Add implicit solvers for heat conduction equation

src/AsteroidThermoPhysicalModels.jl

@@ -40,6 +40,7 @@ export AbstractAsteroidThermoPhysicalModel, SingleAsteroidThermoPhysicalModel, B
 export AbstractAsteroidTPM, SingleAsteroidTPM, BinaryAsteroidTPM
 
 include("heat_conduction.jl")
+include("heat_conduction_analytical.jl")
 include("energy_flux.jl")
 include("non_grav.jl")
 include("thermal_radiation.jl")

src/TPM.jl

@@ -10,37 +10,37 @@ abstract type HeatConductionSolver end
 
 
 """
-Type of the forward Euler method:
+Type of the explicit (forward) Euler method:
 - Explicit in time
 - First order in time
 
-The `ForwardEulerSolver` type includes a vector for the temperature at the next time step.
+The `ExplicitEulerSolver` type includes a vector for the temperature at the next time step.
 """
-struct ForwardEulerSolver <: HeatConductionSolver
-    T::Vector{Float64}
+struct ExplicitEulerSolver <: HeatConductionSolver
+    x::Vector{Float64}  # Temperature vector for the next time step
 end
 
-ForwardEulerSolver(thermo_params::AbstractThermoParams) = ForwardEulerSolver(thermo_params.n_depth)
-ForwardEulerSolver(N::Integer) = ForwardEulerSolver(zeros(N))
+ExplicitEulerSolver(thermo_params::AbstractThermoParams) = ExplicitEulerSolver(thermo_params.n_depth)
+ExplicitEulerSolver(N::Integer) = ExplicitEulerSolver(zeros(N))
 
 
 """
-Type of the backward Euler method:
+Type of the implicit (backward) Euler method:
 - Implicit in time (Unconditionally stable in the heat conduction equation)
 - First order in time
 
-The `BackwardEulerSolver` type has vectors for the tridiagonal matrix algorithm.
+The `ImplicitEulerSolver` type has vectors for the tridiagonal matrix algorithm.
 """
-struct BackwardEulerSolver <: HeatConductionSolver
+struct ImplicitEulerSolver <: HeatConductionSolver
     a::Vector{Float64}
     b::Vector{Float64}
     c::Vector{Float64}
     d::Vector{Float64}
     x::Vector{Float64}
 end
 
-BackwardEulerSolver(thermo_params::AbstractThermoParams) = BackwardEulerSolver(thermo_params.n_depth)
-BackwardEulerSolver(N::Integer) = BackwardEulerSolver(zeros(N), zeros(N), zeros(N), zeros(N), zeros(N))
+ImplicitEulerSolver(thermo_params::AbstractThermoParams) = ImplicitEulerSolver(thermo_params.n_depth)
+ImplicitEulerSolver(N::Integer) = ImplicitEulerSolver(zeros(N), zeros(N), zeros(N), zeros(N), zeros(N))
 
 
 """
@@ -217,8 +217,6 @@ function SingleAsteroidThermoPhysicalModel(shape, thermo_params; SELF_SHADOWING,
 
     broadcast_thermo_params!(thermo_params, shape)
 
-    broadcast_thermo_params!(thermo_params, shape)
-
     n_depth = thermo_params.n_depth
     n_face = length(shape.faces)