[MITgcm-support] Numerical instability when horizontal contrast of initial temperature is large

[赖六娃]

Hi, 

I’m trying to simulate the magma ocean in tidally locked lava planet.
To speed up the simulation, the initial temperature is set to decrease from 3000 K at the substellar point (0,0) to 50 K at the side boundaries. 
Meanwhile, the initial temperature is vertically uniform.

However, there is strong instability	 when I start this simulation. I tried to decrease the maximum initial temperature to 1700 K, and the horizontal contrast becomes  to (1700-50) K, but it is still unstable.

Is there any way I can simulate stably with this initial temperature setup?
By the way, the tilmestep deltaT is 20 s.

Thanks very much!!
Yanhong

Below is my data file:
# ====================
# | Model parameters |
# ====================
#
# Continuous equation parameters
 &PARM01
# tRef= 18.8, 16.3, 13.1, 10.4, 8.1, 6.0, 4.5,
#      3.4, 2.7, 2.2, 1.8, 1.5, 1.2, 1.0, 0.9,
 tRefFile='T0solid_diffusion_160x72.bin',
# tRef=44*1600.,
 sRef= 44*34.7,
 cosPower=1.,
 viscAr=1.E-3,
 viscAh=12.E5,
 no_slip_sides=.FALSE.,
 no_slip_bottom=.TRUE.,
 bottomDragLinear=1.E-3,
#diffK4T=2.E12,
 diffKhT=1.E3,
 diffKrNrT=44*1.E-4,
 ivdc_kappa=100.,
 implicitDiffusion=.TRUE.,
# eosType='JMD95Z',
 eosType='LINEAR',
 tAlpha=4.E-5,
 sBeta =0.E-4,
 saltStepping=.FALSE.,
 gravity=22,
 rhonil=3300.,
 rhoConst=2600.,
 HeatCapacity_Cp=1800.,
 implicitFreeSurface=.TRUE.,
 nonlinFreeSurf=4,
 select_rStar=2,
 hFacInf=0.2,
 hFacSup=2.0,
 exactConserv=.TRUE.,
 staggerTimeStep=.TRUE.,
 useCDscheme=.TRUE.,
 readBinaryPrec=64,
 tempAdvScheme=77,
# usePickupBeforeC54=.TRUE.,
 rotationPeriod=69120.,
# useCoriolis=.FALSE.,
 Tsolidus=1700.,
 Tliquidus=2000.,
 &

# Elliptic solver parameters
 &PARM02
 cg2dMaxIters=1000,
#cg2dTargetResidual=1.E-13,
 cg2dTargetResWunit=1.E-17,
 &

# Time stepping parameters
 &PARM03
 niter0=0,
 nTimeSteps=20000000,
#endTime=3110400000.,
 deltaT=10.0,
# deltaTmom=100.0,
# deltaTfreesurf=2000.0,
# deltaTtracer=600.0,
# deltaTClock =600.0,
 forcing_In_AB=.FALSE.,
 abEps=0.1,
 tauCD=321428.,
 tauThetaClimRelax=2000.0,
# pickupStrictlyMatch=.FALSE.,
 chkptFreq=0.0,
 pChkptFreq=5000000.0,
 taveFreq=0.0,
 dumpFreq=5000000.0,
 diagFreq=31104000000.0,
 monitorFreq=31104000000.0,
# monitorFreq=1.0,
 monitorSelect=2,
 &

# Gridding parameters
 &PARM04
 usingSphericalPolarGrid=.TRUE.,
# delRc= 20.,  60.,  85., 120., 165., 215., 265., 315.,
#       365., 415., 465., 515., 565., 615., 665., 350.,
# delRcFile='delRc.bin',
 delR= 10., 10., 10., 10., 10., 10., 10., 10., 10., 10., 20., 20., 20., 20., 20., 20.,
        40., 40., 40., 40., 40., 60., 60., 60., 60., 80., 80., 80., 100., 100., 100., 100., 
        100., 150., 150., 200., 200., 200., 200., 200., 300., 300., 300., 400.,
 rSphere=9E6,
 ygOrigin=-81.,
 xgOrigin=-180,
 delY=72*2.25,
 delX=160*2.25,
 &

# Input datasets
 &PARM05
 bathyFile='topo3D_160x72_5400m_4walls.bin',
# zonalWindFile='taux_Az1E-5mod_160x72.bin',
# meridWindFile='tauy_Az1E-5mod_160x72.bin',
 thetaClimFile='sst3D_mod_160x72.bin',
 &


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