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Merged
LukasFuchs merged 2 commits into from
Jul 14, 2025
Merged

update and cleanup viscous inclusion #82

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75de263
Cleanup Viscousinclusion
LukasFuchs Jul 14, 2025
f09b13b
Merge branch 'corrections'
LukasFuchs Jul 14, 2025
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196 changes: 75 additions & 121 deletions examples/StokesEquation/2D/ViscousInclusion.jl
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Original file line number Diff line number Diff line change
@@ -1,22 +1,15 @@
using GeoModBox, Printf, Plots
using GeoModBox.InitialCondition, GeoModBox.Tracers.TwoD
using GeoModBox.MomentumEquation.TwoD
using Base.Threads, LinearAlgebra
using Base.Threads, LinearAlgebra, Statistics

function ViscousInclusion()
## ===================== Some initial definitions ======================= #
save_fig = 0
plotfields =:yes
# save_fig = 0
# plotfields =:yes
#Py.scale = 'yes';
FDMethod =:dc
# ----------------------------------------------------------------------- #
# Plot Settings ========================================================= #
Pl = (
qinc = 8,
mainc = 2,
qsc = 1e8# 100*(60*60*24*365.25)
)
# ------------------------------------------------------------------- #
# Define Initial Condition ============================================== #
Ini = (
V=:PureShear,
Expand All @@ -25,21 +18,21 @@ Ini = (
)
# inclusions bedingungen
α = 0; # positive -> counter clockwise
EllA = 2e2 # 1.75e3; [m]
EllB = 2e2 # 0.25e3; [m]
EllA = 2e-1 # 1.75e3; [m]
EllB = 2e-1 # 0.25e3; [m]
# ----------------------------------------------------------------------- #
## ==================== Define model geometry constants ================= #
M = Geometry(
ymin = -1.0e3, # Model depth [ m ]
ymin = -1.0, # Model depth [ m ]
ymax = 0.0,
xmin = 0.0,
xmax = 1.0e3, # Model length [ m ]
xmax = 1.0, # Model length [ m ]
)
# ----------------------------------------------------------------------- #
## ====================== Define the numerical grid ===================== #
NC = (
x = 100,
y = 100,
x = 50,
y = 50,
)
NV = (
x = NC.x + 1,
Expand Down Expand Up @@ -127,17 +120,6 @@ VBC = (
# ----------------------------------------------------------------------- #
# Initial Condition ===================================================== #
IniVelocity!(Ini.V,D,VBC,NC,NV,Δ,M,x,y;Ini.ε)
# for i = 1:NC.x
# for j = 1:NC.y
# D.vxc[i,j] = (D.vx[i,j+1] + D.vx[i+1,j+1])/2
# D.vyc[i,j] = (D.vy[i+1,j] + D.vy[i+1,j+1])/2
# end
# end
# @. D.vc = sqrt(D.vxc^2 + D.vyc^2)
# @show minimum(D.vx),maximum(D.vx), minimum(D.vy),maximum(D.vy)
# vxana = copy(D.vx)
# vyana = copy(D.vy)
# Pta = copy(D.Pt)
# Get analytical Solution
AnaSol = (
Pa = zeros(Float64,NC...),
Expand All @@ -157,21 +139,23 @@ Dani_Solution_vec!(Ini.V,AnaSol,M,x,y,EllA,η₁/η₀,NC,NV)

# Boundary Conditions ---
# Horizontal velocity
VBC.val.S .= AnaSol.Vx_S./1e12
VBC.val.N .= AnaSol.Vx_N./1e12
VBC.val.vxE .= AnaSol.Vx_E./1e12
VBC.val.vxW .= AnaSol.Vx_W./1e12
VBC.val.S .= AnaSol.Vx_S
VBC.val.N .= AnaSol.Vx_N
VBC.val.vxE .= AnaSol.Vx_E
VBC.val.vxW .= AnaSol.Vx_W

# Vertical velocity
VBC.val.E .= AnaSol.Vy_E./1e12
VBC.val.W .= AnaSol.Vy_W./1e12
VBC.val.vyS .= AnaSol.Vy_S./1e12
VBC.val.vyN .= AnaSol.Vy_N./1e12
VBC.val.E .= AnaSol.Vy_E
VBC.val.W .= AnaSol.Vy_W
VBC.val.vyS .= AnaSol.Vy_S
VBC.val.vyN .= AnaSol.Vy_N

@. D.vx[1,2:end-1] = AnaSol.Vx_W
@. D.vx[end,2:end-1] = AnaSol.Vx_E
@. D.vy[2:end-1,1] = AnaSol.Vy_S
@. D.vy[2:end-1,end] = AnaSol.Vy_N

@. D.vx[1,2:end-1] = AnaSol.Vx_W/1e12
@. D.vx[end,2:end-1] = AnaSol.Vx_E/1e12
@. D.vy[2:end-1,1] = AnaSol.Vy_S/1e12
@. D.vy[2:end-1,end] = AnaSol.Vy_N/1e12
# @. AnaSol.Pa -= mean(AnaSol.Pa)
# ----------------------------------------------------------------------- #
# Tracer Advection ====================================================== #
nmx,nmy = 5,5
Expand All @@ -193,20 +177,14 @@ MPC1 = (
MPC = merge(MPC,MPC1)
Ma = IniTracer2D(Aparam,nmx,nmy,Δ,M,NC,noise,Ini.p,phase;
ellA=EllA,ellB=EllB,α=α)
# # Count marker per cell ---
# CountMPC(Ma,nmark,MPC,M,x,y,Δ,NC,NV,1)
# Interpolate from markers to cell ---
Markers2Cells(Ma,nmark,MPC.PG_th,D.ρ,MPC.wt_th,D.wt,x,y,Δ,Aparam,ρ)
Markers2Cells(Ma,nmark,MPC.PG_th,D.ηc,MPC.wt_th,D.wt,x,y,Δ,Aparam,η)
Markers2Cells(Ma,nmark,MPC.PG_th,D.p,MPC.wt_th,D.wt,x,y,Δ,Aparam,phase)
Markers2Vertices(Ma,nmark,MPC.PV_th,D.ηv,MPC.wtv_th,D.wtv,x,y,Δ,Aparam,η)
@. D.ηc = 0.25 * (D.ηv[1:end-1,1:end-1] +
D.ηv[2:end-0,1:end-1] +
D.ηv[1:end-1,2:end-0] +
D.ηv[2:end-0,2:end-0])
# ------------------------------------------------------------------- #
# System of Equations =============================================== #
# Iterations
niter = 50
niter = 20
ϵ = 1e-8
# Numbering, without ghost nodes! ---
off = [ NV.x*NC.y, # vx
Expand Down Expand Up @@ -273,94 +251,70 @@ elseif FDMethod==:direct
D.vy[2:end-1,:] .= χ[Num.Vy]
D.Pt .= χ[Num.Pt]
end
# @. D.Pt -= mean(D.Pt)
# --------------------------------------------------------------- #
@. D.vx *= 1e12
@. D.vy *= 1e12
@. D.Pt *= 1e12
# # Get the velocity on the centroids ---
# for i = 1:NC.x
# for j = 1:NC.y
# D.vxc[i,j] = (D.vx[i,j+1] + D.vx[i+1,j+1])/2
# D.vyc[i,j] = (D.vy[i+1,j] + D.vy[i+1,j+1])/2
# end
# end
# @. D.vc = sqrt(D.vxc^2 + D.vyc^2)
Pe = copy(D.Pt)
@. Pe = abs((D.Pt-AnaSol.Pa))
Pe = abs.((D.Pt.-AnaSol.Pa))./maximum(abs.(AnaSol.Pa)).*100
Vxe = copy(AnaSol.Vxa)
@. Vxe = abs((D.vx[:,2:end-1]-AnaSol.Vxa))
Vxe = abs.((D.vx[:,2:end-1].-AnaSol.Vxa))./maximum(abs.(AnaSol.Vxa)).*100
Vye = copy(AnaSol.Vya)
@. Vye = abs((D.vy[2:end-1,:]-AnaSol.Vya))
Vye = abs.((D.vy[2:end-1,:].-AnaSol.Vya))./maximum(abs.(AnaSol.Vya)).*100

p = heatmap(x.v./1e3,y.ce./1e3,(D.vx)',color=:berlin,
display(heatmap(x.v,y.ce,(D.vx)',color=:berlin,
xlabel="x[km]",ylabel="y[km]",colorbar=true,
title="Numerical",
aspect_ratio=:equal,xlims=(M.xmin/1e3, M.xmax/1e3),
ylims=(M.ymin/1e3, M.ymax/1e3),
layout=(3,3),subplot=1)
heatmap!(p,x.ce./1e3,y.v./1e3,(D.vy)',color=:berlin,
title="Numerical - vx",
aspect_ratio=:equal,xlims=(M.xmin, M.xmax),
ylims=(M.ymin, M.ymax)))
# layout=(3,3),subplot=1)
display(heatmap(x.ce,y.v,(D.vy)',color=:berlin,
xlabel="x[km]",ylabel="y[km]",colorbar=true,
title="v_y [cm/a]",
aspect_ratio=:equal,xlims=(M.xmin/1e3, M.xmax/1e3),
ylims=(M.ymin/1e3, M.ymax/1e3),
layout=(3,3),subplot=4)
heatmap!(p,x.c./1e3,y.c./1e3,D.Pt',color=:glasgow,
title="Numerical - v_y ",
aspect_ratio=:equal,xlims=(M.xmin, M.xmax),
ylims=(M.ymin, M.ymax)))
# layout=(3,3),subplot=4)
display(heatmap(x.c,y.c,D.Pt',color=:glasgow,
xlabel="x[km]",ylabel="y[km]",colorbar=true,
title="P_t",
aspect_ratio=:equal,xlims=(M.xmin/1e3, M.xmax/1e3),
ylims=(M.ymin/1e3, M.ymax/1e3),
layout=(3,3),subplot=7)
heatmap!(p,x.v./1e3,y.c./1e3,(AnaSol.Vxa)',color=:berlin,
title="Numerical - P_t",
aspect_ratio=:equal,xlims=(M.xmin, M.xmax),
ylims=(M.ymin, M.ymax)))
# layout=(3,3),subplot=7)
display(heatmap(x.v,y.c,(AnaSol.Vxa)',color=:berlin,
xlabel="x[km]",ylabel="y[km]",colorbar=true,
title="Analytical",
aspect_ratio=:equal,xlims=(M.xmin/1e3, M.xmax/1e3),
ylims=(M.ymin/1e3, M.ymax/1e3),
layout=(3,3),subplot=2)
heatmap!(p,x.c./1e3,y.v./1e3,(AnaSol.Vya)',color=:berlin,
title="Analytical - vx",
aspect_ratio=:equal,xlims=(M.xmin, M.xmax),
ylims=(M.ymin, M.ymax)))
# layout=(3,3),subplot=2))
display(heatmap(x.c,y.v,(AnaSol.Vya)',color=:berlin,
xlabel="x[km]",ylabel="y[km]",colorbar=true,
title="v_y [cm/a]",
aspect_ratio=:equal,xlims=(M.xmin/1e3, M.xmax/1e3),
ylims=(M.ymin/1e3, M.ymax/1e3),
layout=(3,3),subplot=5)
heatmap!(p,x.c./1e3,y.c./1e3,AnaSol.Pa',color=:glasgow,
title="Analytical - v_y ",
aspect_ratio=:equal,xlims=(M.xmin, M.xmax),
ylims=(M.ymin, M.ymax)))
# layout=(3,3),subplot=5)
display(heatmap(x.c,y.c,AnaSol.Pa',color=:glasgow,
xlabel="x[km]",ylabel="y[km]",colorbar=true,
title="P_t",
aspect_ratio=:equal,xlims=(M.xmin/1e3, M.xmax/1e3),
ylims=(M.ymin/1e3, M.ymax/1e3),
layout=(3,3),subplot=8)
heatmap!(p,x.v./1e3,y.c./1e3,(Vxe)',color=:berlin,
title="Analytical - P_t",
aspect_ratio=:equal,xlims=(M.xmin, M.xmax),
ylims=(M.ymin, M.ymax)))
# layout=(3,3),subplot=8)
display(heatmap(x.v,y.c,(Vxe)',color=:berlin,
xlabel="x[km]",ylabel="y[km]",colorbar=true,
title="Analytical",
aspect_ratio=:equal,xlims=(M.xmin/1e3, M.xmax/1e3),
ylims=(M.ymin/1e3, M.ymax/1e3),
layout=(3,3),subplot=3)
heatmap!(p,x.c./1e3,y.v./1e3,(Vye)',color=:berlin,
title="Error - vy",
aspect_ratio=:equal,xlims=(M.xmin, M.xmax),
ylims=(M.ymin, M.ymax)))
# layout=(3,3),subplot=3)
display(heatmap(x.c,y.v,(Vye)',color=:berlin,
xlabel="x[km]",ylabel="y[km]",colorbar=true,
title="v_y [cm/a]",
aspect_ratio=:equal,xlims=(M.xmin/1e3, M.xmax/1e3),
ylims=(M.ymin/1e3, M.ymax/1e3),
layout=(3,3),subplot=6)
heatmap!(p,x.c./1e3,y.c./1e3,Pe',color=:glasgow,
title="Error - v_y ",
aspect_ratio=:equal,xlims=(M.xmin, M.xmax),
ylims=(M.ymin, M.ymax)))
# layout=(3,3),subplot=6)
display(heatmap(x.c,y.c,Pe',color=:glasgow,
xlabel="x[km]",ylabel="y[km]",colorbar=true,
title="P_t",
aspect_ratio=:equal,xlims=(M.xmin/1e3, M.xmax/1e3),
ylims=(M.ymin/1e3, M.ymax/1e3),
layout=(3,3),subplot=9)


# heatmap!(p,x.c./1e3,y.c./1e3,log10.(D.ηc'),color=reverse(cgrad(:roma)),
# xlabel="x[km]",ylabel="y[km]",colorbar=true,
# title="η",
# aspect_ratio=:equal,xlims=(M.xmin/1e3, M.xmax/1e3),
# ylims=(M.ymin/1e3, M.ymax/1e3),
# layout=(2,2),subplot=4)
# quiver!(p,x.c2d[1:Pl.qinc:end,1:Pl.qinc:end]./1e3,
# y.c2d[1:Pl.qinc:end,1:Pl.qinc:end]./1e3,
# quiver=(D.vxc[1:Pl.qinc:end,1:Pl.qinc:end].*Pl.qsc,
# D.vyc[1:Pl.qinc:end,1:Pl.qinc:end].*Pl.qsc),
# la=0.5,color="white",layout=(2,2),subplot=4)

display(p)
title="Error - P_t",
aspect_ratio=:equal,xlims=(M.xmin, M.xmax),
ylims=(M.ymin, M.ymax)))
# layout=(3,3),subplot=9)
# display(p)

# ----------------------------------------------------------------------- #
# =============================== END =================================== #
Expand Down
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