mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-09-24 19:19:54 +00:00
Jukka Aho
71 lines
1.8 KiB
Julia
71 lines
1.8 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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""" 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 elements
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f = temperature load defined on volume elements
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g = temperature flux defined on boundary elements
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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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type Heat <: FieldProblem
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end
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function get_unknown_field_name(problem::Problem{Heat})
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return "temperature"
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end
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function get_unknown_field_type(problem::Problem{Heat})
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return Float64
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end
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function assemble!(assembly::Assembly, problem::Problem{Heat}, element::Element, time=0.0)
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gdofs = get_gdofs(problem, element)
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field_name = get_unknown_field_name(problem)
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nnodes = length(element)
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K = zeros(nnodes, nnodes)
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fq = zeros(nnodes)
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for ip in get_integration_points(element)
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detJ = element(ip, time, Val{:detJ})
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w = ip.weight*detJ
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N = element(ip, time)
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if haskey(element, "$field_name thermal conductivity")
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dN = element(ip, time, Val{:Grad})
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k = element("$field_name thermal conductivity", ip, time)
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K += w*k*dN'*dN
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end
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if haskey(element, "$field_name load")
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f = element("$field_name load", ip, time)
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fq += w*N'*f
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end
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if haskey(element, "$field_name flux")
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g = element("$field_name flux", ip, time)
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fq += w*N'*g
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end
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end
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T = vec(element[field_name](time))
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fq -= K*T
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add!(assembly.K, gdofs, gdofs, K)
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add!(assembly.f, gdofs, fq)
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end
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