xmhd Module Reference

Detailed Description

Module for modeling extended MHD with a mixed conforming/lagrange basis set.

The equations currently solved are the equations of extended xMHD with scalar temperature and pressure.

\[ \frac{\partial n}{\partial t} + \nabla \cdot \left( n u \right) = D \nabla^2 n \]

\[ \rho \left[ \frac{\partial u}{\partial t} + u \cdot \nabla u \right] = J \times B - \nabla nk(T_e + T_i) - \nabla \cdot \Pi \]

\[ \frac{\partial B}{\partial t} = - \nabla \times \left( -u \times B + \eta J + \frac{1}{ne} \left( J \times B - \nabla nkT_e \right) + \frac{m_e}{ne^2} \frac{\partial J}{\partial t} \right) \]

\[ \frac{n}{\gamma-1} \left[ \frac{\partial T_i}{\partial t} + u \cdot \nabla T_i \right] = -nkT_i \nabla \cdot u - \nabla \cdot q_i + Q_i \]

For two temperature

\[ \frac{n}{\gamma-1} \left[ \frac{\partial T_e}{\partial t} + u_e \cdot \nabla T_e \right] = -nkT_e \nabla \cdot u_e - \nabla \cdot q_e + Q_e \]

\[ u_e = u - \frac{J}{ne} \]

Thermal transport

\[ q_s = - n \left[ \chi_{\parallel,s} \hat{b} \hat{b} + \chi_{\perp,s} \left( I - \hat{b} \hat{b} \right) \right] \cdot \nabla T_s \]

With xmhd_brag=T and single temperature ( \( T_e = T_i \))

\[ \chi_{\parallel,i} = \chi_{\parallel,e}, \chi_{\perp,i} = min(\chi_{\perp,i},\chi_{\parallel,i}) \]

Heat sources

For single temperature ( \( T_e = T_i \))

\[ Q_i = \left[ \eta J^2 - \left( \nabla u \right)^T : \Pi \right] / 2 \]

For two temperature

\[ Q_i = - \left( \nabla u \right)^T : \Pi, Q_e = \eta J^2 \]

Viscosity

\[ W = \left( \nabla u + (\nabla u)^T - \frac{2}{3} I \nabla \cdot u \right) \]

With ‘visc_type='kin’`

\[ \Pi = - \nu \nabla u \]

With ‘visc_type='iso’`

\[ \Pi = - \nu W \]

With ‘visc_type='ani’`

\[ \Pi = - \left[ \nu_{\parallel} \hat{b} \hat{b} + \nu_{\perp} \left( I - \hat{b} \hat{b} \right) \right] \cdot W \]

Runtime options are available when using the driver (xmhd_run) and post-processing (xmhd_plot) routines, see their documentation for available options.

Note

Electron mass is artificially enhanced by a factor using me_factor

Authors

Chris Hansen

Date

September 2013

Data Types
type	ml_xmhd_vecspace
	Needs docs. More...
type	oft_xmhd_driver
	Forcing object class for xMHD. More...
type	oft_xmhd_errmatrix
	NL metric matrix for xMHD. More...
type	oft_xmhd_massmatrix
	Mass metric matrix for Reduced MHD. More...
type	oft_xmhd_probe
	Probe object class for xMHD. More...
interface	xmhd_driver_apply
	Modify solution vectors to apply forcing. More...
type	xmhd_interp
	Interpolate a xMHD operator fields. More...
type	xmhd_interp_cache
	Interpolate a xMHD operator fields. More...
type	xmhd_loc_values
	Unpack object for local fields evaluated by xmhd_interp. More...
type	xmhd_ops
	xMHD operator container More...
interface	xmhd_probe_apply
	Sample probe signals from solution. More...
type	xmhd_sub_fields
	Object for sub-fields used by oft_xmhd_push and oft_xmhd_pop. More...

Functions/Subroutines
subroutine	oft_xmhd_create (new, level, cache, native)
	Create new xMHD solution vector.
subroutine	oft_xmhd_inject (self, afine, acors)
	Inject a fine level xMHD solution to the next coarsest level.
subroutine	oft_xmhd_interp (self, acors, afine)
	Interpolate a coarse level xMHD solution to the next finest level.
subroutine, public	oft_xmhd_pop (u, sub_fields)
	Extract subfields from xMHD solution vector.
subroutine, public	oft_xmhd_push (sub_fields, u)
	Replace subfields in xMHD solution vector with specified fields.
subroutine	oft_xmhd_rst_load (u, filename, path, t, dt, rst_version_out)
	Load xMHD solution state from a restart file.
subroutine	oft_xmhd_rst_save (u, t, dt, filename, path)
	Save xMHD solution state to a restart file.
subroutine	xmhd_alloc_ops
	Setup and allocate operators used in xMHD advance.
subroutine	xmhd_build_ops (fullin)
	Update Jacobian matrix with new fields.
subroutine	xmhd_diag (u, diag_vals, ueq)
	Compute diagnostic values from fields.
subroutine	xmhd_driver_rst_dummy (self, rst_file)
	Save or load driver info from restart file.
subroutine	xmhd_errmatrix_apply (self, a, b)
	Compute the NL metric for solution field.
subroutine	xmhd_interp_apply (self, cell, f, gop, val)
	Reconstruct xMHD solution fields.
subroutine	xmhd_interp_delete (self)
	Destroy interpolator for xMHD solution fields.
subroutine	xmhd_interp_setup (self, mesh)
	Setup interpolator for xMHD solution fields.
subroutine	xmhd_interp_unpack (vals, vloc)
	Unpack interpolation fields into xMHD field structure.
subroutine, public	xmhd_lin_run (equil_fields, pert_fields, escale)
	Main driver subroutine for extended MHD time advance.
subroutine	xmhd_massmatrix_apply (self, a, b)
	Compute the mass matrix for solution field.
subroutine	xmhd_mfnk_update (uin)
	Update Jacobian matrices on all levels with new fields.
subroutine, public	xmhd_plot (probes)
	Plotting subroutine for xMHD post-processing.
subroutine	xmhd_probe_flush (self)
	Flush internal write buffers for probe object.
subroutine	xmhd_profile (u)
	Simple subroutine to compute timing of different solve phases.
subroutine	xmhd_read_settings (dt, lin_tol, nl_tol, rst_ind, nsteps, rst_freq, nclean, maxextrap, ittarget, nl_update)
	Read settings for extended MHD model from input files.
subroutine, public	xmhd_run (initial_fields, driver, probes, profile_only)
	Main driver subroutine for extended MHD time advance.
subroutine	xmhd_set_bc
	Set BC flags.
subroutine	xmhd_set_level (level)
	Set the current level for xMHD model.
subroutine	xmhd_set_ops (uin)
	Update Jacobian matrices on all levels with new solution.
subroutine	xmhd_setup_regions ()
	Setup material regions from XML input file.
subroutine	xmhd_setup_rep
	Setup composite FE representation and ML environment.
pure real(r8) function	xmhd_upwind_weight (v_mag, he, nu)
	Evalute upwinding parameter.

Variables
character(len=2)	bbc = 'bc'
	Magnetic field BC ('bc','ic')
real(r8)	d2_dens = -1.d0
	Particle hyper-diffusivity.
real(r8)	d_dens = 1.E0_r8
	Particle diffusivity.
real(r8), public	den_floor = -1.d0
	Density floor.
real(r8), public	den_scale = -1.d0
	Density scale factor.
real(r8)	dt_scale = 1._r8
	Time step scaling factor.
real(r8)	eta = 1.E-2_r8
	Resistivity \( \eta / \mu_0 \).
real(r8)	eta_hyper = -1.d0
	Hyper resistivity.
real(r8), dimension(:), allocatable	eta_reg
	Resistivity scale factors.
real(r8)	eta_temp = -1._r8
	Reference temperature for resistivity.
real(r8), public	g_accel = 0.d0
	Gravity (oriented in the -Z direction)
integer(i4)	j2_ind = -1
	Index of hyper-res aux field.
real(r8), public	j2_scale = -1.d0
	Hyper-resistivity aux variable scale factor.
real(r8)	jac_dt = 1.E-3_r8
	Time step.
real(r8)	k_boltz = elec_charge
	Boltzmann constant.
real(r8)	kappa_par = 1.d0
	Parallel thermal conductivity factor.
real(r8)	kappa_perp = 1.d0
	Perpendicular thermal conductivity factor.
real(r8)	m_ion = -1.d0
	Ion mass in SI units.
real(r8)	me_factor = 100.E0_r8
	Artificial electron mass factor.
class(oft_mesh), pointer	mesh
type(oft_mf_matrix), target	mfmat
	Matrix free operator.
class(multigrid_mesh), pointer	mg_mesh
type(oft_matrix_ptr), dimension(:), pointer	ml_int => NULL()
	MG interpolation operators.
type(oft_matrix_ptr), dimension(:), pointer	ml_j => NULL()
	MG Jacobian operators.
type(oft_ml_fem_comp_type), target	ml_xmhd_rep
	ML container for field representation.
real(r8)	mu_ion = 2.d0
	Ion mass in atomic units.
integer(i4)	n2_ind = -1
	Index of hyper-diff aux field.
real(r8), public	n2_scale = -1.d0
	Hyper-diffusivity aux variable scale factor.
character(len=1)	nbc = 'd'
	Density BC ('d','n')
real(r8), dimension(:,:), allocatable	neg_flag
real(r8), dimension(:,:), allocatable	neg_source
real(r8)	nu_par = 0.d0
	Fluid (parallel) viscosity (note: dynamic viscosity is nu=nu_par*den_scale/n0)
real(r8)	nu_perp = 0.d0
	Fluid perpendicular viscosity if anisotropic, as nu_par.
integer(i4), dimension(fem_max_levels)	nu_xmhd = 1
	Number of smoother iterations.
class(oft_hcurl_fem), pointer	oft_hcurl => NULL()
class(oft_h1_fem), pointer	oft_hgrad => NULL()
class(oft_scalar_fem), pointer	oft_lagrange => NULL()
type(xmhd_ops), pointer	oft_xmhd_ops => NULL()
	Operator container.
type(xmhd_ops), dimension(:), pointer	oft_xmhd_ops_ml => NULL()
	MG operator container.
procedure(oft_1d_func), pointer, public	res_profile => NULL()
	Resistivity profile.
logical, dimension(:), allocatable	solid_cell
	Solid region flag.
character(len=1)	tbc = 'd'
	Temperature BC ('d','n')
real(r8)	te_factor = 1.d0
	Electron temperature factor (single temperature)
integer(i4)	te_ind = -1
	Index of electron temperature field.
real(r8), public	temp_floor = -1.d0
	Temperature floor.
real(r8)	temp_gamma = 5.d0/3.d0
	Ratio of specific heats.
character(len=4)	vbc = 'all'
	Velocity BC ('all','norm','tang')
integer(i4)	vbc_type = 1
	Velocity BC type.
real(r8), public	vel_scale = 1.d3
	Velocity scale factor.
integer(i4)	visc_itype = 1
	Viscosity type flag (1->kin,2->iso,3->ani)
character(len=3)	visc_type = 'kin'
	Viscosity type ('kin','iso','ani')
logical, public	xmhd_adv_b = .TRUE.
	Advance magnetic field.
logical	xmhd_adv_den = .TRUE.
	Advance density.
logical	xmhd_adv_temp = .TRUE.
	Advance temperature.
logical	xmhd_advec = .TRUE.
	Include fluid advection.
integer(i4)	xmhd_blevel = 0
	Highest level on base meshes.
logical, public	xmhd_bnorm_force = .TRUE.
	Force B-norm to zero in cleaning.
logical	xmhd_brag = .FALSE.
	Braginskii thermal conduction.
logical	xmhd_diss_centered = .FALSE.
	Time-center dissipation terms.
real(r8)	xmhd_eps = 1.d-10
	Epsilon for magnetic field normalization.
logical	xmhd_hall = .FALSE.
	Include Hall terms.
real(r8), dimension(:,:), pointer, contiguous	xmhd_hcurl_cop => NULL()
real(r8), dimension(:,:), pointer, contiguous	xmhd_hcurl_rop => NULL()
real(r8), dimension(:,:), pointer, contiguous	xmhd_hgrad_rop => NULL()
logical	xmhd_jcb = .TRUE.
	Include JxB force on fluid.
real(r8), dimension(:,:), pointer, contiguous	xmhd_lag_gop => NULL()
real(r8), dimension(:), pointer, contiguous	xmhd_lag_rop => NULL()
integer(i4)	xmhd_lev = 1
	Active FE level.
integer(i4)	xmhd_level = 1
	Active FE level.
integer(i4)	xmhd_lin_level = 1
	Highest linear element level.
logical	xmhd_linear = .FALSE.
	Compute linearized matrix.
integer(i4), dimension(:,:), allocatable	xmhd_mat_mask
	Matrix block mask.
logical	xmhd_mfnk = .FALSE.
	Use Jacobian free non-linear advance.
integer(i4), public	xmhd_minlev = -1
	Lowest MG level.
type(oft_ml_fem_type), pointer, public	xmhd_ml_h1 => NULL()
type(oft_ml_fem_type), pointer, public	xmhd_ml_h1grad => NULL()
type(oft_ml_fem_type), pointer, public	xmhd_ml_hcurl => NULL()
type(oft_ml_fem_comp_type), pointer, public	xmhd_ml_hcurl_grad => NULL()
type(oft_ml_fem_type), pointer, public	xmhd_ml_lagrange => NULL()
type(ml_xmhd_vecspace), target	xmhd_ml_vecspace
type(oft_ml_fem_comp_type), pointer, public	xmhd_ml_vlagrange => NULL()
logical	xmhd_monitor_div = .FALSE.
	Monitor div error?
integer(i4)	xmhd_nlevels = 1
	Number of total levels.
integer(i4), dimension(fem_max_levels)	xmhd_nparts = 1
	Number of local partitions for preconditioning.
logical	xmhd_ohmic = .FALSE.
	Resistive heating.
integer(i4)	xmhd_opcount = 1
	Number of time steps since preconditioner update.
real(r8)	xmhd_opdt = 1.d0
	Time step for current preconditioner object.
class(oft_solver), pointer	xmhd_pre => NULL()
	Preconditioner object.
type(xml_node), pointer	xmhd_pre_node => NULL()
	preconditioner XML node
integer(i4)	xmhd_prefreq = 30
	Desired update frequency for preconditioner.
type(oft_fem_comp_type), pointer	xmhd_rep => NULL()
	Active field representation.
type(xml_node), pointer	xmhd_root_node => NULL()
	xMHD XML node
integer(i4), parameter	xmhd_rst_version = 3
	Restart file version number.
logical	xmhd_rw = .FALSE.
	Resistive wall present.
logical	xmhd_skip_update = .FALSE.
	Internal flag for skipping Jac update.
integer(i4), public	xmhd_taxis = 3
	Axis for toroidal flux and current.
logical	xmhd_therm_equil = .FALSE.
	Include cross-species thermalization.
logical	xmhd_two_temp = .FALSE.
	Run 2 Temperature model.
logical	xmhd_upwind = .TRUE.
	Use upwinding.
logical	xmhd_vbcdir = .FALSE.
	Velocity BC type flag.
logical	xmhd_visc_heat = .FALSE.
	Viscous heating.

Function/Subroutine Documentation

oft_xmhd_create()

subroutine oft_xmhd_create ( class(oft_vector), intent(out), pointer  new, integer(i4), intent(in), optional  level, logical, intent(in), optional  cache, logical, intent(in), optional  native  )

private

Create new xMHD solution vector.

Parameters

[out]	new	Vector to create
[in]	level	FE level (optional)
[in]	cache	Allow caching? (optional)
[in]	native	Force native representation? (optional)

oft_xmhd_inject()

subroutine oft_xmhd_inject ( class(ml_xmhd_vecspace), intent(inout)  self, class(oft_vector), intent(inout)  afine, class(oft_vector), intent(inout)  acors  )

private

Inject a fine level xMHD solution to the next coarsest level.

Note

The global xmhd_level is decremented by one in this subroutine

Parameters

[in,out]	afine	Fine level vector to inject
[in,out]	acors	Injected solution on coarse level

oft_xmhd_interp()

subroutine oft_xmhd_interp ( class(ml_xmhd_vecspace), intent(inout)  self, class(oft_vector), intent(inout)  acors, class(oft_vector), intent(inout)  afine  )

private

Interpolate a coarse level xMHD solution to the next finest level.

Note

The global xmhd_level is incremented by one in this subroutine

Parameters

[in,out]	acors	Coarse level vector to interpolate
[in,out]	afine	Interpolated solution on fine level

oft_xmhd_pop()

subroutine, public oft_xmhd_pop	(	class(oft_vector), intent(inout)	u,
		type(xmhd_sub_fields), intent(inout)	sub_fields
	)

Extract subfields from xMHD solution vector.

Parameters

[in,out]	u	Source xMHD vector
[in,out]	sub_fields	Destination fields

oft_xmhd_push()

subroutine, public oft_xmhd_push	(	type(xmhd_sub_fields), intent(inout)	sub_fields,
		class(oft_vector), intent(inout)	u
	)

Replace subfields in xMHD solution vector with specified fields.

Parameters

[in,out]	sub_fields	Source fields
[in,out]	u	Destination xMHD vector

oft_xmhd_rst_load()

subroutine oft_xmhd_rst_load ( class(oft_vector), intent(inout), pointer  u, character(len=*), intent(in)  filename, character(len=*), intent(in)  path, real(r8), intent(out), optional  t, real(r8), intent(out), optional  dt, integer(i4), intent(out), optional  rst_version_out  )

private

Load xMHD solution state from a restart file.

Parameters

[in,out]	u	Solution to load
[in]	filename	Name of restart file
[in]	path	Path to store solution vector in file
[out]	t	Time of loaded solution
[out]	dt	Timestep at loaded time
[out]	rst_version_out	Version number

oft_xmhd_rst_save()

subroutine oft_xmhd_rst_save ( class(oft_vector), intent(inout), pointer  u, real(r8), intent(in)  t, real(r8), intent(in)  dt, character(len=*), intent(in)  filename, character(len=*), intent(in)  path  )

private

Save xMHD solution state to a restart file.

Parameters

[in,out]	u	Solution to save
[in]	t	Current solution time
[in]	dt	Current timestep
[in]	filename	Name of restart file
[in]	path	Path to store solution vector in file

xmhd_alloc_ops()

subroutine xmhd_alloc_ops

private

Setup and allocate operators used in xMHD advance.

xmhd_build_ops()

subroutine xmhd_build_ops ( class(fem_interp), intent(inout)  fullin )

private

Update Jacobian matrix with new fields.

Parameters

[in,out]

fullin

Interpolator to evaluate fields

xmhd_diag()

subroutine xmhd_diag ( class(oft_vector), intent(inout), target  u, real(r8), dimension(7), intent(out)  diag_vals, class(oft_vector), intent(inout), optional  ueq  )

private

Compute diagnostic values from fields.

Parameters

[in,out]	u	Field for diagnostic evaluation
[out]	diag_vals	Resulting diagnostic values [7]
[in,out]	ueq	Equilibrium field (linear calculation)

xmhd_driver_rst_dummy()

subroutine xmhd_driver_rst_dummy ( class(oft_xmhd_driver), intent(inout)  self, character(*), intent(in)  rst_file  )

private

Save or load driver info from restart file.

Parameters

[in,out]	self	Forcing object
[in]	rst_file	Name of restart file

xmhd_errmatrix_apply()

subroutine xmhd_errmatrix_apply ( class(oft_xmhd_errmatrix), intent(inout)  self, class(oft_vector), intent(inout), target  a, class(oft_vector), intent(inout)  b  )

private

Compute the NL metric for solution field.

b = F(a)

Parameters

[in,out]	self	Error matrix object
[in,out]	a	Source field
[in,out]	b	Result of metric function

xmhd_interp_apply()

subroutine xmhd_interp_apply ( class(xmhd_interp), intent(inout)  self, integer(i4), intent(in)  cell, real(r8), dimension(:), intent(in)  f, real(r8), dimension(3,4), intent(in)  gop, real(r8), dimension(:), intent(out)  val  )

private

Reconstruct xMHD solution fields.

Parameters

[in,out]	self	Interpolation object
[in]	cell	Cell for interpolation
[in]	f	Position in cell in logical coord [4]
[in]	gop	Logical gradient vectors at f [3,4]
[out]	val	Reconstructed field at f [30]

xmhd_interp_delete()

subroutine xmhd_interp_delete ( class(xmhd_interp), intent(inout)  self )

private

Destroy interpolator for xMHD solution fields.

Parameters

[in,out]

self

Interpolation object

xmhd_interp_setup()

subroutine xmhd_interp_setup ( class(xmhd_interp), intent(inout)  self, class(oft_mesh), intent(inout), target  mesh  )

private

Setup interpolator for xMHD solution fields.

• Fetches local vector values for interpolation

  Parameters

  [in,out]

  self

  Interpolation object

xmhd_interp_unpack()

subroutine xmhd_interp_unpack ( real(r8), dimension(40), intent(in)  vals, type(xmhd_loc_values), intent(out)  vloc  )

private

Unpack interpolation fields into xMHD field structure.

Parameters

[in]	vals	Packed fields [40]
[out]	vloc	Unpacked fields

xmhd_lin_run()

subroutine, public xmhd_lin_run	(	type(xmhd_sub_fields), intent(inout)	equil_fields,
		type(xmhd_sub_fields), intent(inout)	pert_fields,
		real(r8), intent(in), optional	escale
	)

Main driver subroutine for extended MHD time advance.

Runtime options are set in the main input file using the group xmhd_options group, see xmhd_run.

Note

This method assumes that [B0, V0, Ne0, Ti0, Te0] constitute an equilibrium.

Parameters

[in,out]	equil_fields	Equilibrium fields
[in,out]	pert_fields	Perurbed fields
[in]	escale	Desired total energy to be used for rescaling (optional)

xmhd_massmatrix_apply()

subroutine xmhd_massmatrix_apply ( class(oft_xmhd_massmatrix), intent(inout)  self, class(oft_vector), intent(inout), target  a, class(oft_vector), intent(inout)  b  )

private

Compute the mass matrix for solution field.

b = M(a)

Parameters

[in,out]	self	Mass matrix object
[in,out]	a	Source field
[in,out]	b	Result of metric function

xmhd_mfnk_update()

subroutine xmhd_mfnk_update ( class(oft_vector), intent(inout), target  uin )

private

Update Jacobian matrices on all levels with new fields.

Parameters

[in,out]

uin

Current field

xmhd_plot()

subroutine, public xmhd_plot

(

class(oft_xmhd_probe), intent(inout), optional

probes

)

Plotting subroutine for xMHD post-processing.

Runtime options are set in the main input file using the group xmhd_plot_options. Additionally, options from the xmhd_options group are also read to get run parameters, see xmhd_run for a list of options.

Option group: xmhd_plot_options

Option	Description	Type [dim]
probe_only=F	Sample probes but do not create plots	bool
plot_div=F	Plot \( \nabla \cdot B \) field	bool
file_list="none"	List of history files to read during post-processing (w/o file ext)	str(40)
t0=0	Starting time for sampling	real
t1=1	End time for sampling	real
dt=1E-6	Time between sampling points	real
rst_start=0	First restart file to read	int
rst_end=2000	Last restart file to read	int

Parameters

[in,out]

probes

Probe object (optional)

xmhd_probe_flush()

subroutine xmhd_probe_flush ( class(oft_xmhd_probe), intent(inout)  self )

private

Flush internal write buffers for probe object.

Parameters

[in,out]

self

Probe object

xmhd_profile()

subroutine xmhd_profile ( class(oft_vector), intent(inout)  u )

private

Simple subroutine to compute timing of different solve phases.

xmhd_read_settings()

subroutine xmhd_read_settings ( real(r8), intent(out)  dt, real(r8), intent(out)  lin_tol, real(r8), intent(out)  nl_tol, integer(i4), intent(out)  rst_ind, integer(i4), intent(out)  nsteps, integer(i4), intent(out)  rst_freq, integer(i4), intent(out)  nclean, integer(i4), intent(out)  maxextrap, integer(i4), intent(out)  ittarget, integer(i4), intent(out)  nl_update  )

private

Read settings for extended MHD model from input files.

Runtime options are set in the main input file using the xmhd_options group.

Warning

Most default physical values in the namelist below will not be appropriate for new simulations. They are merely placeholders to indicate the type of the input.

Option group: xmhd_options

Option	Description	Type [dim]
xmhd_jcb=T	Apply magnetic force to fluid	bool
xmhd_advec=T	Advect fluid	bool
xmhd_adv_den=T	Advance density	bool
xmhd_adv_temp=T	Advance temperature	bool
xmhd_hall=F	Include Hall terms in Ohm's law	bool
xmhd_ohmic=F	Include Ohmic heating	bool
xmhd_visc_heat=F	Include Viscous heating	bool
xmhd_brag=F	Use Braginskii thermal conduction coefficients	bool
xmhd_upwind=T	Use upwinding for advection terms	bool
xmhd_therm_equil=F	Include thermal equilibration between electrons/ions	bool
xmhd_diss_centered=F	Use time-centered dissipation terms for (V, Ti, Te)	bool
bbc="bc"	Magnetic field boundary condition ("bc", "ic")	str(2)
vbc="all"	Velocity boundary condition ("all")	str(3)
nbc="d"	Density boundary condition ("d", "n")	str(1)
tbc="d"	Temperature boundary condition ("d", "n")	str(1)
visc_type="kin"	Fluid viscosity type ("kin", "iso", "ani")	str(3)
dt=1	Maximum allowed time step	real
eta=1	Plasma resistivity, in diffusivity units	real
eta_temp=-1	Base resistivity temperature (neg to disable)	real
eta_hyper=-1	Plasma hyper-resistivity, in diffusivity units (neg to disable)	real
nu_par=0	Plasma (parallel) viscosity, in diffusivity units	real
nu_perp=0	Plasma perpendicular viscosity, in diffusivity units	real
d_dens=1	Plasma diffusivity, in diffusivity units	real
d2_dens=-1	Plasma hyper-diffusivity, in diffusivity units (neg to disable)	real
kappa_par=1	Plasma thermal conduction, in diffusivity units	real
kappa_perp=1	Plasma thermal conduction, in diffusivity units	real
nsteps=2000	Number of time steps to take	int
rst_freq=10	Frequency of dump files	int
lin_tol=1E-9	Linear solver tolerance	real
nl_tol=1E-5	Non-Linear solver tolerance	real
nu_xmhd=1	Number of smoother iterations for MG preconditioner	int [nlevels]
xmhd_nparts=1	Number of local partitions for factor based preconditioning	int
nclean=500	Frequency of divergence cleaning	int
rst_ind=0	Index of restart file to initialize from	int
maxextrap=2	Extrapolation order for NL initial guess	int
ittarget=60	Target number of linear iterations per time step	int
mu_ion=2	Ion mass in atomic units	real
me_factor=100	Electron mass factor	real
te_factor=1	Electron temperature factor (single temperature)	real
xmhd_prefreq=30	Frequency of full preconditioner update	int
xmhd_monitor_div=F	Monitor divergence error	bool
xmhd_mfnk=F	Use Matrix-Free NL solve	bool

Parameters

[out]	dt	Maximum timestep
[out]	lin_tol	Linear solver tolerance
[out]	nl_tol	Nonlinear solver tolerance
[out]	rst_ind	Index of file for restart (rst_ind>0)
[out]	nsteps	Number of timesteps
[out]	rst_freq	Frequency to save restart files
[out]	nclean	Frequency to clean divergence
[out]	maxextrap	Extrapolation order for initial guess
[out]	ittarget	Maximum number of linear iterations
[out]	nl_update	Maximum number of linear iterations

xmhd_run()

subroutine, public xmhd_run	(	type(xmhd_sub_fields), intent(inout)	initial_fields,
		class(oft_xmhd_driver), intent(inout), optional	driver,
		class(oft_xmhd_probe), intent(inout), optional	probes,
		logical, intent(in), optional	profile_only
	)

Main driver subroutine for extended MHD time advance.

Runtime options are set in the main input file using the group xmhd_options group, see xmhd_read_settings.

Parameters

[in,out]	initial_fields	Initial conditions
[in,out]	driver	Forcing object
[in,out]	probes	Probe object
[in]	profile_only	Profile operator timing and stop?

xmhd_set_bc()

subroutine xmhd_set_bc

private

Set BC flags.

xmhd_set_level()

subroutine xmhd_set_level ( integer(i4), intent(in)  level )

private

Set the current level for xMHD model.

Parameters

[in]

level

Desired level

xmhd_set_ops()

subroutine xmhd_set_ops ( class(oft_vector), intent(inout), target  uin )

private

Update Jacobian matrices on all levels with new solution.

Parameters

[in,out]

uin

Current solution

xmhd_setup_regions()

subroutine xmhd_setup_regions

private

Setup material regions from XML input file.

xmhd_setup_rep()

subroutine xmhd_setup_rep

private

Setup composite FE representation and ML environment.

xmhd_upwind_weight()

pure real(r8) function xmhd_upwind_weight ( real(r8), intent(in)  v_mag, real(r8), intent(in)  he, real(r8), intent(in)  nu  )

private

Evalute upwinding parameter.

Upwinding parameter for inconsistent streamline upwinded Petrov-Galerkin method (distorted bases applied to advective terms only).

Returns

Upwinding weight

Parameters

[in]	v_mag	Advection velocity [m/s]
[in]	he	Element size [m]
[in]	nu	Dissipation amplitude [m^2/s^2]

Variable Documentation

bbc

character(len=2) bbc = 'bc'

private

Magnetic field BC ('bc','ic')

d2_dens

real(r8) d2_dens = -1.d0

private

Particle hyper-diffusivity.

d_dens

real(r8) d_dens = 1.E0_r8

private

Particle diffusivity.

den_floor

real(r8), public den_floor = -1.d0

Density floor.

den_scale

real(r8), public den_scale = -1.d0

Density scale factor.

dt_scale

real(r8) dt_scale = 1._r8

private

Time step scaling factor.

eta

real(r8) eta = 1.E-2_r8

private

Resistivity \( \eta / \mu_0 \).

eta_hyper

real(r8) eta_hyper = -1.d0

private

Hyper resistivity.

eta_reg

real(r8), dimension(:), allocatable eta_reg

private

Resistivity scale factors.

eta_temp

real(r8) eta_temp = -1._r8

private

Reference temperature for resistivity.

g_accel

real(r8), public g_accel = 0.d0

Gravity (oriented in the -Z direction)

j2_ind

integer(i4) j2_ind = -1

private

Index of hyper-res aux field.

j2_scale

real(r8), public j2_scale = -1.d0

Hyper-resistivity aux variable scale factor.

jac_dt

real(r8) jac_dt = 1.E-3_r8

private

Time step.

k_boltz

real(r8) k_boltz = elec_charge

private

Boltzmann constant.

kappa_par

real(r8) kappa_par = 1.d0

private

Parallel thermal conductivity factor.

kappa_perp

real(r8) kappa_perp = 1.d0

private

Perpendicular thermal conductivity factor.

m_ion

real(r8) m_ion = -1.d0

private

Ion mass in SI units.

me_factor

real(r8) me_factor = 100.E0_r8

private

Artificial electron mass factor.

mesh

class(oft_mesh), pointer mesh

private

mfmat

type(oft_mf_matrix), target mfmat

private

Matrix free operator.

mg_mesh

class(multigrid_mesh), pointer mg_mesh

private

ml_int

type(oft_matrix_ptr), dimension(:), pointer ml_int => NULL()

private

MG interpolation operators.

ml_j

type(oft_matrix_ptr), dimension(:), pointer ml_j => NULL()

private

MG Jacobian operators.

ml_xmhd_rep

type(oft_ml_fem_comp_type), target ml_xmhd_rep

private

ML container for field representation.

mu_ion

real(r8) mu_ion = 2.d0

private

Ion mass in atomic units.

n2_ind

integer(i4) n2_ind = -1

private

Index of hyper-diff aux field.

n2_scale

real(r8), public n2_scale = -1.d0

Hyper-diffusivity aux variable scale factor.

nbc

character(len=1) nbc = 'd'

private

Density BC ('d','n')

neg_flag

real(r8), dimension(:,:), allocatable neg_flag

private

neg_source

real(r8), dimension(:,:), allocatable neg_source

private

nu_par

real(r8) nu_par = 0.d0

private

Fluid (parallel) viscosity (note: dynamic viscosity is nu=nu_par*den_scale/n0)

nu_perp

real(r8) nu_perp = 0.d0

private

Fluid perpendicular viscosity if anisotropic, as nu_par.

nu_xmhd

integer(i4), dimension(fem_max_levels) nu_xmhd = 1

private

Number of smoother iterations.

oft_hcurl

class(oft_hcurl_fem), pointer oft_hcurl => NULL()

private

oft_hgrad

class(oft_h1_fem), pointer oft_hgrad => NULL()

private

oft_lagrange

class(oft_scalar_fem), pointer oft_lagrange => NULL()

private

oft_xmhd_ops

type(xmhd_ops), pointer oft_xmhd_ops => NULL()

private

Operator container.

oft_xmhd_ops_ml

type(xmhd_ops), dimension(:), pointer oft_xmhd_ops_ml => NULL()

private

MG operator container.

res_profile

procedure(oft_1d_func), pointer, public res_profile => NULL()

Resistivity profile.

solid_cell

logical, dimension(:), allocatable solid_cell

private

Solid region flag.

tbc

character(len=1) tbc = 'd'

private

Temperature BC ('d','n')

te_factor

real(r8) te_factor = 1.d0

private

Electron temperature factor (single temperature)

te_ind

integer(i4) te_ind = -1

private

Index of electron temperature field.

temp_floor

real(r8), public temp_floor = -1.d0

Temperature floor.

temp_gamma

real(r8) temp_gamma = 5.d0/3.d0

private

Ratio of specific heats.

vbc

character(len=4) vbc = 'all'

private

Velocity BC ('all','norm','tang')

vbc_type

integer(i4) vbc_type = 1

private

Velocity BC type.

vel_scale

real(r8), public vel_scale = 1.d3

Velocity scale factor.

visc_itype

integer(i4) visc_itype = 1

private

Viscosity type flag (1->kin,2->iso,3->ani)

visc_type

character(len=3) visc_type = 'kin'

private

Viscosity type ('kin','iso','ani')

xmhd_adv_b

logical, public xmhd_adv_b = .TRUE.

Advance magnetic field.

xmhd_adv_den

logical xmhd_adv_den = .TRUE.

private

Advance density.

xmhd_adv_temp

logical xmhd_adv_temp = .TRUE.

private

Advance temperature.

xmhd_advec

logical xmhd_advec = .TRUE.

private

Include fluid advection.

xmhd_blevel

integer(i4) xmhd_blevel = 0

private

Highest level on base meshes.

xmhd_bnorm_force

logical, public xmhd_bnorm_force = .TRUE.

Force B-norm to zero in cleaning.

xmhd_brag

logical xmhd_brag = .FALSE.

private

Braginskii thermal conduction.

xmhd_diss_centered

logical xmhd_diss_centered = .FALSE.

private

Time-center dissipation terms.

xmhd_eps

real(r8) xmhd_eps = 1.d-10

private

Epsilon for magnetic field normalization.

xmhd_hall

logical xmhd_hall = .FALSE.

private

Include Hall terms.

xmhd_hcurl_cop

real(r8), dimension(:,:), pointer, contiguous xmhd_hcurl_cop => NULL()

private

xmhd_hcurl_rop

real(r8), dimension(:,:), pointer, contiguous xmhd_hcurl_rop => NULL()

private

xmhd_hgrad_rop

real(r8), dimension(:,:), pointer, contiguous xmhd_hgrad_rop => NULL()

private

xmhd_jcb

logical xmhd_jcb = .TRUE.

private

Include JxB force on fluid.

xmhd_lag_gop

real(r8), dimension(:,:), pointer, contiguous xmhd_lag_gop => NULL()

private

xmhd_lag_rop

real(r8), dimension(:), pointer, contiguous xmhd_lag_rop => NULL()

private

xmhd_lev

integer(i4) xmhd_lev = 1

private

Active FE level.

xmhd_level

integer(i4) xmhd_level = 1

private

Active FE level.

xmhd_lin_level

integer(i4) xmhd_lin_level = 1

private

Highest linear element level.

xmhd_linear

logical xmhd_linear = .FALSE.

private

Compute linearized matrix.

xmhd_mat_mask

integer(i4), dimension(:,:), allocatable xmhd_mat_mask

private

Matrix block mask.

xmhd_mfnk

logical xmhd_mfnk = .FALSE.

private

Use Jacobian free non-linear advance.

xmhd_minlev

integer(i4), public xmhd_minlev = -1

Lowest MG level.

xmhd_ml_h1

type(oft_ml_fem_type), pointer, public xmhd_ml_h1 => NULL()

xmhd_ml_h1grad

type(oft_ml_fem_type), pointer, public xmhd_ml_h1grad => NULL()

xmhd_ml_hcurl

type(oft_ml_fem_type), pointer, public xmhd_ml_hcurl => NULL()

xmhd_ml_hcurl_grad

type(oft_ml_fem_comp_type), pointer, public xmhd_ml_hcurl_grad => NULL()

xmhd_ml_lagrange

type(oft_ml_fem_type), pointer, public xmhd_ml_lagrange => NULL()

xmhd_ml_vecspace

type(ml_xmhd_vecspace), target xmhd_ml_vecspace

private

xmhd_ml_vlagrange

type(oft_ml_fem_comp_type), pointer, public xmhd_ml_vlagrange => NULL()

xmhd_monitor_div

logical xmhd_monitor_div = .FALSE.

private

Monitor div error?

xmhd_nlevels

integer(i4) xmhd_nlevels = 1

private

Number of total levels.

xmhd_nparts

integer(i4), dimension(fem_max_levels) xmhd_nparts = 1

private

Number of local partitions for preconditioning.

xmhd_ohmic

logical xmhd_ohmic = .FALSE.

private

Resistive heating.

xmhd_opcount

integer(i4) xmhd_opcount = 1

private

Number of time steps since preconditioner update.

xmhd_opdt

real(r8) xmhd_opdt = 1.d0

private

Time step for current preconditioner object.

xmhd_pre

class(oft_solver), pointer xmhd_pre => NULL()

private

Preconditioner object.

xmhd_pre_node

type(xml_node), pointer xmhd_pre_node => NULL()

private

preconditioner XML node

xmhd_prefreq

integer(i4) xmhd_prefreq = 30

private

Desired update frequency for preconditioner.

xmhd_rep

type(oft_fem_comp_type), pointer xmhd_rep => NULL()

private

Active field representation.

xmhd_root_node

type(xml_node), pointer xmhd_root_node => NULL()

private

xMHD XML node

xmhd_rst_version

integer(i4), parameter xmhd_rst_version = 3

Restart file version number.

xmhd_rw

logical xmhd_rw = .FALSE.

private

Resistive wall present.

xmhd_skip_update

logical xmhd_skip_update = .FALSE.

private

Internal flag for skipping Jac update.

xmhd_taxis

integer(i4), public xmhd_taxis = 3

Axis for toroidal flux and current.

xmhd_therm_equil

logical xmhd_therm_equil = .FALSE.

private

Include cross-species thermalization.

xmhd_two_temp

logical xmhd_two_temp = .FALSE.

private

Run 2 Temperature model.

xmhd_upwind

logical xmhd_upwind = .TRUE.

private

Use upwinding.

xmhd_vbcdir

logical xmhd_vbcdir = .FALSE.

private

Velocity BC type flag.

xmhd_visc_heat

logical xmhd_visc_heat = .FALSE.

private

Viscous heating.