Add temperature models that reads from ascii data file

CHANGELOG.md

@@ -17,6 +17,7 @@ This project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.htm
 - There is now a properties_output_size function, which returns the size of the output vector/array returned by the properties functions for a given properties input vector \[Menno Fraters; 2024-10-27; [#765](https://github.com/GeodynamicWorldBuilder/WorldBuilder/pull/765)\]
 - Added 2d and 3d versions of the properties function to the C wrapper \[Menno Fraters; 2024-10-27; [#765](https://github.com/GeodynamicWorldBuilder/WorldBuilder/pull/765)\]
 - Added continental geotherm from Chapman (1986) for the Temperature Model in Continental Plate \[Alan Yu; 2025-01-21; [#778](https://github.com/GeodynamicWorldBuilder/WorldBuilder/issues/778), [#797](https://github.com/GeodynamicWorldBuilder/WorldBuilder/pull/797)\]
+- Added the ability to read the thermal structure of oceanic plates from an ascii data file \[Juliane Dannberg; 2025-01-24; [#830](https://github.com/GeodynamicWorldBuilder/WorldBuilder/pull/830)
 
 ### Changed
 - The tian2019 composition model now returns a mass fraction instead of a mass percentage. \[Daniel Douglas; 2024-11-12; [#767](https://github.com/GeodynamicWorldBuilder/WorldBuilder/pull/767)\]

contrib/1D-diffusion-table/compute-1D-diffusion-table.py

@@ -0,0 +1,229 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.special import erf
+
+# --- 1. Parameters ---
+L = 5.e5         # Depth of the domain (m)
+N = 501          # Number of spatial points
+dx = L / (N - 1) # Grid spacing
+x = np.linspace(0, L, N)
+
+# Physical properties (example)
+alpha         = 3e-5    # 1/K
+cp            = 1200    # Specific heat capacity (J/kg-K), assumed constant for simplicity
+reference_rho = 3300
+k0            = 4       # W/m/K
+reference_T   = 293
+gravity       = 10
+T_surface     = 293.
+
+# 'T-dependent' or 'constant'
+formulation = 'T-dependent' 
+
+# Time stepping
+year_in_seconds = 3600*24*365.25
+dt = 1e4 * year_in_seconds       # Time step (yr) -- must be small enough for stability
+t_max = 2.5e8 * year_in_seconds    # Total time (yr)
+n_steps = int(t_max / dt)
+
+save_interval = int(n_steps / 250) # how often we store temperature, pressure, density
+
+# Let's define a variable density and variable conductivity as functions of x
+def density(T):
+    if formulation == 'T-dependent':
+        return reference_rho * (1. - alpha * (T - reference_T))
+    elif formulation == 'constant':
+        return reference_rho * np.ones(T.shape)
+
+def conductivity(T, p):
+    # Hofmeister
+    if formulation == 'T-dependent':
+        k = k0 * (298.0/T)**0.33 \
+            * np.exp(-(4.0 * 1.2 + 1./3.) * alpha * (T - 298.0)) \
+            * (1. + 4. * p / 1.35e11)  \
+            + 0.01753 - 0.00010365 * T + 2.2451e-7 * T**2 - 3.407e-11 * T**3
+    elif formulation == 'constant':
+        k = k0 * np.ones(T.shape)
+    return k
+
+def integrate_pressure(rho_arr):
+    # Here, for if rho depends on p, we would need to update rho as well
+    p_arr = np.zeros(N)
+    for i in range(1, N):
+        p_arr[i] = p_arr[i-1] + rho_arr[i] * gravity * dx
+    return p_arr
+
+
+# --- 2. Initial Condition ---
+T = np.zeros(N)
+
+# Start with mantle potential temperature
+T_mantle = 1623.0
+T[:] = T_mantle
+T[0] = T_surface
+
+# --- 3. Boundary Conditions (Dirichlet) ---
+# Use the initial conditions
+T_top = T[0]
+T_bottom = T[-1]
+
+# Helper to get "interface conductivity" k_{i+1/2}
+def k_interface(k_top, k_bot):
+    # For simplicity, use average. Could also use harmonic mean, etc.
+    return 0.5 * (k_top + k_bot)
+
+# --- 4. Time-stepping loop (Explicit) ---
+
+for step in range(n_steps):
+    T_new = T.copy()
+
+    # Evaluate properties at the current time
+    rho_arr = density(T)
+
+    # compute pressure
+    p_arr  = integrate_pressure(rho_arr)
+    k_arr   = conductivity(T, p_arr)
+
+    if step == 0:
+        # keep track of solutions for plotting
+        T_history = [T.copy()]
+        p_history   = [p_arr.copy()]  
+        rho_history = [rho_arr.copy()]
+        k_history   = [k_arr.copy()]
+
+    # Enforce Dirichlet boundaries
+    T_new[0] = T_top
+    T_new[-1] = T_bottom
+
+    # Update interior points
+    for i in range(1, N-1):
+        rho_i = rho_arr[i]
+
+        # Compute effective conductivities at the interfaces
+        k_imh = k_interface(k_arr[i-1], k_arr[i])   # k_{i-1/2}
+        k_iph = k_interface(k_arr[i],   k_arr[i+1]) # k_{i+1/2}
+
+        # Finite difference for second derivative with variable k
+        d2T_dx2 = (k_iph*(T[i+1] - T[i]) - k_imh*(T[i] - T[i-1])) / (dx*dx)
+
+        # Explicit update
+        T_new[i] = T[i] + dt/(rho_i * cp) * d2T_dx2
+
+    # Advance in time
+    T = T_new
+
+    # Store in history every so often
+    # Do not store step 0 again
+    # Note that technically, only T is from after solving, the other properties have not been updated
+    if (step+1) % save_interval == 0:
+        T_history.append(T.copy())
+        p_history.append(p_arr.copy())  
+        rho_history.append(rho_arr.copy())
+        k_history.append(k_arr.copy())
+
+# build time array for each saved snapshot
+nt = len(T_history)  # number of snapshots actually stored
+t = np.arange(nt) * (save_interval * dt)
+
+# --- 5. Plot final solution ---
+
+# T_2D is (nt, N), so we can do .T to get (N, nt)
+Temperature_2D = np.array(T_history).T
+pressure_2D = np.array(p_history).T
+density_2D = np.array(rho_history).T
+conductivity_2D = np.array(k_history).T
+
+# Make coordinate grids
+#  - "t" along the 'horizontal' direction (axis=1 or 0 depends on your preference)
+#  - "x" along the 'vertical' direction
+
+Xgrid, timegrid = np.meshgrid(x, t/(year_in_seconds * 1e6), indexing='ij')
+# Now Xgrid and timegrid both have shape (N, nt)
+
+
+plt.figure(figsize=(10,4))
+# Make a "heatmap" of temperature. 
+# Xgrid, timegrid, and Temperature_2D must be the same shape (N, nt).
+
+plt.pcolormesh(timegrid, Xgrid/1000, Temperature_2D, shading='gouraud', edgecolors='face', linewidth=0)
+plt.xlabel("Time [Myr]")
+plt.ylabel("Depth [km]")
+plt.gca().invert_yaxis()
+cbar = plt.colorbar()
+cbar.set_label("Temperature [K]")
+
+plt.title("Temperature evolution")
+plt.savefig('temperature.pdf', format='pdf')
+plt.close()
+
+
+plt.figure(figsize=(10,4))
+plt.pcolormesh(timegrid, Xgrid/1000, pressure_2D - reference_rho * gravity * Xgrid, shading='gouraud', edgecolors='face', linewidth=0)
+plt.xlabel("Time [Myr]")
+plt.ylabel("Depth [km]")
+plt.gca().invert_yaxis()
+cbar = plt.colorbar()
+cbar.set_label("Pressure [Pa]")
+
+plt.title("Pressure difference from $rho_0 g z$")
+plt.savefig('pressure.pdf', format='pdf')
+plt.close()
+
+
+plt.figure(figsize=(10,4))
+plt.pcolormesh(timegrid, Xgrid/1000, density_2D, shading='gouraud', edgecolors='face', linewidth=0)
+plt.xlabel("Time [Myr]")
+plt.ylabel("Depth [km]")
+plt.gca().invert_yaxis()
+cbar = plt.colorbar()
+cbar.set_label("Density [kg/m$^3$]")
+
+plt.title("Density evolution")
+plt.savefig('density.pdf', format='pdf')
+plt.close()
+
+
+plt.figure(figsize=(10,4))
+plt.pcolormesh(timegrid, Xgrid/1000, conductivity_2D, shading='gouraud', edgecolors='face', linewidth=0)
+plt.xlabel("Time [Myr]")
+plt.ylabel("Depth [km]")
+plt.gca().invert_yaxis()
+cbar = plt.colorbar()
+cbar.set_label("Conductivity [W/m/K]")
+
+plt.title("Conductivity evolution")
+plt.savefig('conductivity.pdf', format='pdf')
+plt.close()
+
+# Compare to erfc.
+plt.figure(figsize=(10,4))
+HSC_grid = T_surface + (T_mantle - T_surface) * erf(Xgrid/(2*np.sqrt(conductivity_2D*timegrid*year_in_seconds*1e6/(density_2D*cp))))
+plt.pcolormesh(timegrid, Xgrid/1000, Temperature_2D - HSC_grid, shading='gouraud', edgecolors='face', linewidth=0)
+plt.xlabel("Time [Myr]")
+plt.ylabel("Depth [km]")
+plt.gca().invert_yaxis()
+cbar = plt.colorbar()
+cbar.set_label("Temperature [K]")
+
+plt.title("Temperature - error function")
+plt.savefig('temperature_erfc.pdf', format='pdf')
+plt.close()
+
+
+# Write output into file
+filename = "temperature_data.txt"
+
+with open(filename, "w") as f:
+    f.write("# Columns: time [yrs]   depth [m]   temperature\n")
+    f.write("# POINTS: " + str(len(t)) + " " + str(len(x)) + "\n")
+    for ix in range(len(x)):         # loop over time snapshots
+        for it in range(len(t)):         # loop over the 50 x-values
+            # Each line: time, depth, T
+            # Right align each with chosen width and precision
+            time_str = f"{t[it]/year_in_seconds:9.3e}"
+            x_str    = f"{x[ix]:12.3e}"
+            temp_str = f"{Temperature_2D[ix, it]:12.3f}"
+
+            f.write(time_str + x_str + temp_str + "\n")
+
+print(f"Data written to '{filename}'")

cookbooks/2d_cartesian_plate_ascii/2d_cartesian_plate_ascii.grid

@@ -0,0 +1,14 @@
+# output variables
+grid_type = cartesian
+dim = 2
+compositions = 5
+
+# domain of the grid
+x_min = 0e3
+x_max = 2000e3
+z_min = 0
+z_max = 400e3
+
+# grid properties
+n_cell_x = 2000
+n_cell_z = 400

cookbooks/2d_cartesian_plate_ascii/2d_cartesian_plate_ascii.wb

@@ -0,0 +1,42 @@
+{
+  "version":"1.1",
+  "surface temperature":293,
+  "potential mantle temperature":1623,
+  "thermal expansion coefficient":3e-5,
+  "specific heat":1200,
+  "gravity model":{"model":"uniform", "magnitude":10},
+  "thermal diffusivity":1.06060606e-6,
+  "cross section":[[0,0],[100,0]],
+  "features":
+  [
+    {"model":"mantle layer", "name":"upper mantle", "min depth":95e3, "max depth":660e3, "coordinates":[[-1e3,-1e3],[2001e3,-1e3],[2001e3,1e3],[-1e3,1e3]],
+     "temperature models":[{"model":"adiabatic", "min depth":95e3, "max depth":660e3}],
+     "composition models":[{"model":"uniform", "compositions":[4]}]},
+
+    {"model":"oceanic plate", "name":"oceanic plate", "coordinates":[[-1e3,-1e3],[1150e3,-1e3],[1150e3,1e3],[-1e3,1e3]],
+     "temperature models":[{"model":"ascii data", "data directory":"2d_cartesian_plate_ascii/", "max depth":300e3, "spreading velocity":0.01, "ridge coordinates":[[[100e3,-1e3],[100e3,1e3]]]}],
+     "composition models":[{"model":"uniform", "compositions":[0], "max depth":10e3},
+                           {"model":"uniform", "compositions":[1], "min depth":10e3, "max depth":95e3}]},
+
+    {"model":"continental plate", "name":"continental plate", "coordinates":[[1150e3,-1e3],[2001e3,-1e3],[2001e3,1e3],[1150e3,1e3]],
+     "temperature models":[{"model":"linear", "max depth":95e3, "bottom temperature":1685.018071264}],
+     "composition models":[{"model":"uniform", "compositions":[2], "max depth":30e3},
+                           {"model":"uniform", "compositions":[3], "min depth":30e3, "max depth":95e3}]},
+
+    {"model":"subducting plate", "name":"Subducting plate", "coordinates":[[1150e3,-1e3],[1150e3,1e3]], "dip point":[2000e3,0],
+     "segments":[{"length":200e3, "thickness":[300e3], "angle":[0,45]}, {"length":200e3, "thickness":[300e3], "angle":[45]},
+                 {"length":200e3, "thickness":[300e3], "angle":[45,0]}, {"length":100e3, "thickness":[300e3], "angle":[0]}],
+     "temperature models":[
+                {"model":"mass conserving",
+                "density":3300, "thermal conductivity":4,"adiabatic heating":true,
+                "spreading velocity":0.0135,
+                "subducting velocity":0.0135,
+                "ridge coordinates":[[[100e3,-1e3],[100e3,1e3]]],
+                "coupling depth":80e3,
+                "forearc cooling factor":20.0,
+                "taper distance":100e3,
+                "min distance slab top":-300e3, "max distance slab top":300e3}],
+     "composition models":[{"model":"uniform", "compositions":[0], "max distance slab top":10e3},
+                           {"model":"uniform", "compositions":[1], "min distance slab top":10e3, "max distance slab top":95e3 }]}
+  ]
+}