impl ()
	Initialize a generic regular-grid SSA solver.

virtual void	solve (const Inputs &inputs)=0

void	extrapolate_velocity (const array::CellType1 &cell_type, array::Vector1 &velocity) const

Protected Member Functions inherited from pism::stressbalance::ShallowStressBalance
virtual DiagnosticList	diagnostics_impl () const

Protected Member Functions inherited from pism::Component
virtual MaxTimestep	max_timestep_impl (double t) const

virtual TSDiagnosticList	ts_diagnostics_impl () const

void	regrid (const std::string &module_name, array::Array &variable, RegriddingFlag flag=NO_REGRID_WITHOUT_REGRID_VARS)

Protected Attributes
std::string	m_stdout_ssa

array::Vector	m_velocity_global

Protected Attributes inherited from pism::stressbalance::ShallowStressBalance
IceBasalResistancePlasticLaw *	m_basal_sliding_law

std::shared_ptr< rheology::FlowLaw >	m_flow_law

EnthalpyConverter::Ptr	m_EC

array::Vector2	m_velocity

array::Scalar	m_basal_frictional_heating

double	m_e_factor
	flow enhancement factor

Protected Attributes inherited from pism::Component
const std::shared_ptr< const Grid >	m_grid
	grid used by this component

const Config::ConstPtr	m_config
	configuration database used by this component

const units::System::Ptr	m_sys
	unit system used by this component

const Logger::ConstPtr	m_log
	logger (for easy access)

Additional Inherited Members
Protected Types inherited from pism::Component
enum	RegriddingFlag { REGRID_WITHOUT_REGRID_VARS , NO_REGRID_WITHOUT_REGRID_VARS }
	This flag determines whether a variable is read from the `-regrid_file` file even if it is not listed among variables in `-regrid_vars`. More...

Detailed Description

PISM's SSA solver.

An object of this type solves equations for the vertically-constant horizontal velocity of ice that is sliding over land or is floating. The equations are, in their clearest divergence form

$- \frac{\partial T_{ij}}{\partial x_j} - \tau_{(b)i} = f_i$

where $i,j$ range over $x,y$ , $T_{ij}$ is a depth-integrated viscous stress tensor (i.e. equation (2.6) in [SchoofStream]). These equations determine velocity in a more-or-less elliptic manner. Here $\tau_{(b)i}$ are the components of the basal shear stress applied to the base of the ice. The right-hand side $f_i$ is the driving shear stress,

$f_i = - \rho g H \frac{\partial h}{\partial x_i}.$

Here $H$ is the ice thickness and $h$ is the elevation of the surface of the ice. More concretely, the SSA equations are

$\begin{align*} - 2 \left[\nu H \left(2 u_x + v_y\right)\right]_x - \left[\nu H \left(u_y + v_x\right)\right]_y - \tau_{(b)1} &= - \rho g H h_x, \\ - \left[\nu H \left(u_y + v_x\right)\right]_x - 2 \left[\nu H \left(u_x + 2 v_y\right)\right]_y - \tau_{(b)2} &= - \rho g H h_y, \end{align*}$

where $u$ is the $x$ -component of the velocity and $v$ is the $y$ -component of the velocity [MacAyeal, Morland, WeisGreveHutter].

Derived classes actually implement numerical methods to solve these equations. This class is virtual, but it actually implements some helper functions believed to be common to all implementations (i.e. regular grid implementations) and it provides the basic fields.

Definition at line 110 of file SSA.hh.

The documentation for this class was generated from the following files:

src/stressbalance/ssa/SSA.hh
src/stressbalance/ssa/SSA.cc

Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description