mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-09-25 11:35:30 +00:00
Jukka Aho
71 lines
1.9 KiB
Julia
71 lines
1.9 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 <: AbstractProblem
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function HeatProblem(dim::Int=1, elements=[])
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return Problem{HeatProblem}(dim, elements)
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end
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function get_unknown_field_name{P<:HeatProblem}(::Type{P})
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return "temperature"
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end
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function get_unknown_field_type{P<:HeatProblem}(::Type{P})
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# scalar field
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return Float64
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end
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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, problem::Problem{HeatProblem}, element::Element, time::Number)
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gdofs = get_gdofs(element, problem.dim)
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for ip in get_integration_points(element)
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w = ip.weight*det(element, ip, time)
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N = element(ip, time)
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if haskey(element, "density")
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rho = element("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 = element(ip, time, Val{:grad})
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k = element("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 = element("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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g = element("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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