polarisation_braginskii_m

This module handles the polarisation part in the quasi-neutrality equation, particularly the time discretisation

\f[ \nabla\cdot\left[co\frac{\partial}{\partial t}\nabla_\perp\mathbf{E}\perp\right] = rhs, \f] where \f[ \mathbf{E}\perp = \left(\nabla_\perp\phi+\tau\frac{\nabla_\perp p_i}{n}\right) \f] the perpendicular electric field.

The module solves for the generalised vorticity atr timestep t+1 \f[ Omega^{t+1} = div[co (\nabla_perp\pot^{t+1}) \f] and electrostatic potential

The time-advancement is quite intricate due to the position of the time derivative in the vorticity equation The scheme is described in [W. Zholobenko et al., Contrib. Plasma Phys. 2019;e201900131. (https://doi.org/10.1002/ctpp.201900131.)] Therefore some intricate modifications to the storage values in the time-step integrator tstep_vort are necessary and additional storage of values

Also, parallel advection of vorticity is handeled here.

Further intricate things arise from the use of Shortley-Weller stencil for the elliptic operator

Uses

- variable_m
- helmholtz_netcdfio_m
- params_brag_switches_m
- boundaries_perp_m
- NETCDF
- params_tstep_m
- equilibrium_m
- interpolation_m
- polars_m
- descriptors_m
- penalisation_m
- mpi
- helmholtz_solver_factory_m
- mesh_cart_m
- boundaries_braginskii_m
- polar_operators_m
- error_handling_grillix_m
- helmholtz_solver_m
- multistep_m
- parallel_map_m
- helmholtz_operator_m
- precision_grillix_m
- params_brag_boundaries_parpen_m
- params_brag_model_m
- params_brag_boundaries_perp_m
- descriptors_braginskii_m
- perf_m
- comm_handler_m

Subroutines

polarisation_advance compute_vorticity parallel_polarisation_advection

Subroutines

public subroutine polarisation_advance(comm_handler, equi, mesh_cano, hsolver_cano, penalisation_cano, polars_cano, boundaries, tstep_vort, pot_tseq, ne_tseq, ti_tseq, pot_firstsolve_store, co, nev, tiv, dvort, pot_pen, pot_adv, vort_adv, sinfo, res, sinfo_zon, res_zon)

Advances vorticity in time and solves for pential

Arguments

Type	Intent	Attributes		Name
type(comm_handler_t),	intent(in)		::	comm_handler	Communicators
class(equilibrium_t),	intent(in)		::	equi	Equilibrium
type(mesh_cart_t),	intent(in)		::	mesh_cano	Mesh (canonical)
class(helmholtz_solver_t),	intent(inout)		::	hsolver_cano	Elliptic (2D) solver on canonical mesh
type(penalisation_t),	intent(in)		::	penalisation_cano	Penalisation (canonical)
type(polars_t),	intent(in)		::	polars_cano	Polar grid and operators (canonical)
type(boundaries_braginskii_t),	intent(inout)		::	boundaries	Boundary information for the BRAGINSKII model
type(karniadakis_t),	intent(inout)		::	tstep_vort	Time-step integrator for vorticity equation
real(kind=GP),	intent(in),	dimension(mesh_cano%get_n_points(), tstep_order)	::	pot_tseq	Time sequence of electrostatic potential at time-points, t, t-1, t-2,...t-(order-1)
real(kind=GP),	intent(in),	dimension(mesh_cano%get_n_points(), tstep_order)	::	ne_tseq	Time sequence of density values at time-points, t, t-1, t-2,...t-(order-1)
real(kind=GP),	intent(in),	dimension(mesh_cano%get_n_points(), tstep_order)	::	ti_tseq	Time sequqence of ion temperature values at time-points, t, t-1, t-2,...t-(order-1)
type(multistep_storage_t),	intent(inout)		::	pot_firstsolve_store	Storage of electrostatic potential values at time-points, t, t-1, t-2,...t-(order-1) - first solve - only used with BND_BRAGTYPE_ZONAL_NEUMANN
real(kind=GP),	intent(in),	dimension(mesh_cano%get_n_points())	::	co	Polarisation coefficient
real(kind=GP),	intent(in),	dimension(mesh_cano%get_n_points())	::	nev	Density at t+1
real(kind=GP),	intent(in),	dimension(mesh_cano%get_n_points())	::	tiv	Ion temperature at t+1
real(kind=GP),	intent(in),	dimension(mesh_cano%get_n_points())	::	dvort	Right hand side of vorticity equation
real(kind=GP),	intent(in),	dimension(mesh_cano%get_n_points_inner())	::	pot_pen	Penalisation values for electrostatic potential
real(kind=GP),	intent(inout),	dimension(mesh_cano%get_n_points())	::	pot_adv	Initial guess on input / values of electrostatic potential at time t+1 on output
real(kind=GP),	intent(out),	dimension(mesh_cano%get_n_points())	::	vort_adv	Values of Vorticity at time t+1
integer,	intent(out)		::	sinfo	Infor from solver
real(kind=GP),	intent(out)		::	res	Residual of solve
integer,	intent(out)		::	sinfo_zon	Info of solver required for zonal (second) solve in case of zonal Neumann boundary condition
real(kind=GP),	intent(out)		::	res_zon	Residual of zonal (second) solve in case of zonal Neumann boundary condition

public subroutine compute_vorticity(equi, mesh_cano, boundaries, co, potv, nev, tiv, vortv, swpot, swdia)

Computes generalised vorticity \f[ \nabla\cdot\left[co\nabla_\perp\left(swpot\nabla_\perp\phi+swdia\tau\frac{\nabla_\perp p_i}{n}\right)\right] \f]

Arguments

Type	Intent	Optional	Attributes		Name
class(equilibrium_t),	intent(in)			::	equi	Equilibrium
type(mesh_cart_t),	intent(in)			::	mesh_cano	Mesh (canonical)
type(boundaries_braginskii_t),	intent(in)			::	boundaries	Boundary information for the BRAGINSKII model
real(kind=GP),	intent(in),		dimension(mesh_cano%get_n_points())	::	co	Polarisation coefficient
real(kind=GP),			dimension(mesh_cano%get_n_points())	::	potv	Values of electrostatic potential
real(kind=GP),			dimension(mesh_cano%get_n_points())	::	nev	Values of density
real(kind=GP),			dimension(mesh_cano%get_n_points())	::	tiv	Values of ion temperature
real(kind=GP),	intent(out),		dimension(mesh_cano%get_n_points())	::	vortv	Generalised values for vorticity on inner grid
real(kind=GP),	intent(in),	optional		::	swpot	Switch in front of \nabla_\perp\phi term, default = 1
real(kind=GP),	intent(in),	optional		::	swdia	Switch in front of \nabla_\perp p_i/n term, default = 1

public subroutine parallel_polarisation_advection(comm_handler, equi, mesh_cano, mesh_stag, map, penalisation_cano, boundaries, co, pot, ti, ne, logne, uparv_cano, dvort)

Computes the parallel advection part in the vorticity equation

Arguments

Type	Intent	Attributes		Name
type(comm_handler_t),	intent(in)		::	comm_handler	Communicators
class(equilibrium_t),	intent(in)		::	equi	Equilibrium
type(mesh_cart_t),	intent(in)		::	mesh_cano	Mesh (canonical)
type(mesh_cart_t),	intent(in)		::	mesh_stag	Mesh (staggered)
type(parallel_map_t),	intent(in)		::	map	Parallel map
type(penalisation_t),	intent(in)		::	penalisation_cano	Penalisation (canonical)
type(boundaries_braginskii_t),	intent(in)		::	boundaries	Boundary information for the BRAGINSKII model
real(kind=GP),	intent(in),	dimension(:)	::	co	Polarisation coefficient n/B^2, with n advanced to t+1
type(variable_t),	intent(in)		::	pot	Electrostatic potential
type(variable_t),	intent(in)		::	ti	Ion temperature
type(variable_t),	intent(in)		::	ne	Electron density
type(variable_t),	intent(in)		::	logne	Logarithm of the electron density
real(kind=GP),	intent(in),	dimension(mesh_cano%get_n_points())	::	uparv_cano	Values of parallel velocity mapped to canonical grid
real(kind=GP),	intent(inout),	dimension(mesh_cano%get_n_points())	::	dvort	Change of vorticity

polarisation_braginskii_m Module

Contents

Subroutines

Uses

Contents

Subroutines

Subroutines

public subroutine polarisation_advance(comm_handler, equi, mesh_cano, hsolver_cano, penalisation_cano, polars_cano, boundaries, tstep_vort, pot_tseq, ne_tseq, ti_tseq, pot_firstsolve_store, co, nev, tiv, dvort, pot_pen, pot_adv, vort_adv, sinfo, res, sinfo_zon, res_zon)

Arguments

public subroutine compute_vorticity(equi, mesh_cano, boundaries, co, potv, nev, tiv, vortv, swpot, swdia)

Arguments

public subroutine parallel_polarisation_advection(comm_handler, equi, mesh_cano, mesh_stag, map, penalisation_cano, boundaries, co, pot, ti, ne, logne, uparv_cano, dvort)

Arguments