PHiLiP::Physics::MHD< dim, nspecies, nstate, real > Class Template Reference
Magnetohydrodynamics (MHD) equations. Derived from PhysicsBase. More...
#include <mhd.h>
Inheritance diagram for PHiLiP::Physics::MHD< dim, nspecies, nstate, real >:
Collaboration diagram for PHiLiP::Physics::MHD< dim, nspecies, nstate, real >:
Public Member Functions | |
| MHD (const Parameters::AllParameters *const parameters_input, const double gamma_gas, const dealii::Tensor< 2, 3, double > input_diffusion_tensor=Parameters::ManufacturedSolutionParam::get_default_diffusion_tensor(), std::shared_ptr< ManufacturedSolutionFunction< dim, nspecies, real > > manufactured_solution_function=nullptr, 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 |
| 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 flux: \( \mathbf{F}_{conv} \hat{n} \). | |
| 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 |
| Spectral radius of convective term Jacobian is 'c'. | |
| real | max_convective_eigenvalue (const std::array< real, nstate > &soln) const |
| Maximum convective eigenvalue. | |
| real | max_viscous_eigenvalue (const std::array< real, nstate > &soln) const |
| 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< 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 |
| (function overload) 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 > | source_term (const dealii::Point< dim, real > &pos, const std::array< real, nstate > &conservative_soln, const real current_time) const |
| (function overload) Source term is zero or depends on manufactured solution | |
| std::array< real, nstate > | convert_conservative_to_primitive (const std::array< real, nstate > &conservative_soln) const |
| std::array< real, nstate > | convert_primitive_to_conservative (const std::array< real, nstate > &primitive_soln) const |
| std::array< dealii::Tensor< 1, dim, real >, nstate > | convert_conservative_gradient_to_primitive_gradient (const std::array< real, nstate > &conservative_soln, const std::array< dealii::Tensor< 1, dim, real >, nstate > &conservative_soln_gradient) const |
| std::array< dealii::Tensor< 1, dim, real >, nstate > | convert_primitive_gradient_to_conservative_gradient (const std::array< real, nstate > &primitive_soln, const std::array< dealii::Tensor< 1, dim, real >, nstate > &primitive_soln_gradient) const |
| real | compute_pressure (const std::array< real, nstate > &conservative_soln) const |
| Evaluate pressure from conservative variables. | |
| real | compute_magnetic_energy (const std::array< real, nstate > &conservative_soln) const |
| Evaluate Magnetic Energy. | |
| real | compute_pressure_from_enthalpy (const std::array< real, nstate > &conservative_soln) const |
| Evaluate pressure from conservative variables. | |
| real | compute_specific_enthalpy (const std::array< real, nstate > &conservative_soln, const real pressure) const |
| Evaluate pressure from conservative variables. | |
| 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. | |
| dealii::Tensor< 1, dim, real > | compute_velocities (const std::array< real, nstate > &conservative_soln) const |
| Evaluate velocities from conservative variables. | |
| real | compute_velocity_squared (const dealii::Tensor< 1, dim, real > &velocities) const |
| Given the velocity vector \( \mathbf{u} \), returns the dot-product \( \mathbf{u} \cdot \mathbf{u} \). | |
| dealii::Tensor< 1, dim, real > | extract_velocities_from_primitive (const std::array< real, 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. | |
| real | compute_entropy_measure (const std::array< real, nstate > &conservative_soln) const |
| Evaluate entropy from conservative variables. More... | |
| real | compute_mach_number (const std::array< real, nstate > &conservative_soln) const |
| Given conservative variables, returns Mach number. | |
| real | compute_dimensional_temperature (const std::array< real, nstate > &primitive_soln) const |
| Given primitive variables, returns DIMENSIONALIZED temperature using the equation of state. | |
| real | compute_temperature (const std::array< real, 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... | |
| std::array< real, nstate > | compute_entropy_variables (const std::array< real, nstate > &conservative_soln) const |
| Computes the entropy variables. | |
| std::array< real, nstate > | compute_conservative_variables_from_entropy_variables (const std::array< real, nstate > &entropy_var) const |
| Computes the conservative variables from the entropy 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_energy (const std::array< real, nstate > &conservative_soln1, const std::array< real, nstate > &convervative_soln2) const |
| Mean specific 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 |
| Evaluates boundary values and gradients on the other side of the face. | |
 Public Member Functions inherited from PHiLiP::Physics::PhysicsBase< dim, nspecies, 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, nspecies, 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, nspecies, real > > manufactured_solution_function_input=nullptr) | |
| Constructor that will call default constructor. | |
| virtual | ~PhysicsBase ()=default |
| Virtual destructor required for abstract classes. | |
| virtual real | compute_entropy (const std::array< real, nstate > &conservative_soln) const |
| Compute entropy from conservative solution. | |
| virtual real | compute_gamma (const std::array< real, nstate > &conservative_soln) const |
| Compute gamma from conservative solution. | |
| virtual std::array< real, nstate > | compute_kinetic_energy_variables (const std::array< real, nstate > &conservative_soln) const |
| Compute kinetic energy variables from conservative solution. | |
| virtual 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 |
| Convective Numerical Split Flux for split form. | |
| virtual real | max_convective_normal_eigenvalue (const std::array< real, nstate > &soln, const dealii::Tensor< 1, dim, real > &normal) const |
| Maximum convective normal eigenvalue (used in Lax-Friedrichs) | |
| virtual std::array< real, nstate > | dissipative_flux_dot_normal (const std::array< real, nstate > &solution, const std::array< dealii::Tensor< 1, dim, real >, nstate > &solution_gradient, const std::array< real, nstate > &filtered_solution, const std::array< dealii::Tensor< 1, dim, real >, nstate > &filtered_solution_gradient, const bool on_boundary, const dealii::types::global_dof_index cell_index, const dealii::Tensor< 1, dim, real > &normal, const int boundary_type) |
| Dissipative fluxes dot normal vector. | |
| virtual std::array< dealii::Tensor< 1, dim, real >, nstate > | dissipative_flux (const std::array< real, nstate > &solution, const std::array< dealii::Tensor< 1, dim, real >, nstate > &solution_gradient, const std::array< real, nstate > &filtered_solution, const std::array< dealii::Tensor< 1, dim, real >, nstate > &filtered_solution_gradient, const dealii::types::global_dof_index cell_index) |
| Dissipative fluxes that will be differentiated ONCE in space. | |
| 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 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 > &, 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 |
| Evaluates boundary values and gradients on the other side of the face for the convective flux. | |
| virtual void | boundary_face_values_viscous_flux (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 > &, 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 |
| Evaluates boundary values and gradients on the other side of the face for the viscous flux. | |
| virtual dealii::Vector< double > | post_compute_derived_quantities_vector (const dealii::Vector< double > &uh, const std::vector< dealii::Tensor< 1, dim > > &, const std::vector< dealii::Tensor< 2, dim > > &, const dealii::Tensor< 1, dim > &, const dealii::Point< dim > &) const |
| Returns current vector solution to be used by PhysicsPostprocessor to output current solution. More... | |
| 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... | |
| virtual std::vector< std::string > | post_get_names () const |
| Returns names of the solution to be used by PhysicsPostprocessor to output current solution. More... | |
| virtual std::vector< dealii::DataComponentInterpretation::DataComponentInterpretation > | post_get_data_component_interpretation () const |
| Returns DataComponentInterpretation of the solution to be used by PhysicsPostprocessor to output current solution. More... | |
| virtual dealii::UpdateFlags | post_get_needed_update_flags () const |
| Returns required update flags of the 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 | gam |
| Constant heat capacity ratio of air. | |
| const double | gamm1 |
| Gamma-1.0 used often. | |
| Public Attributes inherited from PHiLiP::Physics::PhysicsBase< dim, nspecies, 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, nspecies, 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... | |
Additional Inherited Members | |
| Public Types inherited from PHiLiP::Physics::PhysicsBase< dim, nspecies, nstate, real > | |
| using | NonPhysicalBehaviorEnum = Parameters::AllParameters::NonPhysicalBehaviorEnum |
| Protected Attributes inherited from PHiLiP::Physics::PhysicsBase< dim, nspecies, nstate, real > | |
| dealii::ConditionalOStream | pcout |
| ConditionalOStream. More... | |
| dealii::Tensor< 2, dim, double > | diffusion_tensor |
| Anisotropic diffusion matrix. More... | |
Detailed Description
template<int dim, int nspecies, int nstate, typename real>
class PHiLiP::Physics::MHD< dim, nspecies, nstate, real >
Magnetohydrodynamics (MHD) equations. Derived from PhysicsBase.
Only 2D and 3D State variable and convective fluxes given by
\[ \mathbf{w} = \begin{bmatrix} \rho \\ \rho v_1 \\ \rho v_2 \\ \rho v_3 \\ \rho E \end{bmatrix} , \qquad \mathbf{F}_{conv} = \begin{bmatrix} \mathbf{f}^x_{conv}, \mathbf{f}^y_{conv}, \mathbf{f}^z_{conv} \end{bmatrix} = \begin{bmatrix} \begin{bmatrix} \rho v_1 \\ \rho v_1 v_1 + p \\ \rho v_1 v_2 \\ \rho v_1 v_3 \\ v_1 (\rho e+p) \end{bmatrix} , \begin{bmatrix} \rho v_2 \\ \rho v_1 v_2 \\ \rho v_2 v_2 + p \\ \rho v_2 v_3 \\ v_2 (\rho e+p) \end{bmatrix} , \begin{bmatrix} \rho v_3 \\ \rho v_1 v_3 \\ \rho v_2 v_3 \\ \rho v_3 v_3 + p \\ v_3 (\rho e+p) \end{bmatrix} \end{bmatrix} \]
where, \( E \) is the specific total energy and \( e \) is the specific internal energy, related by
\[ E = e + |V|^2 / 2 \]
For a calorically perfect gas
\[ p=(\gamma -1)(\rho e-\frac{1}{2}\rho \|\mathbf{v}\|) \]
Dissipative flux \( \mathbf{F}_{diss} = \mathbf{0} \)
Source term \( s(\mathbf{x}) \)
Equation:
\[ \boldsymbol{\nabla} \cdot ( \mathbf{F}_{conv}( w ) + \mathbf{F}_{diss}( w, \boldsymbol{\nabla}(w) ) = s(\mathbf{x}) \]
Still need to provide functions to un-non-dimensionalize the variables. Like, given density_inf
Member Function Documentation
◆ compute_density_from_pressure_temperature()
template<int dim, int nspecies, int nstate, typename real >
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inline |
◆ compute_entropy_measure()
template<int dim, int nspecies, int nstate, typename real >
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inline |
Evaluate entropy from conservative variables.
Note that it is not the actual entropy since it's missing some constants. Used to check entropy convergence See discussion in https://physics.stackexchange.com/questions/116779/entropy-is-constant-how-to-express-this-equation-in-terms-of-pressure-and-densi?answertab=votes#tab-top
◆ compute_mean_density()
template<int dim, int nspecies, int nstate, typename real >
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inline |
◆ compute_mean_pressure()
template<int dim, int nspecies, int nstate, typename real >
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inline |
◆ compute_mean_specific_energy()
template<int dim, int nspecies, int nstate, typename real >
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inline |
◆ compute_mean_velocities()
template<int dim, int nspecies, int nstate, typename real >
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inline |
◆ compute_temperature()
template<int dim, int nspecies, int nstate, typename real >
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inline |
◆ compute_temperature_from_density_pressure()
template<int dim, int nspecies, int nstate, typename real >
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inline |
◆ convert_conservative_gradient_to_primitive_gradient()
template<int dim, int nspecies, int nstate, typename real >
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virtual |
Obtain gradient of primitive variables from gradient of conservative variables
Implements PHiLiP::Physics::PhysicsBase< dim, nspecies, nstate, real >.
◆ convert_conservative_to_primitive()
template<int dim, int nspecies, int nstate, typename real >
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inlinevirtual |
Given conservative variables [density, [momentum], total energy], returns primitive variables [density, [velocities], pressure].
Opposite of convert_primitive_to_conservative
Implements PHiLiP::Physics::PhysicsBase< dim, nspecies, nstate, real >.
◆ convert_primitive_gradient_to_conservative_gradient()
template<int dim, int nspecies, int nstate, typename real >
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virtual |
Obtain gradient of conservative variables from gradient of primitive variables
Implements PHiLiP::Physics::PhysicsBase< dim, nspecies, nstate, real >.
◆ convert_primitive_to_conservative()
template<int dim, int nspecies, int nstate, typename real >
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inlinevirtual |
Given primitive variables [density, [velocities], pressure], returns conservative variables [density, [momentum], total energy].
Opposite of convert_primitive_to_conservative
Implements PHiLiP::Physics::PhysicsBase< dim, nspecies, nstate, real >.
The documentation for this class was generated from the following files:
