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ug::NavierStokes::NavierStokesBase< TDomain > Class Template Referenceabstract

Finite Volume Element Discretization for the incompressible Navier-Stokes Equation. More...

#include <navier_stokes_base.h>

+ Inheritance diagram for ug::NavierStokes::NavierStokesBase< TDomain >:

Public Member Functions

virtual std::string disc_type () const =0
 returns string identifying disc type More...
 
virtual SmartPtr< CplUserData< number, dim > > kinematic_viscosity ()=0
 returns kinematic viscosity More...
 
virtual bool requests_local_time_series ()
 returns if local time series is needed More...
 
void set_exact_jacobian (bool bExactJacobian)
 sets if the exact jacobian is computed (fixpoint approximation else) More...
 
void set_exact_jacobian (number fullNewtonFactor)
 
 NavierStokesBase (const char *functions, const char *subsets)
 
 NavierStokesBase (const std::vector< std::string > &vFct, const std::vector< std::string > &vSubset)
 
virtual void set_kinematic_viscosity (SmartPtr< CplUserData< number, dim > > user)=0
 sets the kinematic viscosity More...
 
void set_kinematic_viscosity (number val)
 sets the kinematic viscosity More...
 
virtual void set_source (SmartPtr< CplUserData< MathVector< dim >, dim > > user)=0
 sets the source function More...
 
void set_source (const std::vector< number > &vSource)
 sets the source function More...
 
- Public Member Functions inherited from ug::IElemDisc< TDomain >
void add_elem_modifier (SmartPtr< IElemDiscModifier< TDomain > > elemModifier)
 
std::vector< SmartPtr< IElemDiscModifier< TDomain > > > & get_elem_modifier ()
 
 IElemDisc (const char *functions, const char *subsets)
 
 IElemDisc (const std::vector< std::string > &vFct, const std::vector< std::string > &vSubset)
 
- Public Member Functions inherited from IElemAssembleFuncs< IElemDisc< TDomain >, TDomain >
virtual void add_def_A_elem (LocalVector &d, const LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])
 
virtual void add_def_A_expl_elem (LocalVector &d, const LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])
 
virtual void add_def_M_elem (LocalVector &d, const LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])
 
virtual void add_jac_A_elem (LocalMatrix &J, const LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])
 
virtual void add_jac_M_elem (LocalMatrix &J, const LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])
 
virtual void add_rhs_elem (LocalVector &rhs, GridObject *elem, const MathVector< dim > vCornerCoords[])
 
IElemDisc< TDomain > & asLeaf ()
 
void check_roid (ReferenceObjectID roid, int discType)
 
void do_add_def_A_elem (LocalVector &d, LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])
 
void do_add_def_A_expl_elem (LocalVector &d, LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])
 
void do_add_def_M_elem (LocalVector &d, LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])
 
void do_add_jac_A_elem (LocalMatrix &J, LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])
 
void do_add_jac_M_elem (LocalMatrix &J, LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])
 
void do_add_rhs_elem (LocalVector &rhs, GridObject *elem, const MathVector< dim > vCornerCoords[])
 
void do_fsh_elem_loop ()
 
void do_fsh_timestep (const number time, VectorProxyBase *u, size_t algebra_id)
 
void do_fsh_timestep_elem (const number time, LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])
 
void do_prep_elem (LocalVector &u, GridObject *elem, const ReferenceObjectID roid, const MathVector< dim > vCornerCoords[])
 
void do_prep_elem_loop (const ReferenceObjectID roid, const int si)
 
void do_prep_timestep (number future_time, const number time, VectorProxyBase *u, size_t algebra_id)
 
void do_prep_timestep_elem (const number time, LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])
 
virtual void fsh_elem_loop ()
 
virtual void fsh_timestep (number time, VectorProxyBase *u)
 
virtual void fsh_timestep_elem (const number time, const LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])
 
 IElemAssembleFuncs ()
 
virtual void post_assemble_loop ()
 
virtual void prep_assemble_loop ()
 
virtual void prep_elem (const LocalVector &u, GridObject *elem, const ReferenceObjectID roid, const MathVector< dim > vCornerCoords[])
 
virtual void prep_elem_loop (const ReferenceObjectID roid, const int si)
 
virtual void prep_timestep (number future_time, number time, VectorProxyBase *u)
 
virtual void prep_timestep_elem (const number time, const LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])
 
void set_roid (ReferenceObjectID id, int discType)
 
virtual ~IElemAssembleFuncs ()
 
- Public Member Functions inherited from ug::IElemError< class >
 IElemError (const char *functions, const char *subsets)
 
 IElemError (const std::vector< std::string > &vFct, const std::vector< std::string > &vSubset)
 
- Public Member Functions inherited from ug::IElemDiscBase< class >
SmartPtr< ApproximationSpace< TDomain > > approx_space ()
 
ConstSmartPtr< ApproximationSpace< TDomain > > approx_space () const
 
void check_setup (bool bNonRegularGrid)
 
void clear_imports ()
 
SmartPtr< TDomain > domain ()
 
ConstSmartPtr< TDomain > domain () const
 
const FunctionGroupfunction_group () const
 
ConstSmartPtr< FunctionPatternfunction_pattern () const
 
IDataImport< dim > & get_import (size_t i)
 
 IElemDiscBase (const char *functions="", const char *subsets="")
 
 IElemDiscBase (const std::vector< std::string > &vFct, const std::vector< std::string > &vSubset)
 
bool is_time_dependent () const
 
bool local_time_series_needed ()
 
const LocalVectorTimeSerieslocal_time_solutions () const
 
const FunctionIndexMappingmap () const
 
number mass_scale () const
 
number mass_scale () const
 
number mass_scale (const size_t timePoint) const
 
number mass_scale (const size_t timePoint) const
 
const std::vector< number > & mass_scales () const
 
const std::vector< number > & mass_scales () const
 
size_t num_fct () const
 
size_t num_imports () const
 
size_t num_subsets () const
 
virtual void prepare_setting (const std::vector< LFEID > &vLfeID, bool bNonRegularGrid)=0
 
void register_import (IDataImport< dim > &Imp)
 
void set_approximation_space (SmartPtr< ApproximationSpace< TDomain > > approxSpace)
 
void set_functions (const std::string &functions)
 
void set_functions (const std::vector< std::string > &functions)
 
void set_stationary ()
 
void set_stationary (bool bStationaryForced=true)
 
void set_subsets (const std::string &subsets)
 
void set_subsets (const std::vector< std::string > &subsets)
 
void set_time_dependent (LocalVectorTimeSeries &locTimeSeries, const std::vector< number > &vScaleMass, const std::vector< number > &vScaleStiff)
 
void set_time_independent ()
 
void set_time_point (const size_t timePoint)
 
number stiff_scale () const
 
number stiff_scale () const
 
number stiff_scale (const size_t timePoint) const
 
number stiff_scale (const size_t timePoint) const
 
const std::vector< number > & stiff_scales () const
 
const std::vector< number > & stiff_scales () const
 
TDomain::subset_handler_typesubset_handler ()
 
const TDomain::subset_handler_typesubset_handler () const
 
const std::vector< std::string > & symb_fcts () const
 
const std::vector< std::string > & symb_subsets () const
 
number time () const
 
size_t time_point () const
 
virtual int type () const
 
virtual bool use_hanging () const
 
virtual ~IElemDiscBase ()
 
- Public Member Functions inherited from IElemEstimatorFuncs< IElemDisc< TDomain >, TDomain >
IElemDisc< TDomain > & asLeaf ()
 
void check_roid (ReferenceObjectID roid, int discType)
 
virtual void compute_err_est_A_elem (const LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[], const number &scale)
 
virtual void compute_err_est_M_elem (const LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[], const number &scale)
 
virtual void compute_err_est_rhs_elem (GridObject *elem, const MathVector< dim > vCornerCoords[], const number &scale)
 
void do_compute_err_est_A_elem (LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[], const number &scale)
 
void do_compute_err_est_M_elem (LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[], const number &scale)
 
void do_compute_err_est_rhs_elem (GridObject *elem, const MathVector< dim > vCornerCoords[], const number &scale)
 
void do_fsh_err_est_elem_loop ()
 
void do_prep_err_est_elem (LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])
 
void do_prep_err_est_elem_loop (const ReferenceObjectID roid, const int si)
 
virtual SmartPtr< IErrEstData< TDomain > > err_est_data ()
 
bool err_est_enabled () const
 
virtual void fsh_err_est_elem_loop ()
 
 IElemEstimatorFuncs ()
 
virtual void prep_err_est_elem (const LocalVector &u, GridObject *elem, const MathVector< dim > vCornerCoords[])
 
virtual void prep_err_est_elem_loop (const ReferenceObjectID roid, const int si)
 
void set_error_estimator (SmartPtr< IErrEstData< TDomain > > ee)
 
void set_roid (ReferenceObjectID id, int discType)
 
virtual ~IElemEstimatorFuncs ()
 

Static Public Attributes

static const int dim = base_type::dim
 World dimension. More...
 
- Static Public Attributes inherited from ug::IElemDisc< TDomain >
static const int dim
 
- Static Public Attributes inherited from IElemAssembleFuncs< IElemDisc< TDomain >, TDomain >
static const int dim
 
- Static Public Attributes inherited from ug::IElemError< class >
static const int dim
 
- Static Public Attributes inherited from ug::IElemDiscBase< class >
static const int dim
 
- Static Public Attributes inherited from IElemEstimatorFuncs< IElemDisc< TDomain >, TDomain >
static const int dim
 

Protected Types

typedef IElemDisc< TDomain > base_type
 Base class type. More...
 
typedef NavierStokesBase< TDomain > this_type
 own type More...
 

Protected Attributes

number m_bFullNewtonFactor
 factor for exact jacobian, (1 for exact jacobian, 0 for fix point) More...
 
- Protected Attributes inherited from ug::IElemDisc< TDomain >
std::vector< SmartPtr< IElemDiscModifier< TDomain > > > m_spElemModifier
 
- Protected Attributes inherited from IElemAssembleFuncs< IElemDisc< TDomain >, TDomain >
ReferenceObjectID m_roid
 
- Protected Attributes inherited from ug::IElemDiscBase< class >
bool m_bStationaryForced
 
FunctionGroup m_fctGrp
 
FunctionIndexMapping m_fctIndexMap
 
LocalVectorTimeSeriesm_pLocalVectorTimeSeries
 
SmartPtr< ApproximationSpace< TDomain > > m_spApproxSpace
 
ConstSmartPtr< FunctionPatternm_spFctPattern
 
size_t m_timePoint
 
std::vector< std::string > m_vFct
 
std::vector< IDataImport< dim > * > m_vIImport
 
std::vector< numberm_vScaleMass
 
std::vector< numberm_vScaleStiff
 
std::vector< std::string > m_vSubset
 
- Protected Attributes inherited from IElemEstimatorFuncs< IElemDisc< TDomain >, TDomain >
ReferenceObjectID m_roid
 
SmartPtr< IErrEstData< TDomain > > m_spErrEstData
 

Additional Inherited Members

- Public Types inherited from ug::IElemDisc< TDomain >
typedef IElemAssembleFuncs< IElemDisc< TDomain >, TDomain > assemble_base_type
 
typedef IElemError< TDomain > base_type
 
typedef TDomain domain_type
 
typedef IElemEstimatorFuncs< IElemDisc< TDomain >, TDomain > estimator_base_type
 
- Public Types inherited from IElemAssembleFuncs< IElemDisc< TDomain >, TDomain >
typedef TDomain domain_type
 
typedef IElemDisc< TDomain > leaf_type
 
- Public Types inherited from ug::IElemError< class >
typedef TDomain domain_type
 
typedef IElemEstimatorFuncs< IElemDisc< TDomain >, TDomain > estimator_base_type
 
- Public Types inherited from ug::IElemDiscBase< class >
typedef TDomain domain_type
 
typedef TDomain::position_type position_type
 
- Public Types inherited from IElemEstimatorFuncs< IElemDisc< TDomain >, TDomain >
typedef TDomain domain_type
 
typedef IElemDisc< TDomain > leaf_type
 
- Protected Member Functions inherited from ug::IElemDisc< TDomain >
void clear_add_fct ()
 
void clear_add_fct (ReferenceObjectID id)
 
void set_default_add_fct ()
 
- Protected Member Functions inherited from IElemAssembleFuncs< IElemDisc< TDomain >, TDomain >
void clear_add_fct ()
 
void clear_add_fct (ReferenceObjectID id)
 
void remove_add_def_A_elem_fct (ReferenceObjectID id)
 
void remove_add_def_A_expl_elem_fct (ReferenceObjectID id)
 
void remove_add_def_M_elem_fct (ReferenceObjectID id)
 
void remove_add_jac_A_elem_fct (ReferenceObjectID id)
 
void remove_add_jac_M_elem_fct (ReferenceObjectID id)
 
void remove_add_rhs_elem_fct (ReferenceObjectID id)
 
void remove_fsh_elem_loop_fct (ReferenceObjectID id)
 
void remove_fsh_timestep_elem_fct (ReferenceObjectID id)
 
void remove_fsh_timestep_fct (size_t algebra_id)
 
void remove_prep_elem_fct (ReferenceObjectID id)
 
void remove_prep_elem_loop_fct (ReferenceObjectID id)
 
void remove_prep_timestep_elem_fct (ReferenceObjectID id)
 
void remove_prep_timestep_fct (size_t algebra_id)
 
void set_add_def_A_elem_fct (ReferenceObjectID id, TAssFunc func)
 
void set_add_def_A_expl_elem_fct (ReferenceObjectID id, TAssFunc func)
 
void set_add_def_M_elem_fct (ReferenceObjectID id, TAssFunc func)
 
void set_add_jac_A_elem_fct (ReferenceObjectID id, TAssFunc func)
 
void set_add_jac_M_elem_fct (ReferenceObjectID id, TAssFunc func)
 
void set_add_rhs_elem_fct (ReferenceObjectID id, TAssFunc func)
 
void set_default_add_fct ()
 
void set_fsh_elem_loop_fct (ReferenceObjectID id, TAssFunc func)
 
void set_fsh_timestep_elem_fct (ReferenceObjectID id, TAssFunc func)
 
void set_fsh_timestep_fct (size_t algebra_id, TAssFunc func)
 
void set_prep_elem_fct (ReferenceObjectID id, TAssFunc func)
 
void set_prep_elem_loop_fct (ReferenceObjectID id, TAssFunc func)
 
void set_prep_timestep_elem_fct (ReferenceObjectID id, TAssFunc func)
 
void set_prep_timestep_fct (size_t algebra_id, TAssFunc func)
 
- Protected Member Functions inherited from ug::IElemError< class >
void clear_add_fct ()
 
void clear_add_fct (ReferenceObjectID id)
 
- Protected Member Functions inherited from ug::IElemDiscBase< class >
virtual void approximation_space_changed ()
 
void set_function_pattern (ConstSmartPtr< FunctionPattern > fctPatt)
 
void update_function_index_mapping ()
 
- Protected Member Functions inherited from IElemEstimatorFuncs< IElemDisc< TDomain >, TDomain >
void clear_add_fct ()
 
void clear_add_fct (ReferenceObjectID id)
 
void remove_compute_err_est_A_elem (ReferenceObjectID id)
 
void remove_compute_err_est_M_elem (ReferenceObjectID id)
 
void remove_compute_err_est_rhs_elem (ReferenceObjectID id)
 
void remove_fsh_err_est_elem_loop (ReferenceObjectID id)
 
void remove_prep_err_est_elem (ReferenceObjectID id)
 
void remove_prep_err_est_elem_loop (ReferenceObjectID id)
 
void set_compute_err_est_A_elem (ReferenceObjectID id, TAssFunc func)
 
void set_compute_err_est_M_elem (ReferenceObjectID id, TAssFunc func)
 
void set_compute_err_est_rhs_elem (ReferenceObjectID id, TAssFunc func)
 
void set_default_add_fct ()
 
void set_fsh_err_est_elem_loop (ReferenceObjectID id, TAssFunc func)
 
void set_prep_err_est_elem (ReferenceObjectID id, TAssFunc func)
 
void set_prep_err_est_elem_loop (ReferenceObjectID id, TAssFunc func)
 

Detailed Description

template<typename TDomain>
class ug::NavierStokes::NavierStokesBase< TDomain >

Finite Volume Element Discretization for the incompressible Navier-Stokes Equation.

This class implements the IElemDisc interface to provide element local assemblings for the incompressible Navier-Stokes equation.

The unknowns of the equation are:

  • \( \vec{u} \) velocity
  • \( p \) pressure.

The equation takes the form

\begin{align*} \frac{\partial \rho \vec{u}}{\partial t} - \nabla \left( \rho \nu (\nabla \vec{u} + (\nabla \vec{u})^T) \right) + \nabla \cdot \left( \rho \vec{u} \vec{u}^T \right) + \nabla p &= \vec{f}\\ \nabla \cdot (\rho \vec{u}) &= 0 \end{align*}

with

  • \( \rho \) is the constant density
  • \( \nu \) is the kinematic viscosity (temporarily constant, implement)
  • \( \vec{f} \equiv f(\vec{x},t) \) is a Source Term (not implemented yet)

The first equation models the conservation of momentum and is therefore referred to as the Momentum equation. The second equation models the conservation of mass and is known as the Mass continuity equation or simply Continuity equation.

In component-wise notation, the equation reads

\begin{align*} \frac{\partial \rho u_{d_1}}{\partial t} - \sum_{d_2 = 1}^{\text{dim}} \frac{\partial}{\partial x_{d_2}} \left( \rho \nu \left( \frac{\partial u_{d_1}}{\partial x_{d_2}} + \frac{\partial u_{d_2}}{\partial x_{d_1}} \right)\right) + \sum_{d_2 = 1}^{\text{dim}} \frac{\partial}{\partial x_{d_2}} \left( \rho u_{d_2} u_{d_1} \right) + \frac{\partial p}{\partial x_{d_1}} &= f_{d_1} \qquad \forall \quad d_1 = 1, \dots, \text{dim}\\ \sum_{d = 1}^{\text{dim}} \frac{\partial \rho u_d}{\partial x_{d}} &= 0 \end{align*}

Since the density is assumed to be constant, it set to \(\rho \equiv 1 \).

The finite volume element discretization uses a dual mesh consisting of Control Volumes \(\mathcal{B}_h\), that cover the domain. For each control volume \(B \in \mathcal{B}_h\) the following equation is solved

\begin{align*} \frac{\partial}{\partial t} \int_{B} \begin{pmatrix} \vec{u} \\ 0 \end{pmatrix} dV + \int_{\partial B} \begin{pmatrix} - \rho \nu \left(\nabla \vec{u} + (\nabla \vec{u})^T \right) \vec{n} + \vec{u} \vec{u}^T \vec{n} + p \vec{n} \\ \vec{u} \vec{n} \end{pmatrix} dS = \int_B \begin{pmatrix} \vec{f} \\ 0 \end{pmatrix} dV \end{align*}

where \( \vec{n}\) is the outer normal on the boundary of the control volume and \(\int_B \cdot \; dV \) and \(\int_{\partial B} \cdot \; dS \) are the integration over the control volume and the integration over the boundary of the control volume. By $f B_{sh} $f is denoted the control volume associated to a shape function (i.e. vertices, since we use P1 Lagrange ansatz functions), T usually denotes the Element.

In order to number the local unknowns, we use the following notation.

  • \( sh = 0, \dots, n_{sh} - 1\) loop the \(n_{sh}\) shape functions. For this implementation these are the corners of the element
  • \( d = 0, \dots, \text{dim} - 1 \) are the velocity component of each corner
  • P := dim indicates the pressure component

The access to local unknowns of local vectors and matrices is now given by

\begin{align*} &\mathbf{d}(d_1, sh), \mathbf{d}(\text{\_P\_}, sh),\\ &\mathcal{J}(d_1, sh_1, d_2, sh_2), \mathcal{J}(d_1, sh_1, \text{\_P\_}, sh_2), \end{align*}

Template Parameters
TDomainDomain
TAlgebraAlgebra

Member Typedef Documentation

◆ base_type

template<typename TDomain >
typedef IElemDisc<TDomain> ug::NavierStokes::NavierStokesBase< TDomain >::base_type
protected

Base class type.

◆ this_type

template<typename TDomain >
typedef NavierStokesBase<TDomain> ug::NavierStokes::NavierStokesBase< TDomain >::this_type
protected

own type

Constructor & Destructor Documentation

◆ NavierStokesBase() [1/2]

template<typename TDomain >
ug::NavierStokes::NavierStokesBase< TDomain >::NavierStokesBase ( const char *  functions,
const char *  subsets 
)

Constructor (setting default values)

◆ NavierStokesBase() [2/2]

template<typename TDomain >
ug::NavierStokes::NavierStokesBase< TDomain >::NavierStokesBase ( const std::vector< std::string > &  vFct,
const std::vector< std::string > &  vSubset 
)

Constructor (setting default values)

Member Function Documentation

◆ disc_type()

◆ kinematic_viscosity()

◆ requests_local_time_series()

template<typename TDomain >
virtual bool ug::NavierStokes::NavierStokesBase< TDomain >::requests_local_time_series ( )
inlinevirtual

◆ set_exact_jacobian() [1/2]

template<typename TDomain >
void ug::NavierStokes::NavierStokesBase< TDomain >::set_exact_jacobian ( bool  bExactJacobian)
inline

sets if the exact jacobian is computed (fixpoint approximation else)

References ug::NavierStokes::NavierStokesBase< TDomain >::m_bFullNewtonFactor.

◆ set_exact_jacobian() [2/2]

template<typename TDomain >
void ug::NavierStokes::NavierStokesBase< TDomain >::set_exact_jacobian ( number  fullNewtonFactor)
inline

◆ set_kinematic_viscosity() [1/2]

template<typename TDomain >
void ug::NavierStokes::NavierStokesBase< TDomain >::set_kinematic_viscosity ( number  val)

sets the kinematic viscosity

This method sets the kinematic viscosity value.

Parameters
[in]datakinematic Viscosity

References make_sp().

◆ set_kinematic_viscosity() [2/2]

◆ set_source() [1/2]

template<typename TDomain >
void ug::NavierStokes::NavierStokesBase< TDomain >::set_source ( const std::vector< number > &  vSource)

sets the source function

This method sets the source value. A zero value is assumed as default.

Parameters
[in]datasource data

◆ set_source() [2/2]

Member Data Documentation

◆ dim

template<typename TDomain >
const int ug::NavierStokes::NavierStokesBase< TDomain >::dim = base_type::dim
static

World dimension.

◆ m_bFullNewtonFactor

template<typename TDomain >
number ug::NavierStokes::NavierStokesBase< TDomain >::m_bFullNewtonFactor
protected

factor for exact jacobian, (1 for exact jacobian, 0 for fix point)

Referenced by ug::NavierStokes::NavierStokesBase< TDomain >::set_exact_jacobian().


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