Navier-Stokes equations. Derived from Euler for the convective terms, which is derived from PhysicsBase. More...

#include <navier_stokes.h>

Inheritance diagram for PHiLiP::Physics::NavierStokes< dim, nstate, real >:

Collaboration diagram for PHiLiP::Physics::NavierStokes< dim, nstate, real >:

Public Types
using	thermal_boundary_condition_enum = Parameters::NavierStokesParam::ThermalBoundaryCondition

using	two_point_num_flux_enum = Parameters::AllParameters::TwoPointNumericalFlux

Public Types inherited from PHiLiP::Physics::Euler< dim, nstate, real >
using	two_point_num_flux_enum = Parameters::AllParameters::TwoPointNumericalFlux

Public Types inherited from PHiLiP::Physics::PhysicsBase< dim, nstate, real >
using	NonPhysicalBehaviorEnum = Parameters::AllParameters::NonPhysicalBehaviorEnum

Public Member Functions
	NavierStokes (const Parameters::AllParameters *const parameters_input, const double ref_length, const double gamma_gas, const double mach_inf, const double angle_of_attack, const double side_slip_angle, const double prandtl_number, const double reynolds_number_inf, const bool use_constant_viscosity, const double constant_viscosity, const double temperature_inf=273.15, const double isothermal_wall_temperature=1.0, const thermal_boundary_condition_enum thermal_boundary_condition_type=thermal_boundary_condition_enum::adiabatic, std::shared_ptr< ManufacturedSolutionFunction< dim, real > > manufactured_solution_function=nullptr, const two_point_num_flux_enum two_point_num_flux_type=two_point_num_flux_enum::KG)
	Constructor.

template<typename real2 >
std::array< dealii::Tensor< 1, dim, real2 >, nstate >	convert_conservative_gradient_to_primitive_gradient (const std::array< real2, nstate > &conservative_soln, const std::array< dealii::Tensor< 1, dim, real2 >, nstate > &conservative_soln_gradient) const

template<typename real2 >
dealii::Tensor< 1, dim, real2 >	compute_temperature_gradient (const std::array< real2, nstate > &primitive_soln, const std::array< dealii::Tensor< 1, dim, real2 >, nstate > &primitive_soln_gradient) const

template<typename real2 >
real2	compute_viscosity_coefficient (const std::array< real2, nstate > &primitive_soln) const

template<typename real2 >
real2	compute_viscosity_coefficient_sutherlands_law (const std::array< real2, nstate > &primitive_soln) const

template<typename real2 >
real2	scale_viscosity_coefficient (const real2 viscosity_coefficient) const

template<typename real2 >
real2	compute_scaled_viscosity_coefficient (const std::array< real2, nstate > &primitive_soln) const

template<typename real2 >
real2	compute_scaled_heat_conductivity_given_scaled_viscosity_coefficient_and_prandtl_number (const real2 scaled_viscosity_coefficient, const double prandtl_number_input) const

template<typename real2 >
real2	compute_scaled_heat_conductivity (const std::array< real2, nstate > &primitive_soln) const

template<typename real2 >
dealii::Tensor< 1, dim, real2 >	compute_heat_flux (const std::array< real2, nstate > &primitive_soln, const std::array< dealii::Tensor< 1, dim, real2 >, nstate > &primitive_soln_gradient) const

template<typename real2 >
dealii::Tensor< 1, dim, real2 >	compute_heat_flux_given_scaled_heat_conductivity_and_temperature_gradient (const real2 scaled_heat_conductivity, const dealii::Tensor< 1, dim, real2 > &temperature_gradient) const

template<typename real2 >
dealii::Tensor< 1, 3, real2 >	compute_vorticity (const std::array< real2, nstate > &conservative_soln, const std::array< dealii::Tensor< 1, dim, real2 >, nstate > &conservative_soln_gradient) const
	Evaluate vorticity from conservative variables and gradient of conservative variables.

real	compute_vorticity_magnitude_sqr (const std::array< real, nstate > &conservative_soln, const std::array< dealii::Tensor< 1, dim, real >, nstate > &conservative_soln_gradient) const
	Evaluate vorticity magnitude squared from conservative variables and gradient of conservative variables.

real	compute_vorticity_magnitude (const std::array< real, nstate > &conservative_soln, const std::array< dealii::Tensor< 1, dim, real >, nstate > &conservative_soln_gradient) const
	Evaluate vorticity magnitude from conservative variables and gradient of conservative variables.

real	compute_enstrophy (const std::array< real, nstate > &conservative_soln, const std::array< dealii::Tensor< 1, dim, real >, nstate > &conservative_soln_gradient) const
	Evaluate enstrophy from conservative variables and gradient of conservative variables.

real	compute_vorticity_based_dissipation_rate_from_integrated_enstrophy (const real integrated_enstrophy) const

real	compute_pressure_dilatation (const std::array< real, nstate > &conservative_soln, const std::array< dealii::Tensor< 1, dim, real >, nstate > &conservative_soln_gradient) const

dealii::Tensor< 2, dim, real >	compute_deviatoric_strain_rate_tensor (const std::array< real, nstate > &conservative_soln, const std::array< dealii::Tensor< 1, dim, real >, nstate > &conservative_soln_gradient) const

real	compute_deviatoric_strain_rate_tensor_magnitude_sqr (const std::array< real, nstate > &conservative_soln, const std::array< dealii::Tensor< 1, dim, real >, nstate > &conservative_soln_gradient) const
	Evaluate the square of the deviatoric strain-rate tensor magnitude (i.e. double dot product) from conservative variables and gradient of conservative variables.

real	compute_deviatoric_strain_rate_tensor_based_dissipation_rate_from_integrated_deviatoric_strain_rate_tensor_magnitude_sqr (const real integrated_deviatoric_strain_rate_tensor_magnitude_sqr) const

template<typename real2 >
dealii::Tensor< 2, dim, real2 >	extract_velocities_gradient_from_primitive_solution_gradient (const std::array< dealii::Tensor< 1, dim, real2 >, nstate > &primitive_soln_gradient) const

template<typename real2 >
dealii::Tensor< 2, dim, real2 >	compute_strain_rate_tensor (const dealii::Tensor< 2, dim, real2 > &vel_gradient) const

real	compute_strain_rate_tensor_magnitude_sqr (const std::array< real, nstate > &conservative_soln, const std::array< dealii::Tensor< 1, dim, real >, nstate > &conservative_soln_gradient) const
	Evaluate the square of the strain-rate tensor magnitude (i.e. double dot product) from conservative variables and gradient of conservative variables.

real	compute_strain_rate_tensor_based_dissipation_rate_from_integrated_strain_rate_tensor_magnitude_sqr (const real integrated_strain_rate_tensor_magnitude_sqr) const

template<typename real2 >
dealii::Tensor< 2, dim, real2 >	compute_viscous_stress_tensor_via_scaled_viscosity_and_strain_rate_tensor (const real2 scaled_viscosity_coefficient, const dealii::Tensor< 2, dim, real2 > &strain_rate_tensor) const

template<typename real2 >
dealii::Tensor< 2, dim, real2 >	compute_viscous_stress_tensor (const std::array< real2, nstate > &primitive_soln, const std::array< dealii::Tensor< 1, dim, real2 >, nstate > &primitive_soln_gradient) const

std::array< dealii::Tensor< 1, dim, real >, nstate >	dissipative_flux (const std::array< real, nstate > &conservative_soln, const std::array< dealii::Tensor< 1, dim, real >, nstate > &solution_gradient) const override

dealii::Tensor< 1, dim, real >	compute_scaled_viscosity_gradient (const std::array< real, nstate > &primitive_soln, const dealii::Tensor< 1, dim, real > &temperature_gradient) const

dealii::Tensor< 2, nstate, real >	dissipative_flux_directional_jacobian (const std::array< real, nstate > &conservative_soln, const std::array< dealii::Tensor< 1, dim, real >, nstate > &solution_gradient, const dealii::Tensor< 1, dim, real > &normal) const

dealii::Tensor< 2, nstate, real >	dissipative_flux_directional_jacobian_wrt_gradient_component (const std::array< real, nstate > &conservative_soln, const std::array< dealii::Tensor< 1, dim, real >, nstate > &solution_gradient, const dealii::Tensor< 1, dim, real > &normal, const int d_gradient) const

std::array< real, nstate >	dissipative_source_term (const dealii::Point< dim, real > &pos) const
	Dissipative flux contribution to the source term.

std::array< real, nstate >	source_term (const dealii::Point< dim, real > &pos, const std::array< real, nstate > &conservative_soln, const real current_time) const override
	Source term is zero or depends on manufactured solution.

dealii::Tensor< 2, nstate, real >	convective_flux_directional_jacobian_via_dfad (std::array< real, nstate > &conservative_soln, const dealii::Tensor< 1, dim, real > &normal) const

real	compute_scaled_viscosity_coefficient_derivative_wrt_temperature_via_dfad (std::array< real, nstate > &conservative_soln) const

template<typename real2 >
std::array< dealii::Tensor< 1, dim, real2 >, nstate >	dissipative_flux_given_velocities_viscous_stress_tensor_and_heat_flux (const dealii::Tensor< 1, dim, real2 > &vel, const dealii::Tensor< 2, dim, real2 > &viscous_stress_tensor, const dealii::Tensor< 1, dim, real2 > &heat_flux) const

Public Member Functions inherited from PHiLiP::Physics::Euler< dim, nstate, real >
	Euler (const Parameters::AllParameters *const parameters_input, const double ref_length, const double gamma_gas, const double mach_inf, const double angle_of_attack, const double side_slip_angle, std::shared_ptr< ManufacturedSolutionFunction< dim, real > > manufactured_solution_function=nullptr, const two_point_num_flux_enum two_point_num_flux_type=two_point_num_flux_enum::KG, const bool has_nonzero_diffusion=false, const bool has_nonzero_physical_source=false)
	Constructor.

std::array< dealii::Tensor< 1, dim, real >, nstate >	convective_flux (const std::array< real, nstate > &conservative_soln) const override
	Convective flux: \( \mathbf{F}_{conv} \).

std::array< real, nstate >	convective_normal_flux (const std::array< real, nstate > &conservative_soln, const dealii::Tensor< 1, dim, real > &normal) const
	Convective normal flux: \( \mathbf{F}_{conv} \cdot \hat{n} \).

dealii::Tensor< 2, nstate, real >	convective_flux_directional_jacobian (const std::array< real, nstate > &conservative_soln, const dealii::Tensor< 1, dim, real > &normal) const
	Convective flux Jacobian: \( \frac{\partial \mathbf{F}_{conv}}{\partial w} \cdot \mathbf{n} \).

std::array< real, nstate >	convective_eigenvalues (const std::array< real, nstate > &, const dealii::Tensor< 1, dim, real > &) const override
	Spectral radius of convective term Jacobian is 'c'.

real	max_convective_eigenvalue (const std::array< real, nstate > &soln) const override
	Maximum convective eigenvalue.

real	max_convective_normal_eigenvalue (const std::array< real, nstate > &soln, const dealii::Tensor< 1, dim, real > &normal) const override
	Maximum convective normal eigenvalue (used in Lax-Friedrichs) More...

real	max_viscous_eigenvalue (const std::array< real, nstate > &soln) const override
	Maximum viscous eigenvalue.

std::array< dealii::Tensor< 1, dim, real >, nstate >	dissipative_flux (const std::array< real, nstate > &conservative_soln, const std::array< dealii::Tensor< 1, dim, real >, nstate > &solution_gradient, const dealii::types::global_dof_index cell_index) const
	Dissipative flux: 0.

std::array< real, nstate >	source_term (const dealii::Point< dim, real > &pos, const std::array< real, nstate > &conservative_soln, const real current_time, const dealii::types::global_dof_index cell_index) const
	Source term is zero or depends on manufactured solution.

std::array< real, nstate >	convective_source_term (const dealii::Point< dim, real > &pos) const
	Convective flux contribution to the source term.

template<typename real2 >
std::array< real2, nstate >	convert_conservative_to_primitive (const std::array< real2, nstate > &conservative_soln) const

std::array< real, nstate >	convert_primitive_to_conservative (const std::array< real, nstate > &primitive_soln) const

template<typename real2 >
real2	compute_pressure (const std::array< real2, nstate > &conservative_soln) const
	Evaluate pressure from conservative variables.

template<typename real2 >
real2	compute_entropy (const real2 density, const real2 pressure) const
	Evaluate physical entropy = log(p ^{-}) from pressure and density.

real	compute_specific_enthalpy (const std::array< real, nstate > &conservative_soln, const real pressure) const
	Evaluate pressure from conservative variables.

real	compute_numerical_entropy_function (const std::array< real, nstate > &conservative_soln) const
	Compute numerical entropy function -rho s.

real	compute_sound (const std::array< real, nstate > &conservative_soln) const
	Evaluate speed of sound from conservative variables.

real	compute_sound (const real density, const real pressure) const
	Evaluate speed of sound from density and pressure.

template<typename real2 >
dealii::Tensor< 1, dim, real2 >	compute_velocities (const std::array< real2, nstate > &conservative_soln) const
	Evaluate velocities from conservative variables.

template<typename real2 >
real2	compute_velocity_squared (const dealii::Tensor< 1, dim, real2 > &velocities) const
	Given the velocity vector \( \mathbf{u} \), returns the dot-product \( \mathbf{u} \cdot \mathbf{u} \).

template<typename real2 >
dealii::Tensor< 1, dim, real2 >	extract_velocities_from_primitive (const std::array< real2, nstate > &primitive_soln) const
	Given primitive variables, returns velocities.

real	compute_total_energy (const std::array< real, nstate > &primitive_soln) const
	Given primitive variables, returns total energy. More...

real	compute_kinetic_energy_from_primitive_solution (const std::array< real, nstate > &primitive_soln) const
	Given primitive variables, returns kinetic energy.

real	compute_kinetic_energy_from_conservative_solution (const std::array< real, nstate > &conservative_soln) const
	Given conservative variables, returns kinetic energy.

real	compute_entropy_measure (const std::array< real, nstate > &conservative_soln) const
	Evaluate entropy from conservative variables. More...

real	compute_entropy_measure (const real density, const real pressure) const
	Evaluate entropy from density and pressure.

real	compute_mach_number (const std::array< real, nstate > &conservative_soln) const
	Given conservative variables, returns Mach number.

template<typename real2 >
real2	compute_temperature (const std::array< real2, nstate > &primitive_soln) const
	Given primitive variables, returns NON-DIMENSIONALIZED temperature using free-stream non-dimensionalization. More...

real	compute_density_from_pressure_temperature (const real pressure, const real temperature) const
	Given pressure and temperature, returns NON-DIMENSIONALIZED density using free-stream non-dimensionalization. More...

real	compute_temperature_from_density_pressure (const real density, const real pressure) const
	Given density and pressure, returns NON-DIMENSIONALIZED temperature using free-stream non-dimensionalization. More...

real	compute_pressure_from_density_temperature (const real density, const real temperature) const
	Given density and temperature, returns NON-DIMENSIONALIZED pressure using free-stream non-dimensionalization. More...

std::array< dealii::Tensor< 1, dim, real >, nstate >	convective_numerical_split_flux (const std::array< real, nstate > &conservative_soln1, const std::array< real, nstate > &conservative_soln2) const override
	Evaluates convective flux based on the chosen split form.

std::array< real, nstate >	compute_entropy_variables (const std::array< real, nstate > &conservative_soln) const

std::array< real, nstate >	compute_conservative_variables_from_entropy_variables (const std::array< real, nstate > &entropy_var) const

std::array< real, nstate >	compute_kinetic_energy_variables (const std::array< real, nstate > &conservative_soln) const
	Computes the kinetic energy variables.

real	compute_mean_density (const std::array< real, nstate > &conservative_soln1, const std::array< real, nstate > &convervative_soln2) const
	Mean density given two sets of conservative solutions. More...

real	compute_mean_pressure (const std::array< real, nstate > &conservative_soln1, const std::array< real, nstate > &convervative_soln2) const
	Mean pressure given two sets of conservative solutions. More...

dealii::Tensor< 1, dim, real >	compute_mean_velocities (const std::array< real, nstate > &conservative_soln1, const std::array< real, nstate > &convervative_soln2) const
	Mean velocities given two sets of conservative solutions. More...

real	compute_mean_specific_total_energy (const std::array< real, nstate > &conservative_soln1, const std::array< real, nstate > &convervative_soln2) const
	Mean specific total energy given two sets of conservative solutions. More...

void	boundary_face_values (const int, const dealii::Point< dim, real > &, const dealii::Tensor< 1, dim, real > &, const std::array< real, nstate > &, const std::array< dealii::Tensor< 1, dim, real >, nstate > &, std::array< real, nstate > &, std::array< dealii::Tensor< 1, dim, real >, nstate > &) const
	Boundary condition handler.

virtual dealii::Vector< double >	post_compute_derived_quantities_vector (const dealii::Vector< double > &uh, const std::vector< dealii::Tensor< 1, dim > > &duh, const std::vector< dealii::Tensor< 2, dim > > &dduh, const dealii::Tensor< 1, dim > &normals, const dealii::Point< dim > &evaluation_points) const
	For post processing purposes (update comment later)

virtual std::vector< std::string >	post_get_names () const
	For post processing purposes, sets the base names (with no prefix or suffix) of the computed quantities.

virtual std::vector< dealii::DataComponentInterpretation::DataComponentInterpretation >	post_get_data_component_interpretation () const
	For post processing purposes, sets the interpretation of each computed quantity as either scalar or vector.

virtual dealii::UpdateFlags	post_get_needed_update_flags () const
	For post processing purposes (update comment later)

Public Member Functions inherited from PHiLiP::Physics::PhysicsBase< dim, nstate, real >
	PhysicsBase (const Parameters::AllParameters *const parameters_input, const bool has_nonzero_diffusion_input, const bool has_nonzero_physical_source_input, const dealii::Tensor< 2, 3, double > input_diffusion_tensor=Parameters::ManufacturedSolutionParam::get_default_diffusion_tensor(), std::shared_ptr< ManufacturedSolutionFunction< dim, real > > manufactured_solution_function_input=nullptr)
	Default constructor that will set the constants.

	PhysicsBase (const Parameters::AllParameters *const parameters_input, const bool has_nonzero_diffusion_input, const bool has_nonzero_physical_source_input, std::shared_ptr< ManufacturedSolutionFunction< dim, real > > manufactured_solution_function_input=nullptr)
	Constructor that will call default constructor.

virtual	~PhysicsBase ()=default
	Virtual destructor required for abstract classes.

virtual std::array< real, nstate >	physical_source_term (const dealii::Point< dim, real > &pos, const std::array< real, nstate > &solution, const std::array< dealii::Tensor< 1, dim, real >, nstate > &solution_gradient, const dealii::types::global_dof_index cell_index) const
	Physical source term that does require differentiation.

virtual std::array< real, nstate >	artificial_source_term (const real viscosity_coefficient, const dealii::Point< dim, real > &pos, const std::array< real, nstate > &solution) const
	Artificial source term that does not require differentiation stemming from artificial dissipation.

virtual dealii::Vector< double >	post_compute_derived_quantities_scalar (const double &uh, const dealii::Tensor< 1, dim > &, const dealii::Tensor< 2, dim > &, const dealii::Tensor< 1, dim > &, const dealii::Point< dim > &) const
	Returns current scalar solution to be used by PhysicsPostprocessor to output current solution. More...

template<typename real2 >
real2	handle_non_physical_result (const std::string message="") const
	Function to handle nonphysical results. More...

Public Attributes
const double	viscosity_coefficient_inf
	Nondimensionalized viscosity coefficient at infinity.

const bool	use_constant_viscosity
	Flag to use constant viscosity instead of Sutherland's law of viscosity.

const double	constant_viscosity
	Nondimensionalized constant viscosity.

const double	prandtl_number
	Prandtl number.

const double	reynolds_number_inf
	Farfield (free stream) Reynolds number.

const double	isothermal_wall_temperature
	Nondimensionalized isothermal wall temperature.

const thermal_boundary_condition_enum	thermal_boundary_condition_type
	Thermal boundary condition type (adiabatic or isothermal)

Public Attributes inherited from PHiLiP::Physics::Euler< dim, nstate, real >
const double	ref_length
	Reference length.

const double	gam
	Constant heat capacity ratio of fluid.

const double	gamm1
	Constant heat capacity ratio (Gamma-1.0) used often.

const double	density_inf

const double	mach_inf
	Farfield Mach number.

const double	mach_inf_sqr

const double	angle_of_attack
	Angle of attack. More...

const double	side_slip_angle
	Sideslip angle. More...

const double	sound_inf
	Non-dimensionalized sound* at infinity.

const double	pressure_inf
	Non-dimensionalized pressure* at infinity.

const double	entropy_inf
	Entropy measure at infinity.

const two_point_num_flux_enum	two_point_num_flux_type
	Two point numerical flux type (for split form)

double	temperature_inf
	Non-dimensionalized temperature* at infinity. Should equal 1/density*(inf)

double	dynamic_pressure_inf
	Non-dimensionalized dynamic pressure* at infinity.

dealii::Tensor< 1, dim, double >	velocities_inf
	Non-dimensionalized Velocity vector at farfield. More...

Public Attributes inherited from PHiLiP::Physics::PhysicsBase< dim, nstate, real >
const bool	has_nonzero_diffusion
	Flag to signal that diffusion term is non-zero.

const bool	has_nonzero_physical_source
	Flag to signal that physical source term is non-zero.

const Parameters::AllParameters *const	all_parameters
	Pointer to parameters object.

const NonPhysicalBehaviorEnum	non_physical_behavior_type
	Determines type of nonphysical behavior.

std::shared_ptr< ManufacturedSolutionFunction< dim, real > >	manufactured_solution_function
	Manufactured solution function.

const double	BIG_NUMBER = 1e100
	BIG_NUMBER which is returned in place of NaN according to handle_non_physical_result() More...

Protected Member Functions
template<typename real2 >
std::array< dealii::Tensor< 1, dim, real2 >, nstate >	dissipative_flux_templated (const std::array< real2, nstate > &conservative_soln, const std::array< dealii::Tensor< 1, dim, real2 >, nstate > &solution_gradient) const

void	boundary_wall (const dealii::Tensor< 1, dim, real > &normal_int, const std::array< real, nstate > &soln_int, const std::array< dealii::Tensor< 1, dim, real >, nstate > &soln_grad_int, std::array< real, nstate > &soln_bc, std::array< dealii::Tensor< 1, dim, real >, nstate > &soln_grad_bc) const override

void	boundary_manufactured_solution (const dealii::Point< dim, real > &pos, const dealii::Tensor< 1, dim, real > &normal_int, const std::array< real, nstate > &soln_int, const std::array< dealii::Tensor< 1, dim, real >, nstate > &soln_grad_int, std::array< real, nstate > &soln_bc, std::array< dealii::Tensor< 1, dim, real >, nstate > &soln_grad_bc) const override
	Evaluate the manufactured solution boundary conditions.

Protected Member Functions inherited from PHiLiP::Physics::Euler< dim, nstate, real >
template<typename real2 >
bool	check_positive_quantity (real2 &quantity, const std::string qty_name) const
	Check positive quantity and modify it according to handle_non_physical_result() More...

void	boundary_slip_wall (const dealii::Tensor< 1, dim, real > &normal_int, const std::array< real, nstate > &soln_int, const std::array< dealii::Tensor< 1, dim, real >, nstate > &soln_grad_int, std::array< real, nstate > &soln_bc, std::array< dealii::Tensor< 1, dim, real >, nstate > &soln_grad_bc) const

void	boundary_pressure_outflow (const real total_inlet_pressure, const real back_pressure, const std::array< real, nstate > &soln_int, std::array< real, nstate > &soln_bc) const

void	boundary_inflow (const real total_inlet_pressure, const real total_inlet_temperature, const dealii::Tensor< 1, dim, real > &normal_int, const std::array< real, nstate > &soln_int, std::array< real, nstate > &soln_bc) const

void	boundary_riemann (const dealii::Tensor< 1, dim, real > &normal_int, const std::array< real, nstate > &soln_int, std::array< real, nstate > &soln_bc) const

void	boundary_farfield (std::array< real, nstate > &soln_bc) const
	Simple farfield boundary conditions based on freestream values.

void	boundary_p0_extrapolation (const std::array< real, nstate > &soln_int, std::array< real, nstate > &soln_bc, std::array< dealii::Tensor< 1, dim, real >, nstate > &soln_grad_bc) const
	p0 extrapolation at the boundary

void	boundary_custom (std::array< real, nstate > &soln_bc) const
	Custom boundary conditions for the left boundary of the astrophysical mach jet case where it is not hypersonic inflow.

void	boundary_astrophysical_inflow (std::array< real, nstate > &soln_bc) const
	Boundary conditions based on user-defined values.

std::array< real, nstate >	get_manufactured_solution_value (const dealii::Point< dim, real > &pos) const
	Get manufactured solution value.

std::array< dealii::Tensor< 1, dim, real >, nstate >	get_manufactured_solution_gradient (const dealii::Point< dim, real > &pos) const
	Get manufactured solution gradient.

std::array< dealii::Tensor< 1, dim, real >, nstate >	convective_numerical_split_flux_kennedy_gruber (const std::array< real, nstate > &conservative_soln1, const std::array< real, nstate > &conservative_soln2) const

std::array< real, nstate >	compute_ismail_roe_parameter_vector_from_primitive (const std::array< real, nstate > &primitive_soln) const
	Compute Ismail-Roe parameter vector from primitive solution.

real	compute_ismail_roe_logarithmic_mean (const real val1, const real val2) const
	Compute Ismail-Roe logarithmic mean.

std::array< dealii::Tensor< 1, dim, real >, nstate >	convective_numerical_split_flux_ismail_roe (const std::array< real, nstate > &conservative_soln1, const std::array< real, nstate > &conservative_soln2) const

std::array< dealii::Tensor< 1, dim, real >, nstate >	convective_numerical_split_flux_chandrashekar (const std::array< real, nstate > &conservative_soln1, const std::array< real, nstate > &conservative_soln2) const
	Chandrashekar entropy conserving flux.

std::array< dealii::Tensor< 1, dim, real >, nstate >	convective_numerical_split_flux_ranocha (const std::array< real, nstate > &conservative_soln1, const std::array< real, nstate > &conservative_soln2) const
	Ranocha pressure equilibrium preserving, entropy and energy conserving flux.

Protected Attributes

const double	sutherlands_temperature
	Sutherland's temperature. Units: [K]. More...

const double	freestream_temperature
	Freestream temperature. Units: [K].

const double	temperature_ratio
	Ratio of Sutherland's temperature to freestream temperature.

Protected Attributes inherited from PHiLiP::Physics::PhysicsBase< dim, nstate, real >
dealii::ConditionalOStream	pcout
	ConditionalOStream. More...

dealii::Tensor< 2, dim, double >	diffusion_tensor
	Anisotropic diffusion matrix. More...

Private Member Functions
real	get_tensor_magnitude_sqr (const dealii::Tensor< 2, dim, real > &tensor) const
	Returns the square of the magnitude of the tensor (i.e. the double dot product of a tensor with itself)

Detailed Description

template<int dim, int nstate, typename real>
class PHiLiP::Physics::NavierStokes< dim, nstate, real >

Navier-Stokes equations. Derived from Euler for the convective terms, which is derived from PhysicsBase.

Definition at line 12 of file navier_stokes.h.

Member Function Documentation

◆ boundary_wall()

template<int dim, int nstate, typename real>

void PHiLiP::Physics::NavierStokes< dim, nstate, real >::boundary_wall	(	const dealii::Tensor< 1, dim, real > &	normal_int,
		const std::array< real, nstate > &	soln_int,
		const std::array< dealii::Tensor< 1, dim, real >, nstate > &	soln_grad_int,
		std::array< real, nstate > &	soln_bc,
		std::array< dealii::Tensor< 1, dim, real >, nstate > &	soln_grad_bc
	)		const

overrideprotectedvirtual

No-slip wall boundary conditions

Given by equations 460-461 of the following paper:
* Hartmann, Ralf. "Numerical analysis of higher order discontinuous Galerkin finite element methods." (2008): 1-107.

Reimplemented from PHiLiP::Physics::Euler< dim, nstate, real >.

Definition at line 886 of file navier_stokes.cpp.

◆ compute_deviatoric_strain_rate_tensor()

template<int dim, int nstate, typename real>

dealii::Tensor< 2, dim, real > PHiLiP::Physics::NavierStokes< dim, nstate, real >::compute_deviatoric_strain_rate_tensor	(	const std::array< real, nstate > &	conservative_soln,
		const std::array< dealii::Tensor< 1, dim, real >, nstate > &	conservative_soln_gradient
	)		const

Evaluate the deviatoric strain-rate tensor from conservative variables and gradient of conservative variables – Reference: de la Llave Plata et al. (2019). "On the performance of a high-order multiscale DG approach to LES at increasing Reynolds number."

Definition at line 347 of file navier_stokes.cpp.

◆ compute_deviatoric_strain_rate_tensor_based_dissipation_rate_from_integrated_deviatoric_strain_rate_tensor_magnitude_sqr()

template<int dim, int nstate, typename real>

real PHiLiP::Physics::NavierStokes< dim, nstate, real >::compute_deviatoric_strain_rate_tensor_based_dissipation_rate_from_integrated_deviatoric_strain_rate_tensor_magnitude_sqr ( const real integrated_deviatoric_strain_rate_tensor_magnitude_sqr ) const

Evaluate non-dimensional theoretical deviatoric strain-rate tensor based dissipation rate from integrated deviatoric strain-rate tensor magnitude squared. – Reference: Cox, Christopher, et al. "Accuracy, stability, and performance comparison between the spectral difference and flux reconstruction schemes." Computers & Fluids 221 (2021): 104922. – Equation (57a) with free-stream nondimensionalization applied

Definition at line 404 of file navier_stokes.cpp.

◆ compute_heat_flux()

template<int dim, int nstate, typename real >

template<typename real2 >

dealii::Tensor< 1, dim, real2 > PHiLiP::Physics::NavierStokes< dim, nstate, real >::compute_heat_flux	(	const std::array< real2, nstate > &	primitive_soln,
		const std::array< dealii::Tensor< 1, dim, real2 >, nstate > &	primitive_soln_gradient
	)		const

Nondimensionalized heat flux, q* Reference: Masatsuka 2018 "I do like CFD", p.148, eq.(4.14.13)

Definition at line 214 of file navier_stokes.cpp.

◆ compute_heat_flux_given_scaled_heat_conductivity_and_temperature_gradient()

template<int dim, int nstate, typename real >

template<typename real2 >

template dealii::Tensor< 1, PHILIP_DIM, FadType > PHiLiP::Physics::NavierStokes< dim, nstate, real >::compute_heat_flux_given_scaled_heat_conductivity_and_temperature_gradient< FadType >	(	const real2	scaled_heat_conductivity,
		const dealii::Tensor< 1, dim, real2 > &	temperature_gradient
	)		const

Nondimensionalized heat flux, q*, given the scaled heat conductivity and temperature gradient Reference: Masatsuka 2018 "I do like CFD", p.148, eq.(4.14.13)

Definition at line 231 of file navier_stokes.cpp.

◆ compute_pressure_dilatation()

template<int dim, int nstate, typename real>

real PHiLiP::Physics::NavierStokes< dim, nstate, real >::compute_pressure_dilatation	(	const std::array< real, nstate > &	conservative_soln,
		const std::array< dealii::Tensor< 1, dim, real >, nstate > &	conservative_soln_gradient
	)		const

Evaluate pressure dilatation from conservative variables and gradient of conservative variables – Reference: Cox, Christopher, et al. "Accuracy, stability, and performance comparison between the spectral difference and flux reconstruction schemes." Computers & Fluids 221 (2021): 104922.

Definition at line 324 of file navier_stokes.cpp.

◆ compute_scaled_heat_conductivity()

template<int dim, int nstate, typename real >

template<typename real2 >

real2 PHiLiP::Physics::NavierStokes< dim, nstate, real >::compute_scaled_heat_conductivity ( const std::array< real2, nstate > & primitive_soln ) const

inline

Scaled nondimensionalized heat conductivity, hat{kappa*} Reference: Masatsuka 2018 "I do like CFD", p.148, eq.(4.14.13)

Definition at line 199 of file navier_stokes.cpp.

◆ compute_scaled_heat_conductivity_given_scaled_viscosity_coefficient_and_prandtl_number()

template<int dim, int nstate, typename real >

template<typename real2 >

template FadType PHiLiP::Physics::NavierStokes< dim, nstate, real >::compute_scaled_heat_conductivity_given_scaled_viscosity_coefficient_and_prandtl_number< FadType >	(	const real2	scaled_viscosity_coefficient,
		const double	prandtl_number_input
	)		const

inline

Scaled nondimensionalized heat conductivity, hat{kappa*}, given scaled nondimensionalized viscosity coefficient and Prandtl number Reference: Masatsuka 2018 "I do like CFD", p.148, eq.(4.14.13)

Definition at line 186 of file navier_stokes.cpp.

◆ compute_scaled_viscosity_coefficient()

template<int dim, int nstate, typename real >

template<typename real2 >

template RadFadType PHiLiP::Physics::NavierStokes< dim, nstate, real >::compute_scaled_viscosity_coefficient< RadFadType > ( const std::array< real2, nstate > & primitive_soln ) const

inline

Scaled nondimensionalized viscosity coefficient, hat{mu*} Reference: Masatsuka 2018 "I do like CFD", p.148, eq.(4.14.14)

Definition at line 172 of file navier_stokes.cpp.

◆ compute_scaled_viscosity_coefficient_derivative_wrt_temperature_via_dfad()

template<int dim, int nstate, typename real>

real PHiLiP::Physics::NavierStokes< dim, nstate, real >::compute_scaled_viscosity_coefficient_derivative_wrt_temperature_via_dfad ( std::array< real, nstate > & conservative_soln ) const

inline

Scaled viscosity coefficient derivative wrt temperature via dfad (automatic differentiation) – Only used for verifying the basic dfad procedure that is extended in convective_flux_directional_jacobian_via_dfad()

Definition at line 800 of file navier_stokes.cpp.

◆ compute_scaled_viscosity_gradient()

template<int dim, int nstate, typename real>

dealii::Tensor< 1, dim, real > PHiLiP::Physics::NavierStokes< dim, nstate, real >::compute_scaled_viscosity_gradient	(	const std::array< real, nstate > &	primitive_soln,
		const dealii::Tensor< 1, dim, real > &	temperature_gradient
	)		const

Gradient of the scaled nondimensionalized viscosity coefficient Reference: Masatsuka 2018 "I do like CFD", p.148, eq.(4.14.14 and 4.14.17)

Definition at line 540 of file navier_stokes.cpp.

◆ compute_strain_rate_tensor()

template<int dim, int nstate, typename real >

template<typename real2 >

template dealii::Tensor< 2, PHILIP_DIM, FadType > PHiLiP::Physics::NavierStokes< dim, nstate, real >::compute_strain_rate_tensor< FadType > ( const dealii::Tensor< 2, dim, real2 > & vel_gradient ) const

Nondimensionalized strain rate tensor, S* Reference: Masatsuka 2018 "I do like CFD", p.148, extracted from eq.(4.14.12)

Definition at line 429 of file navier_stokes.cpp.

◆ compute_strain_rate_tensor_based_dissipation_rate_from_integrated_strain_rate_tensor_magnitude_sqr()

template<int dim, int nstate, typename real>

real PHiLiP::Physics::NavierStokes< dim, nstate, real >::compute_strain_rate_tensor_based_dissipation_rate_from_integrated_strain_rate_tensor_magnitude_sqr ( const real integrated_strain_rate_tensor_magnitude_sqr ) const

Evaluate non-dimensional theoretical strain-rate tensor based dissipation rate from integrated strain-rate tensor magnitude squared. – Reference: Navah, Farshad, et al. "A High-Order Variational Multiscale Approach to Turbulence for Compact Nodal Schemes." – Equation (E.9) with free-stream nondimensionalization applied

Definition at line 463 of file navier_stokes.cpp.

◆ compute_temperature_gradient()

template<int dim, int nstate, typename real >

template<typename real2 >

template dealii::Tensor< 1, PHILIP_DIM, FadType > PHiLiP::Physics::NavierStokes< dim, nstate, real >::compute_temperature_gradient< FadType >	(	const std::array< real2, nstate > &	primitive_soln,
		const std::array< dealii::Tensor< 1, dim, real2 >, nstate > &	primitive_soln_gradient
	)		const

Nondimensionalized temperature gradient

Definition at line 107 of file navier_stokes.cpp.

◆ compute_viscosity_coefficient()

template<int dim, int nstate, typename real >

template<typename real2 >

template FadType PHiLiP::Physics::NavierStokes< dim, nstate, real >::compute_viscosity_coefficient< FadType > ( const std::array< real2, nstate > & primitive_soln ) const

inline

Nondimensionalized viscosity coefficient, mu* Based on the use_constant_viscosity flag, it returns a value based on either: (1) Sutherland's viscosity law, or (2) Constant nondimensionalized viscosity value

Definition at line 124 of file navier_stokes.cpp.

◆ compute_viscosity_coefficient_sutherlands_law()

template<int dim, int nstate, typename real >

template<typename real2 >

real2 PHiLiP::Physics::NavierStokes< dim, nstate, real >::compute_viscosity_coefficient_sutherlands_law ( const std::array< real2, nstate > & primitive_soln ) const

inline

Nondimensionalized viscosity coefficient, mu* Reference: Masatsuka 2018 "I do like CFD", p.148, eq.(4.14.16)

Based on Sutherland's law for viscosity

Reference: Sutherland, W. (1893), "The viscosity of gases and molecular force", Philosophical Magazine, S. 5, 36, pp. 507-531 (1893)
Values: https://www.cfd-online.com/Wiki/Sutherland%27s_law

Definition at line 140 of file navier_stokes.cpp.

◆ compute_viscous_stress_tensor()

template<int dim, int nstate, typename real >

template<typename real2 >

dealii::Tensor< 2, dim, real2 > PHiLiP::Physics::NavierStokes< dim, nstate, real >::compute_viscous_stress_tensor	(	const std::array< real2, nstate > &	primitive_soln,
		const std::array< dealii::Tensor< 1, dim, real2 >, nstate > &	primitive_soln_gradient
	)		const

Nondimensionalized viscous stress tensor, tau* Reference: Masatsuka 2018 "I do like CFD", p.148, eq.(4.14.12)

Definition at line 507 of file navier_stokes.cpp.

◆ compute_viscous_stress_tensor_via_scaled_viscosity_and_strain_rate_tensor()

template<int dim, int nstate, typename real >

template<typename real2 >

template dealii::Tensor< 2, PHILIP_DIM, FadType > PHiLiP::Physics::NavierStokes< dim, nstate, real >::compute_viscous_stress_tensor_via_scaled_viscosity_and_strain_rate_tensor< FadType >	(	const real2	scaled_viscosity_coefficient,
		const dealii::Tensor< 2, dim, real2 > &	strain_rate_tensor
	)		const

Nondimensionalized viscous stress tensor, tau* Reference: Masatsuka 2018 "I do like CFD", p.148, eq.(4.14.12)

Definition at line 473 of file navier_stokes.cpp.

◆ compute_vorticity_based_dissipation_rate_from_integrated_enstrophy()

template<int dim, int nstate, typename real>

real PHiLiP::Physics::NavierStokes< dim, nstate, real >::compute_vorticity_based_dissipation_rate_from_integrated_enstrophy ( const real integrated_enstrophy ) const

Evaluate non-dimensional theoretical vorticity-based dissipation rate integrated enstrophy. Note: For incompressible flows or when dilatation effects are negligible – Reference: Cox, Christopher, et al. "Accuracy, stability, and performance comparison between the spectral difference and flux reconstruction schemes." Computers & Fluids 221 (2021): 104922. – Equation (56) with free-stream nondimensionalization applied

Definition at line 315 of file navier_stokes.cpp.

◆ convective_flux_directional_jacobian_via_dfad()

template<int dim, int nstate, typename real>

dealii::Tensor< 2, nstate, real > PHiLiP::Physics::NavierStokes< dim, nstate, real >::convective_flux_directional_jacobian_via_dfad	(	std::array< real, nstate > &	conservative_soln,
		const dealii::Tensor< 1, dim, real > &	normal
	)		const

Convective flux Jacobian computed via dfad (automatic differentiation) – Only used for verifying the dfad procedure used in dissipative flux jacobian

Definition at line 749 of file navier_stokes.cpp.

◆ convert_conservative_gradient_to_primitive_gradient()

template<int dim, int nstate, typename real >

template<typename real2 >

template std::array< dealii::Tensor< 1, PHILIP_DIM, FadType >, PHILIP_DIM+2 > PHiLiP::Physics::NavierStokes< dim, nstate, real >::convert_conservative_gradient_to_primitive_gradient< FadType >	(	const std::array< real2, nstate > &	conservative_soln,
		const std::array< dealii::Tensor< 1, dim, real2 >, nstate > &	conservative_soln_gradient
	)		const

Obtain gradient of primitive variables from gradient of conservative variables

Definition at line 59 of file navier_stokes.cpp.

◆ dissipative_flux()

template<int dim, int nstate, typename real>

std::array< dealii::Tensor< 1, dim, real >, nstate > PHiLiP::Physics::NavierStokes< dim, nstate, real >::dissipative_flux	(	const std::array< real, nstate > &	conservative_soln,
		const std::array< dealii::Tensor< 1, dim, real >, nstate > &	solution_gradient
	)		const

overridevirtual

Nondimensionalized viscous flux (i.e. dissipative flux) Reference: Masatsuka 2018 "I do like CFD", p.142, eq.(4.12.1-4.12.4)

Reimplemented from PHiLiP::Physics::Euler< dim, nstate, real >.

Definition at line 527 of file navier_stokes.cpp.

◆ dissipative_flux_directional_jacobian()

template<int dim, int nstate, typename real>

dealii::Tensor< 2, nstate, real > PHiLiP::Physics::NavierStokes< dim, nstate, real >::dissipative_flux_directional_jacobian	(	const std::array< real, nstate > &	conservative_soln,
		const std::array< dealii::Tensor< 1, dim, real >, nstate > &	solution_gradient,
		const dealii::Tensor< 1, dim, real > &	normal
	)		const

Dissipative flux Jacobian Note: Only used for computing the manufactured solution source term; computed using automatic differentiation

Definition at line 584 of file navier_stokes.cpp.

◆ dissipative_flux_directional_jacobian_wrt_gradient_component()

template<int dim, int nstate, typename real>

dealii::Tensor< 2, nstate, real > PHiLiP::Physics::NavierStokes< dim, nstate, real >::dissipative_flux_directional_jacobian_wrt_gradient_component	(	const std::array< real, nstate > &	conservative_soln,
		const std::array< dealii::Tensor< 1, dim, real >, nstate > &	solution_gradient,
		const dealii::Tensor< 1, dim, real > &	normal,
		const int	d_gradient
	)		const

Dissipative flux Jacobian wrt gradient component Note: Only used for computing the manufactured solution source term; computed using automatic differentiation

Definition at line 622 of file navier_stokes.cpp.

◆ dissipative_flux_given_velocities_viscous_stress_tensor_and_heat_flux()

template<int dim, int nstate, typename real >

template<typename real2 >

template std::array< dealii::Tensor< 1, PHILIP_DIM, FadType >, PHILIP_DIM+2 > PHiLiP::Physics::NavierStokes< dim, nstate, real >::dissipative_flux_given_velocities_viscous_stress_tensor_and_heat_flux< FadType >	(	const dealii::Tensor< 1, dim, real2 > &	vel,
		const dealii::Tensor< 2, dim, real2 > &	viscous_stress_tensor,
		const dealii::Tensor< 1, dim, real2 > &	heat_flux
	)		const

Nondimensionalized viscous flux (i.e. dissipative flux) computed via given velocities, viscous stress tensor, and heat flux. Reference: Masatsuka 2018 "I do like CFD", p.142, eq.(4.12.1-4.12.4)

Definition at line 854 of file navier_stokes.cpp.

◆ dissipative_flux_templated()

template<int dim, int nstate, typename real >

template<typename real2 >

std::array< dealii::Tensor< 1, dim, real2 >, nstate > PHiLiP::Physics::NavierStokes< dim, nstate, real >::dissipative_flux_templated	(	const std::array< real2, nstate > &	conservative_soln,
		const std::array< dealii::Tensor< 1, dim, real2 >, nstate > &	solution_gradient
	)		const

protected

Nondimensionalized viscous flux (i.e. dissipative flux) Reference: Masatsuka 2018 "I do like CFD", p.142, eq.(4.12.1-4.12.4)

Definition at line 827 of file navier_stokes.cpp.

◆ extract_velocities_gradient_from_primitive_solution_gradient()

template<int dim, int nstate, typename real >

template<typename real2 >

template dealii::Tensor< 2, PHILIP_DIM, FadType > PHiLiP::Physics::NavierStokes< dim, nstate, real >::extract_velocities_gradient_from_primitive_solution_gradient< FadType > ( const std::array< dealii::Tensor< 1, dim, real2 >, nstate > & primitive_soln_gradient ) const

Extract gradient of velocities

Definition at line 414 of file navier_stokes.cpp.

◆ scale_viscosity_coefficient()

template<int dim, int nstate, typename real >

template<typename real2 >

real2 PHiLiP::Physics::NavierStokes< dim, nstate, real >::scale_viscosity_coefficient ( const real2 viscosity_coefficient ) const

inline

Scaled nondimensionalized viscosity coefficient, hat{mu*}, given nondimensionalized viscosity coefficient Reference: Masatsuka 2018 "I do like CFD", p.148, eq.(4.14.14)

Definition at line 159 of file navier_stokes.cpp.

Member Data Documentation

◆ sutherlands_temperature

template<int dim, int nstate, typename real>

const double PHiLiP::Physics::NavierStokes< dim, nstate, real >::sutherlands_temperature

protected

Sutherland's temperature. Units: [K].

Constants for Sutherland's law for viscosity Reference: Sutherland, W. (1893), "The viscosity of gases and molecular force", Philosophical Magazine, S. 5, 36, pp. 507-531 (1893) Values: https://www.cfd-online.com/Wiki/Sutherland%27s_law

Definition at line 66 of file navier_stokes.h.

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

src/physics/navier_stokes.h
src/physics/navier_stokes.cpp

Public Types

Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Private Member Functions

Detailed Description

template<int dim, int nstate, typename real> class PHiLiP::Physics::NavierStokes< dim, nstate, real >

Member Function Documentation

◆ boundary_wall()

◆ compute_deviatoric_strain_rate_tensor()

◆ compute_deviatoric_strain_rate_tensor_based_dissipation_rate_from_integrated_deviatoric_strain_rate_tensor_magnitude_sqr()

◆ compute_heat_flux()

◆ compute_heat_flux_given_scaled_heat_conductivity_and_temperature_gradient()

◆ compute_pressure_dilatation()

◆ compute_scaled_heat_conductivity()

◆ compute_scaled_heat_conductivity_given_scaled_viscosity_coefficient_and_prandtl_number()

◆ compute_scaled_viscosity_coefficient()

◆ compute_scaled_viscosity_coefficient_derivative_wrt_temperature_via_dfad()

◆ compute_scaled_viscosity_gradient()

◆ compute_strain_rate_tensor()

◆ compute_strain_rate_tensor_based_dissipation_rate_from_integrated_strain_rate_tensor_magnitude_sqr()

◆ compute_temperature_gradient()

◆ compute_viscosity_coefficient()

◆ compute_viscosity_coefficient_sutherlands_law()

◆ compute_viscous_stress_tensor()

◆ compute_viscous_stress_tensor_via_scaled_viscosity_and_strain_rate_tensor()

◆ compute_vorticity_based_dissipation_rate_from_integrated_enstrophy()

◆ convective_flux_directional_jacobian_via_dfad()

◆ convert_conservative_gradient_to_primitive_gradient()

◆ dissipative_flux()

◆ dissipative_flux_directional_jacobian()

◆ dissipative_flux_directional_jacobian_wrt_gradient_component()

◆ dissipative_flux_given_velocities_viscous_stress_tensor_and_heat_flux()

◆ dissipative_flux_templated()

◆ extract_velocities_gradient_from_primitive_solution_gradient()

◆ scale_viscosity_coefficient()

Member Data Documentation

◆ sutherlands_temperature

template<int dim, int nstate, typename real>
class PHiLiP::Physics::NavierStokes< dim, nstate, real >