[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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