mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-09-22 18:52:16 +00:00
Jukka Aho
119 lines
3.2 KiB
Julia
119 lines
3.2 KiB
Julia
# This file is a part of JuliaFEM.
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# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
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# Heat problems
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abstract HeatProblem <: Problem
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abstract HeatEquation <: Equation
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function get_unknown_field_name(equation::HeatEquation)
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return "temperature"
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end
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### Formulation ###
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""" Heat equations.
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Formulation
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-----------
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Field equation is:
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ρc∂u/∂t = ∇⋅(k∇u) + f
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Weak form is: find u∈U such that ∀v in V
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∫k∇u∇v dx = ∫fv dx + ∫gv ds,
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where
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k = temperature thermal conductivity defined on volume
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f = temperature load defined on volume
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g = temperature flux defined on boundary
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References
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----------
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https://en.wikipedia.org/wiki/Heat_equation
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"""
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function assemble!(assembly::Assembly, equation::HeatEquation, time::Number=0.0, problem=nothing)
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element = get_element(equation)
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gdofs = get_gdofs(equation)
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basis = get_basis(element)
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dbasis = grad(basis)
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detJ = det(basis)
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for ip in get_integration_points(equation)
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w = ip.weight*detJ(ip)
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N = basis(ip, time)
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if haskey(element, "density")
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rho = basis("density", ip, time)
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add!(assembly.mass_matrix, gdofs, gdofs, w*rho*N'*N)
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end
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if haskey(element, "temperature thermal conductivity")
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dN = dbasis(ip, time)
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k = basis("temperature thermal conductivity", ip, time)
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add!(assembly.stiffness_matrix, gdofs, gdofs, w*k*dN'*dN)
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end
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if haskey(element, "temperature load")
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f = basis("temperature load", ip, time)
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add!(assembly.force_vector, gdofs, w*N'*f)
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end
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if haskey(element, "temperature flux")
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info("assemble boundary flux")
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g = basis("temperature flux", ip, time)
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add!(assembly.force_vector, gdofs, w*N'*g)
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end
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end
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end
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### Equations ###
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""" Diffusive heat transfer for 4-node bilinear element. """
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type DC2D4 <: HeatEquation
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element :: Quad4
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integration_points :: Vector{IntegrationPoint}
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end
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function Base.size(equation::DC2D4)
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return (1, 4)
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end
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""" Diffusive heat transfer for 2-node linear segment. """
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type DC2D2 <: HeatEquation
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element :: Seg2
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integration_points :: Vector{IntegrationPoint}
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end
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function Base.size(equation::DC2D2)
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return (1, 2)
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end
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# Conversions element -> equation
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function Base.convert(::Type{HeatEquation}, element::Quad4)
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integration_points = get_default_integration_points(element)
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haskey(element, "temperature") || (element["temperature"] = 0.0 => zeros(4))
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DC2D4(element, integration_points)
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end
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function Base.convert(::Type{HeatEquation}, element::Seg2)
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integration_points = get_default_integration_points(element)
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haskey(element, "temperature") || (element["temperature"] = 0.0 => zeros(2))
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DC2D2(element, integration_points)
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end
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### Problems ###
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type PlaneHeatProblem <: HeatProblem
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unknown_field_name :: ASCIIString
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unknown_field_dimension :: Int
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equations :: Vector{HeatEquation}
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end
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""" Default constructor for problem takes no arguments. """
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function PlaneHeatProblem(equations=[])
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return PlaneHeatProblem("temperature", 1, equations)
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end
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