Geometry and meshes

create_uniform_mesh(L::Real, n_cells::Int, ::Val{NC}; 
					T_initial::Real=300.0, 
					ξ_initial=nothing,
					cross_section_area::Real=1.0) -> Mesh1D{NC}

Create a uniform 1D mesh.

Arguments

• L: Domain length (thickness) [m]
• n_cells: Number of cells
• Val{NC}: Number of components as a type parameter (use Val(NC))
• T_initial=300.0: Initial temperature [K]
• ξ_initial=nothing: Initial concentrations (NTuple or scalar)
• cross_section_area=1.0: Cross-sectional area [m²]

Returns

A Mesh1D{NC} with uniform cell spacing.

Convention

• z = 0 is the BOTTOM surface (substrate, boundary_id = 2)
• z = L is the TOP surface (exposed surface, boundary_id = 1)
• Cell 1 is at z ≈ 0 (bottom), Cell N is at z ≈ L (top)
• Heat enters from the top (z = L), material shrinks toward bottom

Example

mesh = create_uniform_mesh(0.01, 100, Val(2))  # 1 cm, 100 cells, 2 components

create_stretched_mesh(L::Real, n_cells::Int, ::Val{NC}, stretch::Real;
					  T_initial::Real=300.0,
					  ξ_initial=nothing,
					  cross_section_area::Real=1.0,
					  stretch_from::Symbol=:top) -> Mesh1D{NC}

Create a geometrically stretched 1D mesh with the finest cells at the boundary named by stretch_from and cell sizes growing geometrically (ratio stretch) away from it.

Arguments

• L: Domain length [m]
• n_cells: Number of cells
• Val{NC}: Number of components as a type parameter (use Val(NC))
• stretch: Geometric size ratio between adjacent cells (must be ≥ 1; 1 = uniform). Each cell is stretch times thicker than its neighbor on the refined side.
• T_initial=300.0: Initial temperature [K]
• ξ_initial=nothing: Initial concentrations
• cross_section_area=1.0: Cross-sectional area [m²]
• stretch_from=:top: Which boundary gets the finest cells — :top (exposed surface at z = L, the default) or :bottom (substrate at z = 0)

Returns

A Mesh1D{NC} with geometric stretching.

Example

# Fine mesh near top surface (z=L), coarser toward bottom (z=0)
mesh = create_stretched_mesh(0.01, 50, Val(2), 1.1; stretch_from=:top)

MeshTopology — immutable connectivity.

A MeshTopology{D, NC} carries everything that does not change once the mesh is built: nodes, cells, faces, boundary tags, and dimensional metadata. Its mutable counterpart is MeshGeometry.

The pair is the dimension-parameterised mesh description for a multi-dimensional extension. ProblemDef carries a MeshTopology, but the 1D residual and Jacobian read connectivity from Mesh1D and geometry from the StateCache; neither reads this type.

Type Parameters

• D: Spatial dimension (1 today; 2/3 are the design target)
• NC: Number of components (carried for compile-time dispatch by consumers)

Fields

• nodes::Vector{NodeT}: Node objects (Node1D for D=1)
• cells::Vector{CellT}: Cell objects
• faces::Vector{FaceT}: Face objects
• boundary_tags::Dict{Symbol,Vector{Int}}: tag => face IDs (e.g. :top, :bottom)
• n_active_cells::Int: Active (leaf) cell count for AMR

MeshGeometry — mutable per-step geometry.

A MeshGeometry{D} carries the geometric quantities that change as the mesh moves (ALE) or is regenerated (AMR): node positions, cell volumes, face areas and (for D ≥ 2) face normals. The cross-sectional area A(t) for the 1D specialization lives here as a scalar.

The Workspace carries one, built from the mesh at construction, as the mutable counterpart of the immutable MeshTopology for a multi-dimensional extension. The 1D residual reads its geometry from the StateCache, not from this type.

Type Parameters

• D: Spatial dimension (1 today; 2/3 are the design target)

Fields (1D specialization layout)

• node_positions::Vector{Float64}: current z per node
• node_positions_ref::Vector{Float64}: reference (initial) z per node
• cell_centers::Vector{Float64}: cell center positions
• cell_volumes::Vector{Float64}: cell volumes
• face_positions::Vector{Float64}: face positions
• face_areas::Vector{Float64}: face cross-sectional areas
• node_velocities::Vector{Float64}: ALE mesh velocities
• mesh_time::Base.RefValue{Float64}: timestamp of the geometry snapshot
• cross_section_area::Base.RefValue{Float64}: current A(t) (scalar in 1D)
• cross_section_area_initial::Float64: calibration reference A_0

For D ≥ 2, node_positions and face_normals become Vector{SVector{D,Float64}} and cross_section_area* becomes a per-face scalar.