Plugins
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Finite Volume Element Discretization for the incompressible Navier-Stokes Equation. More...
#include <incompressible_navier_stokes_base.h>
Public Member Functions | |
virtual SmartPtr< CplUserData< number, dim > > | density ()=0 |
returns density More... | |
IncompressibleNavierStokesBase (const char *functions, const char *subsets) | |
IncompressibleNavierStokesBase (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... | |
virtual SmartPtr< CplUserData< number, dim > > | kinematic_viscosity ()=0 |
returns kinematic viscosity More... | |
virtual void | set_density (SmartPtr< CplUserData< number, dim > > user)=0 |
sets the density More... | |
void | set_density (number val) |
sets the kinematic viscosity More... | |
Public Member Functions inherited from ug::NavierStokes::NavierStokesBase< TDomain > | |
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) | |
void | set_kinematic_viscosity (number val) |
sets the kinematic viscosity 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 FunctionGroup & | function_group () const |
ConstSmartPtr< FunctionPattern > | function_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 LocalVectorTimeSeries * | local_time_solutions () const |
const FunctionIndexMapping & | map () 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_type & | subset_handler () |
const TDomain::subset_handler_type & | subset_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::NavierStokes::NavierStokesBase< TDomain > | |
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 NavierStokesBase< TDomain > | base_type |
Base class type. More... | |
typedef IncompressibleNavierStokesBase< TDomain > | this_type |
own type More... | |
Protected Types inherited from ug::NavierStokes::NavierStokesBase< TDomain > | |
typedef IElemDisc< TDomain > | base_type |
Base class type. More... | |
typedef NavierStokesBase< TDomain > | this_type |
own type More... | |
bool | m_bPecletBlend |
flag if using Peclet Blending More... | |
number | m_gradDivFactor |
factor for div grad stabilization More... | |
bool | m_bStokes |
flag if solving the Stokes equation More... | |
bool | m_bLaplace |
flag if using only laplace term More... | |
SmartPtr< DataExport< MathVector< dim >, dim > > | m_exVelocity |
Export for the velocity. More... | |
SmartPtr< DataExport< MathMatrix< dim, dim >, dim > > | m_exVelocityGrad |
Export for the velocity gradient. More... | |
number | m_bFullNewtonFactor |
factor for exact jacobian, (1 for exact jacobian, 0 for fix point) More... | |
virtual void | set_source (SmartPtr< CplUserData< MathVector< dim >, dim > > user)=0 |
sets the source function More... | |
void | set_stokes (bool Stokes) |
switches the convective terms off (to solve the Stokes equation) More... | |
bool | stokes () |
flag if using Peclet Blending More... | |
void | set_laplace (bool bLaplace) |
sets assembling of diffusive term to laplace More... | |
bool | laplace () |
flag if using Peclet Blending More... | |
void | set_peclet_blend (bool pecletBlend) |
sets if peclet blending is used in momentum equation More... | |
void | set_grad_div (number factor) |
flag if using Peclet Blending More... | |
virtual bool | requests_local_time_series () |
returns if local time series is needed More... | |
virtual std::string | disc_type () const =0 |
returns string identifying disc type More... | |
SmartPtr< CplUserData< MathVector< dim >, dim > > | velocity () |
returns the export of the velocity More... | |
SmartPtr< CplUserData< MathMatrix< dim, dim >, dim > > | velocity_grad () |
returns the export of the velocity gradient More... | |
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:
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
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.
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*}
TDomain | Domain |
TAlgebra | Algebra |
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Base class type.
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own type
ug::NavierStokes::IncompressibleNavierStokesBase< TDomain >::IncompressibleNavierStokesBase | ( | const char * | functions, |
const char * | subsets | ||
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Constructor (setting default values)
References ug::NavierStokes::IncompressibleNavierStokesBase< TDomain >::dim, ug::NavierStokes::IncompressibleNavierStokesBase< TDomain >::m_exVelocity, ug::NavierStokes::IncompressibleNavierStokesBase< TDomain >::m_exVelocityGrad, and make_sp().
ug::NavierStokes::IncompressibleNavierStokesBase< TDomain >::IncompressibleNavierStokesBase | ( | const std::vector< std::string > & | vFct, |
const std::vector< std::string > & | vSubset | ||
) |
Constructor (setting default values)
References ug::NavierStokes::IncompressibleNavierStokesBase< TDomain >::dim, ug::NavierStokes::IncompressibleNavierStokesBase< TDomain >::m_exVelocity, ug::NavierStokes::IncompressibleNavierStokesBase< TDomain >::m_exVelocityGrad, and make_sp().
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returns string identifying disc type
Implements ug::NavierStokes::NavierStokesBase< TDomain >.
Implemented in ug::NavierStokes::NavierStokesFVCR< TDomain >, ug::NavierStokes::NavierStokesFV1< TDomain >, ug::NavierStokes::NavierStokesFV< TDomain >, and ug::NavierStokes::NavierStokesFE< TDomain >.
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returns kinematic viscosity
Implements ug::NavierStokes::NavierStokesBase< TDomain >.
Implemented in ug::NavierStokes::NavierStokesFVCR< TDomain >, ug::NavierStokes::NavierStokesFV1< TDomain >, ug::NavierStokes::NavierStokesFV< TDomain >, and ug::NavierStokes::NavierStokesFE< TDomain >.
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flag if using Peclet Blending
References ug::NavierStokes::IncompressibleNavierStokesBase< TDomain >::m_bLaplace.
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returns if local time series is needed
Reimplemented from ug::NavierStokes::NavierStokesBase< TDomain >.
Reimplemented in ug::NavierStokes::NavierStokesFV< TDomain >.
void ug::NavierStokes::IncompressibleNavierStokesBase< TDomain >::set_density | ( | number | val | ) |
sets the kinematic viscosity
This method sets the kinematic viscosity value.
[in] | data | kinematic Viscosity |
References make_sp().
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sets the density
This method sets the density value.
[in] | data | density |
Implemented in ug::NavierStokes::NavierStokesFVCR< TDomain >, ug::NavierStokes::NavierStokesFV1< TDomain >, ug::NavierStokes::NavierStokesFV< TDomain >, and ug::NavierStokes::NavierStokesFE< TDomain >.
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flag if using Peclet Blending
References ug::NavierStokes::IncompressibleNavierStokesBase< TDomain >::m_gradDivFactor.
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sets the kinematic viscosity
This method sets the kinematic viscosity value.
[in] | data | kinematic Viscosity |
Implements ug::NavierStokes::NavierStokesBase< TDomain >.
Implemented in ug::NavierStokes::NavierStokesFVCR< TDomain >, ug::NavierStokes::NavierStokesFV1< TDomain >, ug::NavierStokes::NavierStokesFV< TDomain >, and ug::NavierStokes::NavierStokesFE< TDomain >.
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sets assembling of diffusive term to laplace
Flag to indicate, that in the diffusive term only the laplacian should be computed. This is valid only in cases, where the viscosity is constant, since then it holds that
div ( \nu (grad) v + (grad v)^T ) = \nu laplace v + \nu grad( div v ) = \nu laplace v
for incompressible flow (i.e. div v = 0).
References ug::NavierStokes::IncompressibleNavierStokesBase< TDomain >::m_bLaplace.
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sets if peclet blending is used in momentum equation
References ug::NavierStokes::IncompressibleNavierStokesBase< TDomain >::m_bPecletBlend.
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sets the source function
This method sets the source value. A zero value is assumed as default.
[in] | data | source data |
Implements ug::NavierStokes::NavierStokesBase< TDomain >.
Implemented in ug::NavierStokes::NavierStokesFVCR< TDomain >, ug::NavierStokes::NavierStokesFV1< TDomain >, ug::NavierStokes::NavierStokesFV< TDomain >, and ug::NavierStokes::NavierStokesFE< TDomain >.
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switches the convective terms off (to solve the Stokes equation)
[in] | Stokes | true to solve Stokes (i.e. without the convective terms) |
References ug::NavierStokes::IncompressibleNavierStokesBase< TDomain >::m_bStokes.
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flag if using Peclet Blending
References ug::NavierStokes::IncompressibleNavierStokesBase< TDomain >::m_bStokes.
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returns the export of the velocity
References ug::NavierStokes::IncompressibleNavierStokesBase< TDomain >::m_exVelocity.
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returns the export of the velocity gradient
References ug::NavierStokes::IncompressibleNavierStokesBase< TDomain >::m_exVelocityGrad.
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World dimension.
Referenced by ug::NavierStokes::IncompressibleNavierStokesBase< TDomain >::IncompressibleNavierStokesBase().
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factor for exact jacobian, (1 for exact jacobian, 0 for fix point)
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flag if using only laplace term
Referenced by ug::NavierStokes::IncompressibleNavierStokesBase< TDomain >::laplace(), and ug::NavierStokes::IncompressibleNavierStokesBase< TDomain >::set_laplace().
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flag if using Peclet Blending
Referenced by ug::NavierStokes::IncompressibleNavierStokesBase< TDomain >::set_peclet_blend().
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flag if solving the Stokes equation
Referenced by ug::NavierStokes::IncompressibleNavierStokesBase< TDomain >::set_stokes(), and ug::NavierStokes::IncompressibleNavierStokesBase< TDomain >::stokes().
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Export for the velocity.
Referenced by ug::NavierStokes::IncompressibleNavierStokesBase< TDomain >::IncompressibleNavierStokesBase(), and ug::NavierStokes::IncompressibleNavierStokesBase< TDomain >::velocity().
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Export for the velocity gradient.
Referenced by ug::NavierStokes::IncompressibleNavierStokesBase< TDomain >::IncompressibleNavierStokesBase(), and ug::NavierStokes::IncompressibleNavierStokesBase< TDomain >::velocity_grad().
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factor for div grad stabilization
Referenced by ug::NavierStokes::IncompressibleNavierStokesBase< TDomain >::set_grad_div().