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Merge pull request #13 from Iddingsite/fugacity
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add oxygen fugacity
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@Iddingsite
Iddingsite authored Mar 9, 2024
2 parents fdb0d3a + ab33cb5 commit 45afce1
Showing 1 changed file with 42 additions and 25 deletions.
67 changes: 42 additions & 25 deletions src/input/initialconditions.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -201,7 +201,7 @@ function InitialConditions3D(CMg0::AbstractArray{<:Real, 3}, CFe0::AbstractArray
end


function D_ini!(D0,T,P)
function D_ini!(D0, T, P, fugacity_O2=1e-25) # by defaut 1e-25 Pa is graphite buffer
R = 8.314462618 # constant of gas in J mol−1 K−1

# Magnesium
Expand All @@ -224,16 +224,30 @@ function D_ini!(D0,T,P)
DMn = D0Mn * exp(- (Eₐ_Mn + (100 * (P-0.001) * ΔV⁺Mn)) / (R * (T+273.15))) # in µm2 / s
DCa = 0.5 * DFe

D0[1] = DMg .* (365.25 * 24 * 3600 * 1e6) # in Myr
D0[2] = DFe .* (365.25 * 24 * 3600 * 1e6) # in Myr
D0[3] = DMn .* (365.25 * 24 * 3600 * 1e6) # in Myr
D0[4] = DCa .* (365.25 * 24 * 3600 * 1e6) # in Myr
fugacity_ratio = fugacity_O2/1e-25 # current fO2 over fO2 buffered with graphite

DMg = DMg .* (365.25 * 24 * 3600 * 1e6) # in Myr
DFe = DFe .* (365.25 * 24 * 3600 * 1e6) # in Myr
DMn = DMn .* (365.25 * 24 * 3600 * 1e6) # in Myr
DCa = DCa .* (365.25 * 24 * 3600 * 1e6) # in Myr

# after Chakraborty and Ganguly, 1991 (page 142, equation 2)
DMg = exp(log(DMg) + 1/6 * log(fugacity_ratio))
DFe = exp(log(DFe) + 1/6 * log(fugacity_ratio))
DMn = exp(log(DMn) + 1/6 * log(fugacity_ratio))
DCa = exp(log(DCa) + 1/6 * log(fugacity_ratio))

D0[1] = DMg # in Myr
D0[2] = DFe # in Myr
D0[3] = DMn # in Myr
D0[4] = DCa # in Myr
end

@with_kw struct Domain1D{T1, T2, T3, T4} <: Domain
IC::T4
T::T1
P::T1
fugacity_O2::T1
time_update::T1
D0::Vector{T2}
D::NamedTuple{(:DMgMg, :DMgFe, :DMgMn, :DFeMg, :DFeFe, :DFeMn, :DMnMg, :DMnFe, :DMnMn),
Expand All @@ -246,7 +260,7 @@ end
tfinal_ad::T2
time_update_ad::T1
bc_neumann::T3
function Domain1D(IC::InitialConditions1D, T::T1, P::T1, time_update::T1, bc_neumann::T3) where {T1 <: Union{Float64, AbstractArray{Float64, 1}}, T3 <: Tuple}
function Domain1D(IC::InitialConditions1D, T::T1, P::T1, time_update::T1, fugacity_O2::T1, bc_neumann::T3) where {T1 <: Union{Float64, AbstractArray{Float64, 1}}, T3 <: Tuple}

#check that T, P and time_update have the same size
if size(T, 1) ≠ size(P, 1) || size(T, 1) ≠ size(time_update, 1)
Expand All @@ -258,7 +272,7 @@ end
T2 = eltype(CMg0)

D0 = zeros(T2, 4)
D_ini!(D0, T[1], P[1]) # compute initial diffusion coefficients
D_ini!(D0, T[1], P[1], fugacity_O2[1]) # compute initial diffusion coefficients

D = (DMgMg = zeros(T2, nx), DMgFe = zeros(T2, nx), DMgMn = zeros(T2, nx), DFeMg = zeros(T2, nx), DFeFe = zeros(T2, nx), DFeMn = zeros(T2, nx), DMnMg = zeros(T2, nx), DMnFe = zeros(T2, nx), DMnMn = zeros(T2, nx)) # tensor of interdiffusion coefficients

Expand All @@ -277,14 +291,15 @@ end

T4 = typeof(IC)

new{T1, T2, T3, T4}(IC, T, P, time_update, D0, D, L_charact, D_charact, t_charact, Δxad_, u0, tfinal_ad, time_update_ad, bc_neumann)
new{T1, T2, T3, T4}(IC, T, P, fugacity_O2, time_update, D0, D, L_charact, D_charact, t_charact, Δxad_, u0, tfinal_ad, time_update_ad, bc_neumann)
end
end

@with_kw struct DomainSpherical{T1, T2, T3} <: Domain
IC::T3
T::T1
P::T1
fugacity_O2::T1
time_update::T1
D0::Vector{T2}
D::NamedTuple{(:DMgMg, :DMgFe, :DMgMn, :DFeMg, :DFeFe, :DFeMn, :DMnMg, :DMnFe, :DMnMn),
Expand All @@ -298,7 +313,7 @@ end
u0::Matrix{T2}
tfinal_ad::T2
time_update_ad::T1
function DomainSpherical(IC::InitialConditionsSpherical, T::T1, P::T1, time_update::T1) where {T1 <: Union{Float64, AbstractArray{Float64, 1}}}
function DomainSpherical(IC::InitialConditionsSpherical, T::T1, P::T1, time_update::T1, fugacity_O2::T1) where {T1 <: Union{Float64, AbstractArray{Float64, 1}}}

#check that T, P and time_update have the same size
if size(T, 1) ≠ size(P, 1) || size(T, 1) ≠ size(time_update, 1)
Expand All @@ -310,7 +325,7 @@ end
T2 = eltype(CMg0)

D0 = zeros(T2, 4)
D_ini!(D0, T[1], P[1]) # compute initial diffusion coefficients
D_ini!(D0, T[1], P[1], fugacity_O2[1]) # compute initial diffusion coefficients

D = (DMgMg = zeros(T2, nr), DMgFe = zeros(T2, nr), DMgMn = zeros(T2, nr), DFeMg = zeros(T2, nr), DFeFe = zeros(T2, nr), DFeMn = zeros(T2, nr), DMnMg = zeros(T2, nr), DMnFe = zeros(T2, nr), DMnMn = zeros(T2, nr)) # tensor of interdiffusion coefficients

Expand All @@ -331,14 +346,15 @@ end

T3 = typeof(IC)

new{T1, T2, T3}(IC, T, P, time_update, D0, D, L_charact, D_charact, t_charact, Δrad, Δrad_, r_ad, u0, tfinal_ad, time_update_ad)
new{T1, T2, T3}(IC, T, P, fugacity_O2, time_update, D0, D, L_charact, D_charact, t_charact, Δrad, Δrad_, r_ad, u0, tfinal_ad, time_update_ad)
end
end

@with_kw struct Domain2D{T1, T2, T3, T4, T5, T6} <: Domain
IC::T6
T::T1
P::T1
fugacity_O2::T1
time_update::T1
D0::T3
D::T4 # tensor of interdiffusion coefficients
Expand All @@ -350,13 +366,13 @@ end
u0::T5
tfinal_ad::T2
time_update_ad::T1
function Domain2D(IC::InitialConditions2D, T::T1, P::T1, time_update::T1) where {T1 <: Union{Float64, AbstractArray{Float64, 1}}}
function Domain2D(IC::InitialConditions2D, T::T1, P::T1, time_update::T1, fugacity_O2::T1) where {T1 <: Union{Float64, AbstractArray{Float64, 1}}}
@unpack nx, ny, Δx, Δy, tfinal, Lx, CMg0, CFe0, CMn0 = IC
similar(CMg0, (nx,ny))


D0 = similar(CMg0, 4)
D_ini!(D0, T[1], P[1]) # compute initial diffusion coefficients
D_ini!(D0, T[1], P[1], fugacity_O2[1]) # compute initial diffusion coefficients

D = (DMgMg = similar(CMg0, (nx,ny)), DMgFe = similar(CMg0, (nx,ny)), DMgMn = similar(CMg0, (nx,ny)), DFeMg = similar(CMg0, (nx,ny)), DFeFe = similar(CMg0, (nx,ny)), DFeMn = similar(CMg0, (nx,ny)), DMnMg = similar(CMg0, (nx,ny)), DMnFe = similar(CMg0, (nx,ny)), DMnMn = similar(CMg0, (nx,ny))) # tensor of interdiffusion coefficients

Expand All @@ -383,14 +399,15 @@ end
T5 = typeof(u0)
T6 = typeof(IC)

new{T1, T2, T3, T4, T5, T6}(IC, T, P, time_update, D0, D, L_charact, D_charact, t_charact, Δxad_, Δyad_, u0, tfinal_ad, time_update_ad)
new{T1, T2, T3, T4, T5, T6}(IC, T, P, fugacity_O2, time_update, D0, D, L_charact, D_charact, t_charact, Δxad_, Δyad_, u0, tfinal_ad, time_update_ad)
end
end

@with_kw struct Domain3D{T1, T2, T3, T4, T5, T6} <: Domain
IC::T6
T::T1
P::T1
fugacity_O2::T1
time_update::T1
D0::T3
D::T4
Expand All @@ -403,11 +420,11 @@ end
u0::T5
tfinal_ad::T2
time_update_ad::T1
function Domain3D(IC::InitialConditions3D, T::T1, P::T1, time_update::T1) where {T1 <: Union{Float64, Array{Float64, 1}}}
function Domain3D(IC::InitialConditions3D, T::T1, P::T1, time_update::T1, fugacity_O2::T1) where {T1 <: Union{Float64, Array{Float64, 1}}}
@unpack nx, ny, nz, Δx, Δy, Δz, tfinal, Lx, CMg0, CFe0, CMn0 = IC

D0 = similar(CMg0, 4)
D_ini!(D0, T[1], P[1]) # compute initial diffusion coefficients
D_ini!(D0, T[1], P[1], fugacity_O2[1]) # compute initial diffusion coefficients

D = (DMgMg = similar(CMg0, (nx, ny, nz)), DMgFe = similar(CMg0, (nx, ny, nz)), DMgMn = similar(CMg0, (nx, ny, nz)), DFeMg = similar(CMg0, (nx, ny, nz)), DFeFe = similar(CMg0, (nx, ny, nz)), DFeMn = similar(CMg0, (nx, ny, nz)), DMnMg = similar(CMg0, (nx, ny, nz)), DMnFe = similar(CMg0, (nx, ny, nz)), DMnMn = similar(CMg0, (nx, ny, nz))) # tensor of interdiffusion coefficients

Expand Down Expand Up @@ -436,7 +453,7 @@ end
T5 = typeof(u0)
T6 = typeof(IC)

new{T1, T2, T3, T4, T5, T6}(IC, T, P, time_update, D0, D, L_charact, D_charact, t_charact, Δxad_, Δyad_, Δzad_, u0, tfinal_ad, time_update_ad)
new{T1, T2, T3, T4, T5, T6}(IC, T, P, fugacity_O2, time_update, D0, D, L_charact, D_charact, t_charact, Δxad_, Δyad_, Δzad_, u0, tfinal_ad, time_update_ad)
end
end

Expand All @@ -453,33 +470,33 @@ function Domain end
When applied to 1D initial conditions, define corresponding 1D domain. `bc_neumann` can be used to define Neumann boundary conditions on the left or right side of the domain if set to true.
"""
function Domain(IC::InitialConditions1D, T::Union{Unitful.Temperature,Array{<:Unitful.Temperature{<:Real}, 1}}, P::Union{Unitful.Pressure,Array{<:Unitful.Pressure{<:Real}, 1}}, time_update::Union{Unitful.Time,Array{<:Unitful.Time{<:Real}, 1}}=0u"Myr"; bc_neumann::Tuple=(false, false))
Domain1D(IC, convert.(Float64,ustrip.(u"°C", T)), convert.(Float64,ustrip.(u"kbar", P)), convert.(Float64,ustrip.(u"Myr", time_update)), bc_neumann)
function Domain(IC::InitialConditions1D, T::Union{Unitful.Temperature,Array{<:Unitful.Temperature{<:Real}, 1}}, P::Union{Unitful.Pressure,Array{<:Unitful.Pressure{<:Real}, 1}}, time_update::Union{Unitful.Time,Array{<:Unitful.Time{<:Real}, 1}}=0u"Myr", fugacity_O2::Union{Unitful.Pressure,Array{<:Unitful.Pressure{<:Real}, 1}}=ones(size(P)) .* 1e-25u"Pa"; bc_neumann::Tuple=(false, false))
Domain1D(IC, convert.(Float64,ustrip.(u"°C", T)), convert.(Float64,ustrip.(u"kbar", P)), convert.(Float64,ustrip.(u"Myr", time_update)), convert.(Float64,ustrip.(u"Pa", fugacity_O2)), bc_neumann)
end

"""
Domain(IC::InitialConditionsSpherical, T::Union{Unitful.Temperature,Array{<:Unitful.Temperature{<:Real}, 1}}, P::Union{Unitful.Pressure,Array{<:Unitful.Pressure{<:Real}, 1}}, time_update::Union{Unitful.Time,Array{<:Unitful.Time{<:Real}, 1}}=0u"Myr")
When applied to spherical initial conditions, define corresponding spherical domain. Assume that the center of the grain is on the left side.
"""
function Domain(IC::InitialConditionsSpherical, T::Union{Unitful.Temperature,Array{<:Unitful.Temperature{<:Real}, 1}}, P::Union{Unitful.Pressure,Array{<:Unitful.Pressure{<:Real}, 1}}, time_update::Union{Unitful.Time,Array{<:Unitful.Time{<:Real}, 1}}=0u"Myr")
DomainSpherical(IC, convert.(Float64,ustrip.(u"°C", T)), convert.(Float64,ustrip.(u"kbar", P)), convert.(Float64,ustrip.(u"Myr", time_update)))
function Domain(IC::InitialConditionsSpherical, T::Union{Unitful.Temperature,Array{<:Unitful.Temperature{<:Real}, 1}}, P::Union{Unitful.Pressure,Array{<:Unitful.Pressure{<:Real}, 1}}, time_update::Union{Unitful.Time,Array{<:Unitful.Time{<:Real}, 1}}=0u"Myr", fugacity_O2::Union{Unitful.Pressure,Array{<:Unitful.Pressure{<:Real}, 1}}=ones(size(P)) .* 1e-25u"Pa")
DomainSpherical(IC, convert.(Float64,ustrip.(u"°C", T)), convert.(Float64,ustrip.(u"kbar", P)), convert.(Float64,ustrip.(u"Myr", time_update)), convert.(Float64,ustrip.(u"Pa", fugacity_O2)))
end

"""
Domain(IC::InitialConditions2D, T::Union{Unitful.Temperature,Array{<:Unitful.Temperature{<:Real}, 1}}, P::Union{Unitful.Pressure,Array{<:Unitful.Pressure{<:Real}, 1}}, time_update::Union{Unitful.Time,Array{<:Unitful.Time{<:Real}, 1}}=0u"Myr")
When applied to 2D initial conditions, define corresponding 2D domain.
"""
function Domain(IC::InitialConditions2D, T::Union{Unitful.Temperature,Array{<:Unitful.Temperature{<:Real}, 1}}, P::Union{Unitful.Pressure,Array{<:Unitful.Pressure{<:Real}, 1}}, time_update::Union{Unitful.Time,Array{<:Unitful.Time{<:Real}, 1}}=0u"Myr")
Domain2D(IC, convert.(Float64,ustrip.(u"°C", T)), convert.(Float64,ustrip.(u"kbar", P)), convert.(Float64,ustrip.(u"Myr", time_update)))
function Domain(IC::InitialConditions2D, T::Union{Unitful.Temperature,Array{<:Unitful.Temperature{<:Real}, 1}}, P::Union{Unitful.Pressure,Array{<:Unitful.Pressure{<:Real}, 1}}, time_update::Union{Unitful.Time,Array{<:Unitful.Time{<:Real}, 1}}=0u"Myr", fugacity_O2::Union{Unitful.Pressure,Array{<:Unitful.Pressure{<:Real}, 1}}=ones(size(P)) .* 1e-25u"Pa")
Domain2D(IC, convert.(Float64,ustrip.(u"°C", T)), convert.(Float64,ustrip.(u"kbar", P)), convert.(Float64,ustrip.(u"Myr", time_update)), convert.(Float64,ustrip.(u"Pa", fugacity_O2)))
end

"""
Domain(IC::InitialConditions3D, T::Union{Unitful.Temperature,Array{<:Unitful.Temperature{<:Real}, 1}}, P::Union{Unitful.Pressure,Array{<:Unitful.Pressure{<:Real}, 1}}, time_update::Union{Unitful.Time,Array{<:Unitful.Time{<:Real}, 1}}=0u"Myr")
When applied to 3D initial conditions, define corresponding 3D domain.
"""
function Domain(IC::InitialConditions3D, T::Union{Unitful.Temperature,Array{<:Unitful.Temperature{<:Real}, 1}}, P::Union{Unitful.Pressure,Array{<:Unitful.Pressure{<:Real}, 1}}, time_update::Union{Unitful.Time,Array{<:Unitful.Time{<:Real}, 1}}=0u"Myr")
Domain3D(IC, convert.(Float64,ustrip.(u"°C", T)), convert.(Float64,ustrip.(u"kbar", P)), convert.(Float64,ustrip.(u"Myr", time_update)))
function Domain(IC::InitialConditions3D, T::Union{Unitful.Temperature,Array{<:Unitful.Temperature{<:Real}, 1}}, P::Union{Unitful.Pressure,Array{<:Unitful.Pressure{<:Real}, 1}}, time_update::Union{Unitful.Time,Array{<:Unitful.Time{<:Real}, 1}}=0u"Myr", fugacity_O2::Union{Unitful.Pressure,Array{<:Unitful.Pressure{<:Real}, 1}}=ones(size(P)) .* 1e-25u"Pa")
Domain3D(IC, convert.(Float64,ustrip.(u"°C", T)), convert.(Float64,ustrip.(u"kbar", P)), convert.(Float64,ustrip.(u"Myr", time_update)), convert.(Float64,ustrip.(u"Pa", fugacity_O2)))
end

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