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Fix Biharmonic Viscosity on Cubed-Sphere Grid #3850

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Fix Biharmonic Viscosity on Cubed-Sphere Grid #3850

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0c09c1f
allow vector invariant form
simone-silvestri Oct 18, 2024
1a72658
Rename Laplacian operators and correct ∇²v formula
siddharthabishnu Oct 18, 2024
116aed2
Define vector-invariant ζ★ᶠᶠᶜ
siddharthabishnu Oct 18, 2024
8a1f70e
Define VectorInvariantForm struct and fix bugs
siddharthabishnu Oct 18, 2024
5cf8017
Remove spurious parameters
siddharthabishnu Oct 19, 2024
dedd0da
Merge branch 'main' into ss-sb-jmc/biharmonic-vector-invariant
navidcy Oct 19, 2024
12117f4
Define Δy_∇²v and Δx_∇²u, and fix bugs
siddharthabishnu Oct 22, 2024
eac550c
Union{AHBD, VectorInvariantASBD} --> AHBD
siddharthabishnu Oct 22, 2024
8138819
Fix adapt_structure and on_architecture for νhb
siddharthabishnu Oct 23, 2024
31cb273
Fix bug
siddharthabishnu Oct 23, 2024
fe6701a
Merge branch 'main' into ss-sb-jmc/biharmonic-vector-invariant
navidcy Oct 25, 2024
1c04419
Update src/TurbulenceClosures/turbulence_closure_implementations/scal…
siddharthabishnu Oct 30, 2024
cc0773d
Update src/TurbulenceClosures/turbulence_closure_implementations/scal…
siddharthabishnu Oct 30, 2024
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89 changes: 51 additions & 38 deletions src/TurbulenceClosures/abstract_scalar_biharmonic_diffusivity_closure.jl
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Expand Up @@ -5,11 +5,12 @@ using Oceananigans.Grids: peripheral_node

Abstract type for closures with scalar biharmonic diffusivities.
"""
abstract type AbstractScalarBiharmonicDiffusivity{F, N} <: AbstractTurbulenceClosure{ExplicitTimeDiscretization, N} end
abstract type AbstractScalarBiharmonicDiffusivity{F, N, VI} <: AbstractTurbulenceClosure{ExplicitTimeDiscretization, N} end

@inline formulation(::AbstractScalarBiharmonicDiffusivity{F}) where {F} = F()

const ASBD = AbstractScalarBiharmonicDiffusivity
const VectorInvariantASBD = AbstractScalarBiharmonicDiffusivity{<:HorizontalFormulation, <:Nothing, <:VectorInvariantForm}

#####
##### Coefficient extractors
Expand All @@ -34,27 +35,31 @@ const AHBD = AbstractScalarBiharmonicDiffusivity{<:HorizontalFormulation}
const ADBD = AbstractScalarBiharmonicDiffusivity{<:HorizontalDivergenceFormulation}
const AVBD = AbstractScalarBiharmonicDiffusivity{<:VerticalFormulation}

@inline viscous_flux_ux(i, j, k, grid, closure::AIBD, K, clk, fields, b) = + ν_σᶜᶜᶜ(i, j, k, grid, closure, K, clk, fields, ∂xᶜᶜᶜ, biharmonic_mask_x, ∇²ᶠᶜᶜ, fields.u)
@inline viscous_flux_vx(i, j, k, grid, closure::AIBD, K, clk, fields, b) = + ν_σᶠᶠᶜ(i, j, k, grid, closure, K, clk, fields, biharmonic_mask_x, ∂xᶠᶠᶜ, ∇²ᶜᶠᶜ, fields.v)
@inline viscous_flux_wx(i, j, k, grid, closure::AIBD, K, clk, fields, b) = + ν_σᶠᶜᶠ(i, j, k, grid, closure, K, clk, fields, biharmonic_mask_x, ∂xᶠᶜᶠ, ∇²ᶜᶜᶠ, fields.w)
@inline viscous_flux_uy(i, j, k, grid, closure::AIBD, K, clk, fields, b) = + ν_σᶠᶠᶜ(i, j, k, grid, closure, K, clk, fields, biharmonic_mask_y, ∂yᶠᶠᶜ, ∇²ᶠᶜᶜ, fields.u)
@inline viscous_flux_vy(i, j, k, grid, closure::AIBD, K, clk, fields, b) = + ν_σᶜᶜᶜ(i, j, k, grid, closure, K, clk, fields, ∂yᶜᶜᶜ, biharmonic_mask_y, ∇²ᶜᶠᶜ, fields.v)
@inline viscous_flux_wy(i, j, k, grid, closure::AIBD, K, clk, fields, b) = + ν_σᶜᶠᶠ(i, j, k, grid, closure, K, clk, fields, biharmonic_mask_y, ∂yᶜᶠᶠ, ∇²ᶜᶜᶠ, fields.w)
@inline viscous_flux_uz(i, j, k, grid, closure::AIBD, K, clk, fields, b) = + ν_σᶠᶜᶠ(i, j, k, grid, closure, K, clk, fields, biharmonic_mask_z, ∂zᶠᶜᶠ, ∇²ᶠᶜᶜ, fields.u)
@inline viscous_flux_vz(i, j, k, grid, closure::AIBD, K, clk, fields, b) = + ν_σᶜᶠᶠ(i, j, k, grid, closure, K, clk, fields, biharmonic_mask_z, ∂zᶜᶠᶠ, ∇²ᶜᶠᶜ, fields.v)
@inline viscous_flux_wz(i, j, k, grid, closure::AIBD, K, clk, fields, b) = + ν_σᶜᶜᶜ(i, j, k, grid, closure, K, clk, fields, ∂zᶜᶜᶜ, biharmonic_mask_z, ∇²ᶜᶜᶠ, fields.w)
@inline viscous_flux_ux(i, j, k, grid, closure::AHBD, K, clk, fields, b) = + ν_σᶜᶜᶜ(i, j, k, grid, closure, K, clk, fields, δ★ᶜᶜᶜ, fields.u, fields.v)
@inline viscous_flux_vx(i, j, k, grid, closure::AHBD, K, clk, fields, b) = + ν_σᶠᶠᶜ(i, j, k, grid, closure, K, clk, fields, ζ★ᶠᶠᶜ, fields.u, fields.v)
@inline viscous_flux_wx(i, j, k, grid, closure::AHBD, K, clk, fields, b) = + ν_σᶠᶜᶠ(i, j, k, grid, closure, K, clk, fields, biharmonic_mask_x, ∂xᶠᶜᶠ, ∇²ᶜᶜᶠ, fields.w)
@inline viscous_flux_uy(i, j, k, grid, closure::AHBD, K, clk, fields, b) = - ν_σᶠᶠᶜ(i, j, k, grid, closure, K, clk, fields, ζ★ᶠᶠᶜ, fields.u, fields.v)
@inline viscous_flux_vy(i, j, k, grid, closure::AHBD, K, clk, fields, b) = + ν_σᶜᶜᶜ(i, j, k, grid, closure, K, clk, fields, δ★ᶜᶜᶜ, fields.u, fields.v)
@inline viscous_flux_wy(i, j, k, grid, closure::AHBD, K, clk, fields, b) = + ν_σᶜᶠᶠ(i, j, k, grid, closure, K, clk, fields, biharmonic_mask_y, ∂yᶜᶠᶠ, ∇²ᶜᶜᶠ, fields.w)
@inline viscous_flux_uz(i, j, k, grid, closure::AVBD, K, clk, fields, b) = + ν_σᶠᶜᶠ(i, j, k, grid, closure, K, clk, fields, biharmonic_mask_z, ∂zᶠᶜᶠ, ∂²zᶠᶜᶜ, fields.u)
@inline viscous_flux_vz(i, j, k, grid, closure::AVBD, K, clk, fields, b) = + ν_σᶜᶠᶠ(i, j, k, grid, closure, K, clk, fields, biharmonic_mask_z, ∂zᶜᶠᶠ, ∂²zᶜᶠᶜ, fields.v)
@inline viscous_flux_wz(i, j, k, grid, closure::AVBD, K, clk, fields, b) = + ν_σᶜᶜᶜ(i, j, k, grid, closure, K, clk, fields, ∂zᶜᶜᶜ, biharmonic_mask_z, ∂²zᶜᶜᶠ, fields.w)

@inline viscous_flux_ux(i, j, k, grid, closure::ADBD, K, clk, fields, b) = + ν_σᶜᶜᶜ(i, j, k, grid, closure, K, clk, fields, δ★ᶜᶜᶜ, fields.u, fields.v)
@inline viscous_flux_vy(i, j, k, grid, closure::ADBD, K, clk, fields, b) = + ν_σᶜᶜᶜ(i, j, k, grid, closure, K, clk, fields, δ★ᶜᶜᶜ, fields.u, fields.v)
@inline ν_σᶜᶜᶜ(i, j, k, grid, closure::Union{AHBD, VectorInvariantASBD}, K, clock, fields, σᶜᶜᶜ, args...) = νᶜᶜᶜ(i, j, k, grid, closure, K, clock, fields) * σᶜᶜᶜ(i, j, k, grid, closure, args...)
@inline ν_σᶠᶠᶜ(i, j, k, grid, closure::Union{AHBD, VectorInvariantASBD}, K, clock, fields, σᶠᶠᶜ, args...) = νᶠᶠᶜ(i, j, k, grid, closure, K, clock, fields) * σᶠᶠᶜ(i, j, k, grid, closure, args...)
@inline ν_σᶠᶜᶠ(i, j, k, grid, closure::Union{AHBD, VectorInvariantASBD}, K, clock, fields, σᶠᶜᶠ, args...) = νᶠᶜᶠ(i, j, k, grid, closure, K, clock, fields) * σᶠᶜᶠ(i, j, k, grid, closure, args...)
@inline ν_σᶜᶠᶠ(i, j, k, grid, closure::Union{AHBD, VectorInvariantASBD}, K, clock, fields, σᶜᶠᶠ, args...) = νᶜᶠᶠ(i, j, k, grid, closure, K, clock, fields) * σᶜᶠᶠ(i, j, k, grid, closure, args...)

@inline viscous_flux_ux(i, j, k, grid, closure::AIBD, K, clk, fields, b) = + ν_σᶜᶜᶜ(i, j, k, grid, closure, K, clk, fields, ∂xᶜᶜᶜ, biharmonic_mask_x, ∇²ᶠᶜᶜ, fields.u)
@inline viscous_flux_vx(i, j, k, grid, closure::AIBD, K, clk, fields, b) = + ν_σᶠᶠᶜ(i, j, k, grid, closure, K, clk, fields, biharmonic_mask_x, ∂xᶠᶠᶜ, ∇²ᶜᶠᶜ, fields.v)
@inline viscous_flux_wx(i, j, k, grid, closure::AIBD, K, clk, fields, b) = + ν_σᶠᶜᶠ(i, j, k, grid, closure, K, clk, fields, biharmonic_mask_x, ∂xᶠᶜᶠ, ∇²ᶜᶜᶠ, fields.w)
@inline viscous_flux_uy(i, j, k, grid, closure::AIBD, K, clk, fields, b) = + ν_σᶠᶠᶜ(i, j, k, grid, closure, K, clk, fields, biharmonic_mask_y, ∂yᶠᶠᶜ, ∇²ᶠᶜᶜ, fields.u)
@inline viscous_flux_vy(i, j, k, grid, closure::AIBD, K, clk, fields, b) = + ν_σᶜᶜᶜ(i, j, k, grid, closure, K, clk, fields, ∂yᶜᶜᶜ, biharmonic_mask_y, ∇²ᶜᶠᶜ, fields.v)
@inline viscous_flux_wy(i, j, k, grid, closure::AIBD, K, clk, fields, b) = + ν_σᶜᶠᶠ(i, j, k, grid, closure, K, clk, fields, biharmonic_mask_y, ∂yᶜᶠᶠ, ∇²ᶜᶜᶠ, fields.w)
@inline viscous_flux_uz(i, j, k, grid, closure::AIBD, K, clk, fields, b) = + ν_σᶠᶜᶠ(i, j, k, grid, closure, K, clk, fields, biharmonic_mask_z, ∂zᶠᶜᶠ, ∇²ᶠᶜᶜ, fields.u)
@inline viscous_flux_vz(i, j, k, grid, closure::AIBD, K, clk, fields, b) = + ν_σᶜᶠᶠ(i, j, k, grid, closure, K, clk, fields, biharmonic_mask_z, ∂zᶜᶠᶠ, ∇²ᶜᶠᶜ, fields.v)
@inline viscous_flux_wz(i, j, k, grid, closure::AIBD, K, clk, fields, b) = + ν_σᶜᶜᶜ(i, j, k, grid, closure, K, clk, fields, ∂zᶜᶜᶜ, biharmonic_mask_z, ∇²ᶜᶜᶠ, fields.w)
@inline viscous_flux_ux(i, j, k, grid, closure::Union{AHBD, VectorInvariantASBD}, K, clk, fields, b) = + ν_σᶜᶜᶜ(i, j, k, grid, closure, K, clk, fields, δ★ᶜᶜᶜ, fields.u, fields.v)
@inline viscous_flux_vx(i, j, k, grid, closure::Union{AHBD, VectorInvariantASBD}, K, clk, fields, b) = + ν_σᶠᶠᶜ(i, j, k, grid, closure, K, clk, fields, ζ★ᶠᶠᶜ, fields.u, fields.v)
@inline viscous_flux_wx(i, j, k, grid, closure::Union{AHBD, VectorInvariantASBD}, K, clk, fields, b) = + ν_σᶠᶜᶠ(i, j, k, grid, closure, K, clk, fields, biharmonic_mask_x, ∂xᶠᶜᶠ, ∇²ᶜᶜᶠ, fields.w)
@inline viscous_flux_uy(i, j, k, grid, closure::Union{AHBD, VectorInvariantASBD}, K, clk, fields, b) = - ν_σᶠᶠᶜ(i, j, k, grid, closure, K, clk, fields, ζ★ᶠᶠᶜ, fields.u, fields.v)
@inline viscous_flux_vy(i, j, k, grid, closure::Union{AHBD, VectorInvariantASBD}, K, clk, fields, b) = + ν_σᶜᶜᶜ(i, j, k, grid, closure, K, clk, fields, δ★ᶜᶜᶜ, fields.u, fields.v)
@inline viscous_flux_wy(i, j, k, grid, closure::Union{AHBD, VectorInvariantASBD}, K, clk, fields, b) = + ν_σᶜᶠᶠ(i, j, k, grid, closure, K, clk, fields, biharmonic_mask_y, ∂yᶜᶠᶠ, ∇²ᶜᶜᶠ, fields.w)
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@inline viscous_flux_uz(i, j, k, grid, closure::AVBD, K, clk, fields, b) = + ν_σᶠᶜᶠ(i, j, k, grid, closure, K, clk, fields, biharmonic_mask_z, ∂zᶠᶜᶠ, ∂²zᶠᶜᶜ, fields.u)
@inline viscous_flux_vz(i, j, k, grid, closure::AVBD, K, clk, fields, b) = + ν_σᶜᶠᶠ(i, j, k, grid, closure, K, clk, fields, biharmonic_mask_z, ∂zᶜᶠᶠ, ∂²zᶜᶠᶜ, fields.v)
@inline viscous_flux_wz(i, j, k, grid, closure::AVBD, K, clk, fields, b) = + ν_σᶜᶜᶜ(i, j, k, grid, closure, K, clk, fields, ∂zᶜᶜᶜ, biharmonic_mask_z, ∂²zᶜᶜᶠ, fields.w)
@inline viscous_flux_ux(i, j, k, grid, closure::ADBD, K, clk, fields, b) = + ν_σᶜᶜᶜ(i, j, k, grid, closure, K, clk, fields, δ★ᶜᶜᶜ, fields.u, fields.v)
@inline viscous_flux_vy(i, j, k, grid, closure::ADBD, K, clk, fields, b) = + ν_σᶜᶜᶜ(i, j, k, grid, closure, K, clk, fields, δ★ᶜᶜᶜ, fields.u, fields.v)

#####
##### Diffusive fluxes
Expand All @@ -71,27 +76,35 @@ const AVBD = AbstractScalarBiharmonicDiffusivity{<:VerticalFormulation}
##### Biharmonic-specific viscous operators
#####

# See https://mitgcm.readthedocs.io/en/latest/algorithm/algorithm.html#horizontal-dissipation
@inline function δ★ᶜᶜᶜ(i, j, k, grid, u, v)
@inline ∇²u_vector_invariantᶠᶜᶜ(i, j, k, grid, u, v) = δxᶠᶜᶜ(i, j, k, grid, div_xyᶜᶜᶜ, u, v) - δyᶠᶜᶜ(i, j, k, grid, ζ₃ᶠᶠᶜ, u, v)
@inline ∇²v_vector_invariantᶜᶠᶜ(i, j, k, grid, u, v) = δxᶜᶠᶜ(i, j, k, grid, ζ₃ᶠᶠᶜ, u, v) + δyᶜᶠᶜ(i, j, k, grid, div_xyᶜᶜᶜ, u, v)

# These closures seem to be needed to help the compiler infer types
# (either of u and v or of the function arguments)
@inline Δy_∇²u(i, j, k, grid, u) = Δy_qᶠᶜᶜ(i, j, k, grid, biharmonic_mask_x, ∇²hᶠᶜᶜ, u)
@inline Δx_∇²v(i, j, k, grid, v) = Δx_qᶜᶠᶜ(i, j, k, grid, biharmonic_mask_y, ∇²hᶜᶠᶜ, v)
# These closures seem to be needed to help the compiler infer types
# (either of u and v or of the function arguments)
@inline Δy_∇²u(i, j, k, grid, closure, u, v) = Δy_qᶠᶜᶜ(i, j, k, grid, biharmonic_mask_x, ∇²hᶠᶜᶜ, u)
@inline Δx_∇²v(i, j, k, grid, closure, u, v) = Δx_qᶜᶠᶜ(i, j, k, grid, biharmonic_mask_y, ∇²hᶜᶠᶜ, v)
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Are ∇²v and ∇²u still appropriate names for these operators? It's a bit confusing.


return 1 / Azᶜᶜᶜ(i, j, k, grid) * (δxᶜᵃᵃ(i, j, k, grid, Δy_∇²u, u) +
δyᵃᶜᵃ(i, j, k, grid, Δx_∇²v, v))
end
@inline Δy_∇²v(i, j, k, grid, closure, u, v) = Δy_qᶜᶠᶜ(i, j, k, grid, biharmonic_mask_y, ∇²hᶜᶠᶜ, v)
@inline Δx_∇²u(i, j, k, grid, closure, u, v) = Δx_qᶠᶜᶜ(i, j, k, grid, biharmonic_mask_x, ∇²hᶠᶜᶜ, u)

@inline Δy_∇²u(i, j, k, grid, ::VectorInvariantASBD, u, v) = Δy_qᶠᶜᶜ(i, j, k, grid, biharmonic_mask_x, ∇²u_vector_invariantᶠᶜᶜ, u, v)
@inline Δx_∇²v(i, j, k, grid, ::VectorInvariantASBD, u, v) = Δx_qᶜᶠᶜ(i, j, k, grid, biharmonic_mask_y, ∇²v_vector_invariantᶜᶠᶜ, u, v)

@inline function ζ★ᶠᶠᶜ(i, j, k, grid, u, v)
# See https://mitgcm.readthedocs.io/en/latest/algorithm/algorithm.html#horizontal-dissipation
@inline function δ★ᶜᶜᶜ(i, j, k, grid, closure, u, v)
return 1 / Azᶜᶜᶜ(i, j, k, grid) * (δxᶜᵃᵃ(i, j, k, grid, Δy_∇²u, closure, u, v) +
δyᵃᶜᵃ(i, j, k, grid, Δx_∇²v, closure, u, v))
end

# These closures seem to be needed to help the compiler infer types
# (either of u and v or of the function arguments)
@inline Δy_∇²v(i, j, k, grid, v) = Δy_qᶜᶠᶜ(i, j, k, grid, biharmonic_mask_y, ∇²hᶜᶠᶜ, v)
@inline Δx_∇²u(i, j, k, grid, u) = Δx_qᶠᶜᶜ(i, j, k, grid, biharmonic_mask_x, ∇²hᶠᶜᶜ, u)
@inline function ζ★ᶠᶠᶜ(i, j, k, grid, closure, u, v)
return 1 / Azᶠᶠᶜ(i, j, k, grid) * (δxᶠᵃᵃ(i, j, k, grid, Δy_∇²v, closure, u, v) -
δyᵃᶠᵃ(i, j, k, grid, Δx_∇²u, closure, u, v))
end

return 1 / Azᶠᶠᶜ(i, j, k, grid) * (δxᶠᵃᵃ(i, j, k, grid, Δy_∇²v, v) -
δyᵃᶠᵃ(i, j, k, grid, Δx_∇²u, u))
@inline function ζ★ᶠᶠᶜ(i, j, k, grid, ::VectorInvariantASBD, u, v)
∇²u = ∇²u_vector_invariantᶠᶜᶜ(i, j, k, grid, u, v)
∇²v = ∇²v_vector_invariantᶜᶠᶜ(i, j, k, grid, u, v)
return ζ₃ᶠᶠᶜ(i, j, k, grid, ∇²u, ∇²v)
end

#####
Expand Down
7 changes: 7 additions & 0 deletions src/TurbulenceClosures/abstract_scalar_diffusivity_closure.jl
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Expand Up @@ -27,6 +27,13 @@ Specifies a horizontally-isotropic, `VectorInvariant`, `ScalarDiffusivity`.
"""
struct HorizontalFormulation <: AbstractDiffusivityFormulation end

"""
struct VectorInvariantForm end

Specifies a `VectorInvariant` `ScalarDiffusivity`.
"""
struct VectorInvariantForm <: AbstractDiffusivityFormulation end

"""
struct HorizontalDivergenceFormulation end

Expand Down
17 changes: 10 additions & 7 deletions src/TurbulenceClosures/turbulence_closure_implementations/scalar_biharmonic_diffusivity.jl
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Expand Up @@ -6,10 +6,10 @@ using Oceananigans.Utils: prettysummary

Holds viscosity and diffusivities for models with prescribed isotropic diffusivities.
"""
struct ScalarBiharmonicDiffusivity{F, N, V, K} <: AbstractScalarBiharmonicDiffusivity{F, N}
struct ScalarBiharmonicDiffusivity{F, N, VI, V, K} <: AbstractScalarBiharmonicDiffusivity{F, N, VI}
ν :: V
κ :: K
ScalarBiharmonicDiffusivity{F, N}(ν::V, κ::K) where {F, V, K, N} = new{F, N, V, K}(ν, κ)
ScalarBiharmonicDiffusivity{F, N, VI}(ν::V, κ::K) where {F, N, VI, V, K} = new{F, N, VI, V, K}(ν, κ)
end

# Aliases that allow specify the floating type, assuming that the discretization is Explicit in time
Expand Down Expand Up @@ -76,26 +76,29 @@ function ScalarBiharmonicDiffusivity(formulation = ThreeDimensionalFormulation()
ν = 0,
κ = 0,
discrete_form = false,
vector_invariant_form = true,
loc = (nothing, nothing, nothing),
parameters = nothing,
required_halo_size::Int = 2)

ν = convert_diffusivity(FT, ν; discrete_form, loc, parameters)
κ = convert_diffusivity(FT, κ; discrete_form, loc, parameters)


VI = vector_invariant_form ? VectorInvariantForm : nothing

# Force a type-stable constructor if ν and κ are numbers
# This particular short-circuiting of the required_halo_size kwargs is necessary to perform parameter
# estimation of the diffusivity coefficients using autodiff.
if ν isa Number && κ isa Number
return ScalarBiharmonicDiffusivity{typeof(formulation), 2}(ν, κ)
return ScalarBiharmonicDiffusivity{typeof(formulation), 2, VI}(ν, κ)
end

return ScalarBiharmonicDiffusivity{typeof(formulation), required_halo_size}(ν, κ)
return ScalarBiharmonicDiffusivity{typeof(formulation), required_halo_size, VI}(ν, κ)
end

function with_tracers(tracers, closure::ScalarBiharmonicDiffusivity{F, N, V, K}) where {F, N, V, K}
function with_tracers(tracers, closure::ScalarBiharmonicDiffusivity{F, N, VI}) where {F, N, VI}
κ = tracer_diffusivities(tracers, closure.κ)
return ScalarBiharmonicDiffusivity{F, N}(closure.ν, κ)
return ScalarBiharmonicDiffusivity{F, N, VI}(closure.ν, κ)
end

@inline viscosity(closure::ScalarBiharmonicDiffusivity, K) = closure.ν
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