[Users] GlobalDerivative becomes 0 for certain grid points (Llama)
Severin Frank
severin.frank at uni-tuebingen.de
Wed Dec 4 11:13:42 CST 2019
Thank you Erik for your last reply and your helpful advice!
In the last days I changed a lot of my code and I noticed another
(different?) issue:
I'm calculating spatial derivatives in r-direction for different grid
functions by using Llama GlobalDerivative thorn, such as this example:
call globalDiff_gv (cctkGH, 0, PHI, param_dx, J11, J21, J31, &
J12, J22, J32, J13, J23, J33, -1_ik)
call globalDiff_gv (cctkGH, 1, PHI, param_dy, J11, J21, J31, &
J12, J22, J32, J13, J23, J33, -1_ik)
call globalDiff_gv (cctkGH, 2, PHI, param_dz, J11, J21, J31, &
J12, J22, J32, J13, J23, J33, -1_ik)
param_dr = dxdr * param_dx + dydr * param_dy + dzdr * param_dz
, where dxdr, dydr, dzdr are the specific coordinate transformations and
my coordinates are again Thornburg04 multipatch.
I noticed that I receive very odd (and wrong) zero-values on specific
grid points in the positive x-sphere. Not only for param_dr, but also
for param_dx, param_dy as well as param_dz. I should mention, that I did
not change the GlobalDerivative thorn and this problem also appears,
when calculating the derivatives of other variables then PHI. Also PHI
itself is continuous in this area. I also initiate all "param"-variables
with 1 so that the call of GlobalDerivative is actively changing them
(to 0).
The same error also appears, when calling GlobalDiff directly with the
inverse Jacobians like:
call globalDiff_gv (cctkGH, 2, PHI, param_dr, J11, J21, J31, J12, J22,
J32, iJ13, iJ23, iJ33, -1_ik).
Furthermore it makes no difference whether this is scheduled at initial
or in MoL_CalcRHS.
I attached plots from PHI, param_dx and param_dr so that you can see
where those points are on the x-z plane. These are for an angular
resolution of Coordinates::n_angular = 9. If I increase the angular
resolution this affects also more grid points along the same radius (for
example 8 points in the x-z plane for n_angular = 15).
Since I'm assuming, that the GobalDerivative thorn is working correct I
don't know where this issue might come from. Does anyone have an idea
for this?
Thank you all a lot!
Best regards,
Severin
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# Schedule definitions for thorn SWTNS
# Evolved variables
STORAGE: pressuredensity
STORAGE: metricpots
STORAGE: trafo
STORAGE: paramcheck
STORAGE: scalar[2] density[2] velocity[2]
STORAGE: drscalar[2] drvelocity[2]
STORAGE: drdensity[2]
STORAGE: tovradius
STORAGE: scalardot densitydot velocitydot
STORAGE: tovsurface
STORAGE: fluidscalar
#################################################
# Startup and initial
#################################################
SCHEDULE SWTNS_startup AT startup
{
LANG: C
OPTIONS: meta
} "Register banner with Cactus"
SCHEDULE SWTNS_register_MoL IN MoL_Register
{
LANG: C
OPTIONS: meta
} "Register variables with MoL"
SCHEDULE SWTNS_init AT initial AFTER TOV_C_Exact
{
LANG: Fortran
} "Initialise the system"
#SCHEDULE SWTNS_inittest IN CCTK_PREREGRID
#{
# LANG: Fortran
#} "TEST the system"
#SCHEDULE SWTNS_regridtest AT CCTK_POSTREGRID AFTER SpatialCoordinates
#{
# LANG: Fortran
#} "TEST the system"
##################################################
# Calculate the RHS
##################################################
SCHEDULE SWTNS_calc_rhs IN MoL_CalcRHS
{
LANG: Fortran
} "Calculate the RHS"
#SCHEDULE SWTNS_surface IN MoL_CalcRHS AFTER SWTNS_calc_rhs
#{
# LANG: Fortran
#} "Calculate TOV radius"
##################################################
# Apply the boundary conditions
##################################################
#SCHEDULE SWTNS_outerboundary IN MoL_PostStep
#{
# LANG: Fortran
#} "Apply outer boundaries"
#SCHEDULE SWTNS_RHS_outerboundary IN MoL_RHSBoundaries
#{
# LANG: Fortran
#} "Apply MoL RHS outer boundaries (TOV_surface)"
#SCHEDULE SWTNS_boundaries IN MoL_PostStep AFTER SWTNS_outerboundary
#{
# LANG: Fortran
# OPTIONS: level
# SYNC: scalar density velocity drscalar drvelocity scalardot drdensity densitydot velocitydot
#} "Select the boundary condition"
#SCHEDULE GROUP ApplyBCs AS SWTNS_ApplyBCs IN MoL_PostStep AFTER SWTNS_boundaries
#{
#} "Apply boundary conditions"
##################################################
# Analysis: Frequencies, speed of sound?
##################################################
#if (recalculate_rhs)
#{
# SCHEDULE SWTNS_calc_rhs AT analysis
# {
# LANG: Fortran
# SYNC: scalardot densitydot
# STORAGE: scalardot densitydot
# TRIGGERS: scalardot densitydot
# } "Calculate the RHS"
#}
#todo
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# This Thorn is based on LlamaWaveToy and SevesWaveToy
# Interface definition for thorn SWTNS
IMPLEMENTS: SWTNS
INHERITS: grid, Coordinates, GlobalDerivative, SummationByParts, Interpolate, ADMBase, HydroBase, Constants, StaticConformal, TOVSolver
USES INCLUDE: constants.h
CCTK_INT FUNCTION \
MultiPatch_GetMap \
(CCTK_POINTER_TO_CONST IN cctkGH)
REQUIRES FUNCTION MultiPatch_GetMap
CCTK_INT FUNCTION \
MultiPatch_GetBbox \
(CCTK_POINTER_TO_CONST IN cctkGH, \
CCTK_INT IN size, \
CCTK_INT OUT ARRAY bbox)
REQUIRES FUNCTION MultiPatch_GetBbox
SUBROUTINE globalDiff_gv ( CCTK_POINTER_TO_CONST IN cctkGH, \
CCTK_INT IN dir, \
CCTK_REAL IN ARRAY var, \
CCTK_REAL OUT ARRAY dvar, \
CCTK_REAL IN ARRAY J_dxda, \
CCTK_REAL IN ARRAY J_dxdb, \
CCTK_REAL IN ARRAY J_dxdc, \
CCTK_REAL IN ARRAY J_dyda, \
CCTK_REAL IN ARRAY J_dydb, \
CCTK_REAL IN ARRAY J_dydc, \
CCTK_REAL IN ARRAY J_dzda, \
CCTK_REAL IN ARRAY J_dzdb, \
CCTK_REAL IN ARRAY J_dzdc, \
CCTK_INT IN table_handle )
USES FUNCTION globalDiff_gv
SUBROUTINE globalDiff2_gv( CCTK_POINTER_TO_CONST IN cctkGH, \
CCTK_INT IN dir1, \
CCTK_INT IN dir2, \
CCTK_REAL IN ARRAY var, \
CCTK_REAL OUT ARRAY dvar, \
CCTK_REAL IN ARRAY J_dadx, \
CCTK_REAL IN ARRAY J_dbdx, \
CCTK_REAL IN ARRAY J_dcdx, \
CCTK_REAL IN ARRAY J_dady, \
CCTK_REAL IN ARRAY J_dbdy, \
CCTK_REAL IN ARRAY J_dcdy, \
CCTK_REAL IN ARRAY J_dadz, \
CCTK_REAL IN ARRAY J_dbdz, \
CCTK_REAL IN ARRAY J_dcdz, \
CCTK_REAL IN ARRAY dJ_dadxdx, \
CCTK_REAL IN ARRAY dJ_dbdxdx, \
CCTK_REAL IN ARRAY dJ_dcdxdx, \
CCTK_REAL IN ARRAY dJ_dadxdy, \
CCTK_REAL IN ARRAY dJ_dbdxdy, \
CCTK_REAL IN ARRAY dJ_dcdxdy, \
CCTK_REAL IN ARRAY dJ_dadxdz, \
CCTK_REAL IN ARRAY dJ_dbdxdz, \
CCTK_REAL IN ARRAY dJ_dcdxdz, \
CCTK_REAL IN ARRAY dJ_dadydy, \
CCTK_REAL IN ARRAY dJ_dbdydy, \
CCTK_REAL IN ARRAY dJ_dcdydy, \
CCTK_REAL IN ARRAY dJ_dadydz, \
CCTK_REAL IN ARRAY dJ_dbdydz, \
CCTK_REAL IN ARRAY dJ_dcdydz, \
CCTK_REAL IN ARRAY dJ_dadzdz, \
CCTK_REAL IN ARRAY dJ_dbdzdz, \
CCTK_REAL IN ARRAY dJ_dcdzdz, \
CCTK_INT IN table_handle )
USES FUNCTION globalDiff2_gv
CCTK_INT FUNCTION \
MoLRegisterEvolvedGroup \
(CCTK_INT IN EvolvedIndex, \
CCTK_INT IN RHSIndex)
REQUIRES FUNCTION MoLRegisterEvolvedGroup
CCTK_INT FUNCTION \
MoLRegisterEvolved \
(CCTK_INT IN EvolvedIndex, \
CCTK_INT IN RHSIndex)
REQUIRES FUNCTION MoLRegisterEvolved
CCTK_INT FUNCTION \
Boundary_SelectGroupForBC \
(CCTK_POINTER_TO_CONST IN cctkGH, \
CCTK_INT IN faces, \
CCTK_INT IN boundary_width, \
CCTK_INT IN table_handle, \
CCTK_STRING IN group_name, \
CCTK_STRING IN bc_name)
REQUIRES FUNCTION Boundary_SelectGroupForBC
CCTK_INT FUNCTION \
Boundary_SelectVarForBC \
(CCTK_POINTER_TO_CONST IN cctkGH, \
CCTK_INT IN faces, \
CCTK_INT IN boundary_width, \
CCTK_INT IN table_handle, \
CCTK_STRING IN var_name, \
CCTK_STRING IN bc_name)
REQUIRES FUNCTION Boundary_SelectVarForBC
CCTK_INT FUNCTION \
Boundary_SelectedGVs \
(CCTK_POINTER_TO_CONST IN cctkGH, \
CCTK_INT IN array_size, \
CCTK_INT ARRAY OUT var_indicies, \
CCTK_INT ARRAY OUT faces, \
CCTK_INT ARRAY OUT boundary_widths, \
CCTK_INT ARRAY OUT table_handles, \
CCTK_STRING IN bc_name)
REQUIRES FUNCTION Boundary_SelectedGVs
CCTK_INT FUNCTION \
SymmetryTableHandleForGrid (CCTK_POINTER_TO_CONST IN cctkGH)
REQUIRES FUNCTION SymmetryTableHandleForGrid
CCTK_POINTER_TO_CONST FUNCTION SymmetryNameOfHandle (CCTK_INT IN sym_handle)
REQUIRES FUNCTION SymmetryNameOfHandle
CCTK_INT FUNCTION SymmetryHandleOfName (CCTK_STRING IN sym_name)
REQUIRES FUNCTION SymmetryHandleOfName
CCTK_REAL FUNCTION GetScalProdCoeff ()
USES FUNCTION GetScalProdCoeff
SUBROUTINE Diff_gv ( CCTK_POINTER_TO_CONST IN cctkGH, \
CCTK_INT IN dir, \
CCTK_REAL IN ARRAY var, \
CCTK_REAL OUT ARRAY dvar, \
CCTK_INT IN table_handle )
USES FUNCTION Diff_gv
REAL pressuredensity TYPE=gf TAGS='tensortypealias="scalar"'
{
gappa
} "gamma=(rho+p)/p*dp/drho"
REAL tovsurface TYPE=scalar
{
TOV_surface
} "TOV_R+Xi(TOV_R)"
REAL metricpots TYPE=gf TAGS='tensortypealias="scalar"'
{
PHI, LAMBDA, drPHI, drLAMBDA, A, B, C, drrho, drpress
} "metric potentials: ds^2= -exp(2*PHI) dt^2 + exp(2*LAMBDA)dr^2 + ... and depending quantities,"
REAL trafo TYPE=gf TAGS='tensortypealias="scalar"'
{
dxdr, dydr, dzdr, grid_r
} "coordiante transformation for derivatives... dxdrr, dydrr, dzdrr and griddpoint radius"
REAL paramcheck TYPE=gf TAGS='tensortypealias="scalar"'
{
param_dr, param_dx, param_dy, param_dz
} "to check critical derivatives"
REAL scalar TYPE=gf TIMELEVELS=2 TAGS='tensortypealias="scalar"'
{
Xi
} "The scalar of the scalar wave equation fame"
REAL fluidscalar TYPE=gf
{
Xeta
} "fluid element displ."
REAL density TYPE=gf TIMELEVELS=2 TAGS='tensortypealias="scalar"'
{
Pi
} "Time derivative of Xi"
REAL drscalar TYPE=gf TIMELEVELS=2 TAGS='tensortypealias="scalar"'
{
drXi
} "Spatial derivatives of Xi"
REAL drdensity TYPE=gf TIMELEVELS=2 TAGS='tensortypealias="scalar"'
{
drPi
} "Time derivative of Xi"
REAL scalardot TYPE=gf TAGS='tensortypealias="scalar" Prolongation="None"'
{
Xidot
} "RHS of Xi"
REAL densitydot TYPE=gf TAGS='tensortypealias="scalar" Prolongation="None"'
{
Pidot
} "RHS of Pi"
REAL velocity TYPE=gf TIMELEVELS=2 TAGS='tensortypealias="scalar"'
{
H
} "H=drXi"
REAL drvelocity TYPE=gf TIMELEVELS=2 TAGS='tensortypealias="scalar"'
{
drH
} "Spatial derivatives of Xi"
REAL velocitydot TYPE=gf TAGS='tensortypealias="scalar" Prolongation="None"'
{
Hdot
} "RHS of H"
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#===============================================================
# Testing SWTNS on a static TOV star
#
# Severin Frank
#===============================================================
#################### Thorns ####################################
ActiveThorns = "Time MoL"
ActiveThorns = "TOVSolver ADMBase HydroBase Constants StaticConformal SpaceMask"
ActiveThorns = "CoordBase CartGrid3D SymBase InitBase Boundary"
ActiveThorns = "LocalInterp AEILocalInterp LoopControl Carpet CarpetReduce"
ActiveThorns = "IOUtil CarpetIOASCII CarpetIOScalar CarpetIOHDF5 CarpetIOBasic"
ActiveThorns = "NaNChecker"
ActiveThorns = "Coordinates CoordinatesSymmetry Interpolate2 CarpetInterp2 GlobalDerivative SWTNS"
#################### Terminate #################################
Cactus::terminate = "time"
Cactus::cctk_final_time = 2
#################### Time Integration ##########################
Time::timestep_method = "given"
Time::timestep = 0.09
MoL::ODE_Method = "Generic"
MoL::Generic_Type = "RK"
MoL::MoL_Intermediate_Steps = 4
MoL::MoL_Num_Scratch_Levels = 3
#MoL::verbose = "extreme"
#################### Grid Setup ################################
Carpet::domain_from_multipatch = yes
CartGrid3D::type = "multipatch"
CartGrid3D::set_coordinate_ranges_on = "all maps"
Coordinates::coordinate_system = "Thornburg04"
Coordinates::h_cartesian = 0.1
Coordinates::h_radial = 0.1
SWTNS::rprec = 0.1
TOVSolver::tovrprec = 0.1
SWTNS::SWTNS_amplitude = 0.001 #0.0031830989
SWTNS::gridboundary = 2 # ueberfluessig
Coordinates::sphere_inner_radius = 1 #
Coordinates::sphere_outer_radius = 10 #7.5284600798562327 #100
Coordinates::n_angular = 9
Driver::ghost_size = 3
Coordinates::patch_boundary_size = 3
Coordinates::outer_boundary_size = 3
Coordinates::additional_overlap_size = 3
#stagger_patch_boundaries
Interpolate2::interpolator_order = 4
Interpolate2::continue_if_selftest_fails = no
#Interpolate2::verbose = yes
Coordinates::store_inverse_jacobian = "yes"
#################### Initial Data ##############################
InitBase::initial_data_setup_method = "init_some_levels"
HydroBase::timelevels = 1
ADMBase::metric_type = "physical"
ADMBase::initial_data = "tov"
ADMBase::initial_lapse = "tov"
ADMBase::initial_shift = "tov"
ADMBase::initial_dtlapse = "zero"
ADMBase::initial_dtshift = "zero"
SpaceMask::use_mask = "yes"
TOVSolver::TOV_Rho_Central[0] = 1.62e-3 #1e-3 1.62e-3 3.24e-3 1.24e-3
TOVSolver::TOV_Gamma = 2.0
SWTNS::TOV_Gamma = 2.0
TOVSolver::TOV_K = 100.0
SWTNS::TOV_K = 100.0
#TOVSolver::TOV_Num_Radial = 10000
SWTNS::outer_bound ="dirichlet"
#################### Finite Differencing ########################
SummationByParts::order = 2
SummationByParts::use_dissipation = no
SummationByParts::onesided_interpatch_boundaries = no
SummationByParts::onesided_outer_boundaries = yes
SummationByParts::sbp_upwind_deriv = yes
SummationByParts::sbp_1st_deriv = yes
SummationByParts::sbp_2nd_deriv = yes
#################### NaN Checker ################################
NaNChecker::check_every = 1
NaNChecker::action_if_found = "just warn" #"terminate", "just warn", "abort"
NaNChecker::check_vars = "HydroBase::rho HydroBase::press TOVSolver::TOV_mr
SWTNS::TOV_surface SWTNS::PHI SWTNS::drPHI SWTNS::LAMBDA
SWTNS::drLAMBDA SWTNS::drpress SWTNS::drrho
SWTNS::A SWTNS::B SWTNS::C SWTNS::H
SWTNS::Hdot SWTNS::drH SWTNS::drPi
SWTNS::Xi SWTNS::Xidot SWTNS::Pi SWTNS::Pidot
SWTNS::Xeta SWTNS::drXi SWTNS::param_dr SWTNS::param_dx SWTNS::param_dy SWTNS::param_dz"
#################### Output #####################################
IOBasic::outInfo_every = 1
IOBasic::outInfo_vars = "
#HydroBase::rho
#HydroBase::press
#SWTNS::gappa
SWTNS::Xi
#SWTNS::Xeta
SWTNS::drXi
SWTNS::H
SWTNS::drH
SWTNS::TOV_surface
#TOVSolver::TOV_mr
#SWTNS::drPHI
#SWTNS::Xidot
#SWTNS::Pi
#SWTNS::Pidot
#SWTNS::PHI
#SWTNS::LAMBDA
#TOVSolver::TOV_PHI
#TOVSolver::TOV_R
"
#CarpetIOASCII::out1d_vars = "SWTNS::Xi"
#CarpetIOASCII::out1d_z = yes
IOASCII::compact_format = yes
# IOASCII::use_grid_coordinates = yes
#IOASCII::separate_grids = no
# IOASCII::one_file_per_group =yes
IOASCII::out0D_every = 1
IOASCII::out0D_point_x = 0
IOASCII::out0D_point_y = 0
IOASCII::out0D_point_z = 2
IOASCII::out0D_vars ="
grid::coordinates{out_every=1000000000}
SWTNS::Xeta
SWTNS::Xi
SWTNS::TOV_surface
#SWTNS::PHI{out_every=100000000000000}
#SWTNS::LAMBDA{out_every=100000000000000}
SWTNS::Xidot
SWTNS::Pi
SWTNS::Pidot
#HydroBase::rho{out_every=1000000000}
#HydroBase::press{out_every=1000000000}
"
IOHDF5::out_every = 1
IOHDF5::out_vars = "
grid::coordinates{out_every=100000000000}
Coordinates::Seve_in_cube{out_every=100000000000000}
HydroBase::rho{out_every=1000000000000000}
HydroBase::press{out_every=100000000000000}
SWTNS::A{out_every=100000000000000}
SWTNS::B{out_every=100000000000000}
SWTNS::C{out_every=100000000000000}
SWTNS::drpress{out_every=100000000000000}
SWTNS::drrho{out_every=100000000000000}
SWTNS::dxdr{out_every=100000000000000}
SWTNS::dydr{out_every=100000000000000}
SWTNS::dzdr{out_every=100000000000000}
SWTNS::Xi
SWTNS::Xeta
SWTNS::Xidot
SWTNS::Pi
SWTNS::Pidot
SWTNS::drXi
SWTNS::drH
SWTNS::H
SWTNS::Hdot
SWTNS::grid_r{out_every=1000000000000000}
SWTNS::param_dr
SWTNS::param_dx{out_every=1000000000000000}
SWTNS::param_dy{out_every=1000000000000000}
SWTNS::param_dz{out_every=1000000000000000}
TOVSolver::TOV_mr{out_every=100000000000000}
SWTNS::PHI{out_every=100000000000000}
SWTNS::drPHI{out_every=100000000000000}
SWTNS::LAMBDA{out_every=100000000000000}
SWTNS::drLAMBDA{out_every=100000000000000}
"
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