Variables
str	torder = 'SSPRK3'

str	sorder = 'thirdOrder'

float	gamma = 5.0/3.0

str	gradient_method = "ip"

float	penalty_beta = +1.0

float	penalty_eta = 1.0

str	imhd_numerical_flux_type = "HLLD"

float	cfl = 0.05

float	skin_depth_norm = 1.0/3.0

int	nu_p_norm = 1

float	length = 1.0

int	resistivity = 1

int	viscosity = 1

float	Bx = 1.0

float	density = 1.0

float	pressure = 1.0

float	dpdy = +0.0

float	wall_velocity = 1.0

float	minus_dpdy = -dpdy

int	eps = 1E-16

float	Hartmann = 1.0/(skin_depth_norm+eps) * Bx * length /math.sqrt(resistivity*viscosity)

bool	use_steady_state_solution = True

int	num_elems = 64

warpy	mesh

list	component_names = ['rho', 'px', 'py', 'pz', 'e', 'Bx', 'By', 'Bz']

warpy	fluid = warpy.variable(name='fluid',components=component_names,basis_array_set=sorder)

list	gradient_component_names = [prefix+"_"+suffix for prefix in component_names for suffix in ['x','y','z']]

warpy	fluid_gradient = warpy.variable(name='fluid_gradient', components=gradient_component_names,basis_array_set=sorder)

warpy	fluid_gradient2 = warpy.variable(name='fluid_gradient2', components=gradient_component_names,basis_array_set=sorder)

warpy	fluid_analytic = warpy.variable(name='fluid_analytic',components=component_names,basis_array_set=sorder)

warpy	hartmann_flow_mhd_ic

list	ic_applicators

list	apps = []

list	analytic_solution_apps = []

list	boundary_condition_q_apps = []

list	boundary_condition_grad_q_apps = []

list	variable_adjusters = []

warpy	spatial_solver

warpy	ti

list	integrator_apps = []

warpy	dg_integrator

warpy	integrator_host_action

warpy	diag_writer

warpy	writer

	else :

int	dt = 1E-6

warpy	dt_controller = warpy.dt_calc.stability_dt(init_dt=dt)

int	write_steps = 100

Variable Documentation

◆ analytic_solution_apps

list examples.dg.mhd.hartmann_flow_mhd.analytic_solution_apps = []

◆ apps

list examples.dg.mhd.hartmann_flow_mhd.apps = []

◆ boundary_condition_grad_q_apps

list examples.dg.mhd.hartmann_flow_mhd.boundary_condition_grad_q_apps = []

◆ boundary_condition_q_apps

list examples.dg.mhd.hartmann_flow_mhd.boundary_condition_q_apps = []

◆ Bx

float examples.dg.mhd.hartmann_flow_mhd.Bx = 1.0

◆ cfl

float examples.dg.mhd.hartmann_flow_mhd.cfl = 0.05

◆ component_names

list examples.dg.mhd.hartmann_flow_mhd.component_names = ['rho', 'px', 'py', 'pz', 'e', 'Bx', 'By', 'Bz']

◆ density

float examples.dg.mhd.hartmann_flow_mhd.density = 1.0

◆ dg_integrator

warpy examples.dg.mhd.hartmann_flow_mhd.dg_integrator

Initial value:

=  warpy.integrators.dg_integrator(name="dg",
                                          spatial_order=sorder,
                                          applications=integrator_apps,
                                          )

◆ diag_writer

warpy examples.dg.mhd.hartmann_flow_mhd.diag_writer

Initial value:

=  warpy.host_actions.diagnostics_writer(name = 'diagnostics',
                                                    write_interval = 1e-3,
                                                    diagnostics = {integrator_host_action: "L2"},
                                                    output_file = "diagnostics.csv")

◆ dpdy

float examples.dg.mhd.hartmann_flow_mhd.dpdy = +0.0

◆ dt

int examples.dg.mhd.hartmann_flow_mhd.dt = 1E-6

◆ dt_controller

warpy examples.dg.mhd.hartmann_flow_mhd.dt_controller = warpy.dt_calc.stability_dt(init_dt=dt)

◆ else

examples.dg.mhd.hartmann_flow_mhd.else :

◆ eps

int examples.dg.mhd.hartmann_flow_mhd.eps = 1E-16

◆ fluid

warpy examples.dg.mhd.hartmann_flow_mhd.fluid = warpy.variable(name='fluid',components=component_names,basis_array_set=sorder)

◆ fluid_analytic

warpy examples.dg.mhd.hartmann_flow_mhd.fluid_analytic = warpy.variable(name='fluid_analytic',components=component_names,basis_array_set=sorder)

◆ fluid_gradient

warpy examples.dg.mhd.hartmann_flow_mhd.fluid_gradient = warpy.variable(name='fluid_gradient', components=gradient_component_names,basis_array_set=sorder)

◆ fluid_gradient2

warpy examples.dg.mhd.hartmann_flow_mhd.fluid_gradient2 = warpy.variable(name='fluid_gradient2', components=gradient_component_names,basis_array_set=sorder)

◆ gamma

float examples.dg.mhd.hartmann_flow_mhd.gamma = 5.0/3.0

◆ gradient_component_names

list examples.dg.mhd.hartmann_flow_mhd.gradient_component_names = [prefix+"_"+suffix for prefix in component_names for suffix in ['x','y','z']]

◆ gradient_method

str examples.dg.mhd.hartmann_flow_mhd.gradient_method = "ip"

◆ Hartmann

float examples.dg.mhd.hartmann_flow_mhd.Hartmann = 1.0/(skin_depth_norm+eps) * Bx * length /math.sqrt(resistivity*viscosity)

◆ hartmann_flow_mhd_ic

warpy examples.dg.mhd.hartmann_flow_mhd.hartmann_flow_mhd_ic

Initial value:

=  warpy.functions.hartmann_flow_mhd(name='hartmann_flow_mhd_ic',
                                                         gamma=gamma,
                                                         skin_depth_norm=skin_depth_norm,
                                                         nu_p_norm=nu_p_norm,
                                                         density=density,
                                                         pressure=pressure,
                                                         wall_velocity=wall_velocity,
                                                         # width=1.0,
                                                         # transition_aspect=0.5,
                                                         Bx=Bx,
                                                         use_steady_state_solution = use_steady_state_solution,
                                                         pressure_gradient=dpdy,
                                                         length=length,
                                                         resistive_eta=1.0,
                                                         dynamic_viscosity=1.0)

◆ ic_applicators

list examples.dg.mhd.hartmann_flow_mhd.ic_applicators

Initial value:

=  [warpy.applicator(spatial_order=sorder,
                                   fun=hartmann_flow_mhd_ic,
                                   var=fluid,
                                   components=None,
                                   spatial_scheme='Nodal')]

◆ imhd_numerical_flux_type

str examples.dg.mhd.hartmann_flow_mhd.imhd_numerical_flux_type = "HLLD"

◆ integrator_apps

list examples.dg.mhd.hartmann_flow_mhd.integrator_apps = []

◆ integrator_host_action

warpy examples.dg.mhd.hartmann_flow_mhd.integrator_host_action

Initial value:

=  warpy.host_actions.integrator(name="integrator",
                                                       patch_process_integrators=[dg_integrator],
                                                       time_integrator=ti)

◆ length

float examples.dg.mhd.hartmann_flow_mhd.length = 1.0

◆ mesh

warpy examples.dg.mhd.hartmann_flow_mhd.mesh

Initial value:

=  warpy.mesh.block(Bounds=[-length, length],
                        NumCells=[num_elems],
                        NodeSets=['leftWall', 'rightWall'],
                        NumLayers=1,
                        basis_array_set=sorder)

◆ minus_dpdy

float examples.dg.mhd.hartmann_flow_mhd.minus_dpdy = -dpdy

◆ nu_p_norm

int examples.dg.mhd.hartmann_flow_mhd.nu_p_norm = 1

◆ num_elems

int examples.dg.mhd.hartmann_flow_mhd.num_elems = 64

◆ penalty_beta

float examples.dg.mhd.hartmann_flow_mhd.penalty_beta = +1.0

◆ penalty_eta

float examples.dg.mhd.hartmann_flow_mhd.penalty_eta = 1.0

◆ pressure

float examples.dg.mhd.hartmann_flow_mhd.pressure = 1.0

◆ resistivity

int examples.dg.mhd.hartmann_flow_mhd.resistivity = 1

◆ skin_depth_norm

float examples.dg.mhd.hartmann_flow_mhd.skin_depth_norm = 1.0/3.0

◆ sorder

str examples.dg.mhd.hartmann_flow_mhd.sorder = 'thirdOrder'

◆ spatial_solver

warpy examples.dg.mhd.hartmann_flow_mhd.spatial_solver

Initial value:

=  warpy.spatial_solvers.dg(name="dg",
                                          spatial_order=sorder,
                                          applications=apps,
                                          penalty_beta=penalty_beta,
                                          penalty_eta=penalty_eta,
                                          cfl=cfl)

◆ ti

warpy examples.dg.mhd.hartmann_flow_mhd.ti

Initial value:

=  warpy.host_actions.erk(name="ti",
                            scheme=torder,
                            spatial_solvers=[spatial_solver],
                            variable_adjusters=variable_adjusters)

◆ torder

str examples.dg.mhd.hartmann_flow_mhd.torder = 'SSPRK3'

◆ use_steady_state_solution

bool examples.dg.mhd.hartmann_flow_mhd.use_steady_state_solution = True

◆ variable_adjusters

list examples.dg.mhd.hartmann_flow_mhd.variable_adjusters = []

◆ viscosity

int examples.dg.mhd.hartmann_flow_mhd.viscosity = 1

◆ wall_velocity

float examples.dg.mhd.hartmann_flow_mhd.wall_velocity = 1.0

◆ write_steps

int examples.dg.mhd.hartmann_flow_mhd.write_steps = 100

◆ writer

warpy examples.dg.mhd.hartmann_flow_mhd.writer

Initial value:

=  warpy.host_actions.writer(name='writer',
                                       ReadVars=[fluid,
                                                 fluid_analytic,
                                                 fluid_gradient,
                                                 fluid_gradient2] )

Variables

Variable Documentation

◆ analytic_solution_apps

◆ apps

◆ boundary_condition_grad_q_apps

◆ boundary_condition_q_apps

◆ Bx

◆ cfl

◆ component_names

◆ density

◆ dg_integrator

◆ diag_writer

◆ dpdy

◆ dt

◆ dt_controller

◆ else

◆ eps

◆ fluid

◆ fluid_analytic

◆ fluid_gradient

◆ fluid_gradient2

◆ gamma

◆ gradient_component_names

◆ gradient_method

◆ Hartmann

◆ hartmann_flow_mhd_ic

◆ ic_applicators

◆ imhd_numerical_flux_type

◆ integrator_apps

◆ integrator_host_action

◆ length

◆ mesh

◆ minus_dpdy

◆ nu_p_norm

◆ num_elems

◆ penalty_beta

◆ penalty_eta

◆ pressure

◆ resistivity

◆ skin_depth_norm

◆ sorder

◆ spatial_solver

◆ ti

◆ torder

◆ use_steady_state_solution

◆ variable_adjusters

◆ viscosity

◆ wall_velocity

◆ write_steps

◆ writer