I3ELVIS User Guide

User Manual:

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Page Count: 29

Contents
1 Physics 2
2 t3c files 9
3 Raw output files: .prn 22
4 Numerical problems and solutions 26
5 Usage of paraview 27
References 28
1 Physics
1.1 Basic physical principals
1.1.1 The continuity equation
Dρ
Dt +ρ∇ ·~v = 0,
ρ ~v D
Dt
Dρ
Dt =∂ρ
∂t +~v∇ρ= 0,
∇ ·~v = 0,
1.1.2 The Navier-Stokes Euqation
∂σ0
ij
∂xj−∂P
∂xi
+ρgi=ρDvi
Dt ,
σij ~g = (gx, gy, gz)
ρDvi
Dt
∂σ0
ij
∂xj−∂P
∂xi
+ρgi= 0.
ρ(T, P, c)ρgi
T P c
∂σ0
ij
∂xj−∂P
∂xi
=−ρ(T, P, c)gi.
1.1.3 Heat conservation equation
ρCpDT
Dt =−∇ · ~q +Hr+Ha+Hs+HL,
~q =−k(T, p, c)∇T k(T, P, c)
c Hr, Ha, Hs, HL
Hr=const.
Ha=T α~v∇P
Hs=σ0
ij ˙0
ij −˙ij(elastic)
HL=const.
1.1.4 Rheology
Equation of State
ρ=ρr[1 + β(P−Pr)] ×[1 −α(T−Tr)]
ρrPr= 1.0bar
Tr= 298.15 K α
β
Viscosity
Plastic yield strength
σyield =C+sin(φdry)(1 −λ)P
σyield C
φdry λ= 1 −Pfluid
Psolid
P=Psolid
Peirl’s creep (Katayamo & Karato, 2008)
˙II =AP eirlσ2
II exp (−Ea+P Va
RT "1−σII
σP eirl k#q)
˙0
ij
˙0
ij = ˙0
ij(viscous)+ ˙0
ij(elastic)+ ˙0
ij(plastic,
˙0
ij(viscous)=1
2ησ0
ij ,
˙0
ij(elastic)=1
2µ
Dσ0
ij
Dt ,
˙0
ij(plastic)=χ∂G
∂σ0
ij
=χσ0
ij
2σII
G=σII =σyield.
η σ0
ij µ
G σyield σII =q1
2σ02
ij
χ
ij ~u = (ux, uy, uz)
ij =1
2∂ui
∂xj
+∂uj
xi.
˙II =q1
2˙02
ij
η
η=2
σII (n−1) Fn
AD
expE+P V
RT ,
AD, E, V n R
F
σij ij
σ0
ij = 2η˙0
ij +δij ηbulk ˙kk,
σ0
ij ˙0
ij ˙kk
η ηbulk
1.1.5 Impact treatment
Ric = 3
1
3rimp
Ric rimp
∆T=4π
9
ψ
F
ρPGR2
P
cP
ψ
0.3
r > Ric ∆T
T(r)=∆TRic
r4.4
1.1.6 Computation of crust
ddepthmelt = 2e5
1% 20%
1.1.7 Phase transitions, melting and hydration reactions
Melting
Freezing
Hydrated Peridotite
Mantle hydration
Crust hydration
Layered Sedimentation
Formation of new crust
Antigorite weakening
Eclogitization
1.2 I2ELVIS
1.3 I3ELVIS
RMars 3389 km
ric 232 −500 km
Rplanet rcore 0.5 %
Tic 1300 −2300 K
Tp1300 −2500 K
Td1300 −2300 K
¯
Tc−K
¯
Tm−K
¯
Ttot −K
¯ρc−kg m−3
¯ρm−kg m−3
¯ρtot −kg m−3
fF e,vol 0.1 %
fF e,mass 0.2 %
g3.73 m s−2
2 t3c files
2.1 file.t3c
2.2 init.t3c
2.2.1 Grid parameter description
16N+ 5
16N+ 5
16N+ 5
[m]
[m]
[m]
(xnumx −1)/2
(ynumy −1)/2
[P a]
[m/s2]
[m/s2]
[m/s2]
[years]
2.2.2 Rock type description
[P aMM ∗s]
Ea[J]
Va[J/bar]
σcrit [P a]
(P ower)
1−λ(koef)
[P a]
[kg/M3]
α[1/K]
β[1/kbar]
[J/kg]
[W t/(m∗K)]
[W t/m]
[1/bar]
[W t/kg]
2.2.3 Boundary conditions
P, Vx, Vy, Vz, T boundary conditions [m10, m11] ×
[m20, m21] ×[m30, m31]
A(x, y, z) = Const +Koef ·A(x+nshiftx, y +nshifty, z +nshiftz)
− − −
Vx(x, y, z) = 3 ×10−10 |x= 0, y ∈[0, y −1], z ∈[0, z −1]
X, Y, Z coordinates definition [m10, m11] ×[m20, m21] ×
[m30, m31]
X(x, y, z) = X(x−1, y, z) + Const + (Koef −Const)·(x−m10)
(m11 −m10) |Koef1=0
X(x, y, z) = X(x−1, y, z) + explog(Const) + logKoef1
Const ·(x−m10)
(m11 −m10)
M marker grid set to cell [m10, m11] ×[m20, m21] ×
[m30, m31] Koef Koef1Koef 2nshif tx
nshiftx1nshiftz1nshiftz2nshiftx x nshifty1
y nshiftz2z Koef
X
markx =x+rand()% (bConstc ∗ 2 + 1) − bConstc
Const ·X(x+ 1, y, z)−X(x, y, z)
nshiftx ·Koef
Y Koef1>0Z Koef2>0
2.2.4 Box description
0−140
[x0, y0, z0]
[x1, y1, z1]
[x2, y2, z2]
[x3, y3, z3]
[x4, y4, z4]
[x5, y5, z5]
[x6, y6, z6]
[x7, y7, z7]
2.2.5 Temperature box description
0 1&4 5&6
[x0, y0, z0]
[x1, y1, z1]x1=x0z1=z0
[x2, y2, z2]z2=z0
[x3, y3, z3]x3=x2z3=z0
[x4, y4, z4]x4=x5z4=z7
[x5, y5, z5]z4=z7
[x6, y6, z6]x6=x7z6=z7
[x7, y7, z7]
t0P0
t1P1
t2P2κ P0
t3P3κ P2
t4P4κ P4
t5P5κ P6
t6P6
t7P7[/m]
Box type 0: simple box
Box type 1&4: age box
T(y, t) = T1−(1 −erf(y
2√κτ ))(T1−T0),
κ=k
ρcp
τ=l2
κ
Box type 5&6: transitional box
∼17 K/km 12 km
273 K90 km
− −
−
2.3 mode.t3c
2.3.1 Timestepping description
2.3.2 General parameters
100 km
2.3.3 Erosion and Sedimentation parameters
2.3.4 Velocity- and Pressure-iterations parameters
3000
3e−03
5e+01
0e−03
3e−03
4
1
4 16 16 32 0
4 16 16 32 64
3.0e−01
1.0e−00
0.0e−00
1.0e−00
1.0e−00
1e+18
1e+25
ν0.0
0
2
0
viscmod: Effective viscosity interpolation
ηeff =1
8X
i
ηi
ηeff =exp 1
8X
i
(log (ηi))!
ηeff =1
1
8P
i
1
ηi
2.3.5 Temperature-iterations parameters
2500
1e−4
0
1
1 0
1.0e−00
1.0e−00
1.0
1
1
2.3.6 Hydration and melting parameters
97300000.0
75000
−3e−09
−3e−09
1e−1
1880.0
100.0
000.0
660000.0
670000.0
1e+21
2e+3
2e+3
2e+3
5e−1
1e−2
1e−2
2.3.7 Collision velocity parameters
20e+6
25e+6
0
3 Raw output files: .prn
3.1 Part I: General Information
16N+ 5
16N+ 5
16N+ 5
[m]
[m]
[m]
(xnumx −1)/2
(ynumy −1)/2
[P a]
[m/s2]
[m/s2]
[m/s2]
[years]
3.2 Part II: Rock type information
[P aMM ∗s]
[J]
[J/bar]
[P a]
(P ower)
(koef)
[P a]
[P a]
[kg/M3]
[1/K]
[1/kbar]
[J/kg]
[W t/(m∗K)]
(W t/kg)
3.3 Part III: Nodes information
n
nodenum
pr0, vx0, ...ht0, pr1, .., ht1, .., prn, .., htn
[P a]
[m/s]
[m/s]
[m/s]
[kg/m3]
[P a ∗s]
[K]
[J/kg]
[1/K]
[W t/m/K]
[W t/kg]
3.4 Part IV: Gridline positions
Position of gridlines in x direction xnumx
Position of gridlines in y direction ynumy
Position of gridlines in z direction znumz
3.5 Part V: Boundary Condition Equations
5
bondnum
CU RP AR =CONST +KOEF 1∗P AR1
CONST
KOEF 1
P AR1+1 P AR1=0
3.6 Part VI: Markers
marknum
4 Numerical problems and solutions
[0.5,0.3,0.1,0.001]
3e−3
3
[0.05,0.11,0.31,0.41]
1e−3
[0.31,1.00,0,0] [0.41,1.00,0,0] [0.11,0.50,0,0]
4
500 100
5e3 1e3
1018 1019
5 Usage of paraview
5.1 Conversion from raw output to Paraview files
5.2 Visualisation with Paraview
5.2.1 Visualize composition
References

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