[Users] Boundary issues solving wave equations with MoL
Severin Frank
severin.frank at uni-tuebingen.de
Sun Jan 12 19:09:00 CST 2020
Thank you Roland for this detailed answer!
First of all, some things in my thorn have been changed in the last
weeks. Therefore I attached the updated files to this mail. I
reformulated the coefficients in my initial data. Now, the code runs
much better but is still diverging. However the divergence seems to come
from the center of the star instead. Right now I'm using the thornburgnc
coordinates and made the spherical part as large as possible as this is
the currently most stable configuration for my code.
I attached also a plot of the values of my evolved variable for a point
at r=2 for two different time steps, where you can see the behavior of
the evolution.
To be honest I'm not 100% sure what you meant with "stable solutions
when implemented eg in
spherical symmetry?"
What I'm basically trying to do is to have a wave equation that
approximates the radial oscillation equations for small amplitudes. The
coefficients of this wave equation are filled with static values using
the TOVSolver. Then I only evolve the the differential equations, using
the MoL thorn. There is no evolution of the GRHydro quantities or the
ADM quantities themselves. In principal, time integration of these
equations should be possible.
I wonder if I'm using the MoL (or other) thorn(s) wrong for this purpose?
Thank you a lot!
Best regards,
Severin
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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"
ActiveThorns = "IOUtil CarpetIOASCII CarpetIOScalar CarpetIOHDF5 CarpetIOBasic"
ActiveThorns = "NaNChecker CarpetReduce"
ActiveThorns = "Coordinates Interpolate2 CarpetInterp2 GlobalDerivative SWTNS"
#ActiveThorns = "GenericFD TmunuBase ADMCoupling ADMMacros CoordGauge LocalReduce SphericalSurface Vectors CarpetInterp"
ActiveThorns = "Formaline"
#CoordinatesSymmetry
#################### Terminate #################################
Cactus::terminate = "time"
Cactus::cctk_final_time = 30
#################### Time Integration ##########################
Time::timestep_method = "given"
Time::timestep = 0.006
#MoL::ODE_Method = "rk4"
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 = "Thornburg04nc"
#Coordinates::h_cartesian = 0.1
Coordinates::h_radial = 0.1
SWTNS::smoothrad = 0.1
SWTNS::rprec = 0.1
TOVSolver::tovrprec = 0.1
SWTNS::SWTNS_amplitude = -1e-9 #-4.41e-5
Coordinates::sphere_inner_radius = 0.2 #
Coordinates::sphere_outer_radius = 9
Coordinates::n_angular = 9
Driver::ghost_size = 1
Coordinates::patch_boundary_size = 2
Coordinates::outer_boundary_size = 1
Coordinates::additional_overlap_size = 2
#stagger_patch_boundaries
Interpolate2::interpolator_order = 4
Interpolate2::continue_if_selftest_fails = no
#Interpolate2::verbose = yes
Coordinates::store_inverse_jacobian = "yes"
#TmunuBase::stress_energy_storage = yes
#TmunuBase::stress_energy_at_RHS = yes
#TmunuBase::timelevels = 1
#TmunuBase::prolongation_type = none
#ADMMacros::spatial_order = 4
#GenericFD::jacobian_group = "Coordinates::jacobian"
#GenericFD::jacobian_derivative_group = "Coordinates::jacobian2"
#GenericFD::jacobian_identity_map = 0
#################### 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] = 1.24e-3 #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
#################### 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 HydroBase::eps
TOVSolver::TOV_mr
SWTNS::TOV_surface SWTNS::PHI SWTNS::drPHI SWTNS::LAMBDA
SWTNS::drLAMBDA SWTNS::drpress SWTNS::mu
SWTNS::A SWTNS::B SWTNS::C
SWTNS::Hdot SWTNS::drH SWTNS::drPi SWTNS::H
SWTNS::Xi SWTNS::Xidot SWTNS::Pi SWTNS::Pidot
SWTNS::Xeta SWTNS::drXi"
#################### Output #####################################
IOBasic::outInfo_every = 12
IOBasic::outInfo_vars = "
#HydroBase::rho
#HydroBase::press
#SWTNS::gappa
SWTNS::Xi
#SWTNS::Xeta
#SWTNS::drXi
SWTNS::H
SWTNS::drH
#SWTNS::omega
#SWTNS::deriv_error
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=10000000000000}
HydroBase::rho{out_every=1000000000000000}
HydroBase::press{out_every=100000000000000}
HydroBase::eps{out_every=100000000000000}
SWTNS::Cs_square{out_every=100000000000000}
SWTNS::mu{out_every=100000000000000}
SWTNS::Xi
SWTNS::Xeta
SWTNS::deriv_error
SWTNS::TOV_surface
TOVSolver::TOV_mr{out_every=100000000000000}
SWTNS::PHI{out_every=100000000000000}
SWTNS::LAMBDA{out_every=100000000000000}
"
IOHDF5::out_every = 64
IOHDF5::out_vars = "
grid::coordinates{out_every=100000000000}
#Coordinates::patchnumber{out_every=100000000000000}
#SWTNS::dxdr{out_every=100000000000000}
#SWTNS::dydr{out_every=100000000000000}
#SWTNS::dzdr{out_every=100000000000000}
#SWTNS::grid_r{out_every=1000000000000000}
HydroBase::rho{out_every=1000000000000000}
HydroBase::press{out_every=100000000000000}
HydroBase::eps{out_every=100000000000000}
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}
SWTNS::drpress{out_every=100000000000000}
SWTNS::Cs_square{out_every=100000000000000}
SWTNS::mu{out_every=100000000000000}
SWTNS::A{out_every=100000000000000}
SWTNS::B{out_every=100000000000000}
SWTNS::C{out_every=100000000000000}
SWTNS::Xi
SWTNS::Xeta
SWTNS::Xidot
SWTNS::Pi
SWTNS::drPi
SWTNS::Pidot
SWTNS::drXi
SWTNS::drH
SWTNS::H
SWTNS::Hdot
#SWTNS::param_dr{out_every=1000000000000000}
SWTNS::deriv_error
"
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