mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-08-06 04:21:33 +00:00
Jukka Aho
62 lines
1.8 KiB
Julia
62 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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# unit tests for heat equations
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module HeatTests # always wrap tests to module ending with "Tests"
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using JuliaFEM.Test # always use JuliaFEM.Test, not Base.Test
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using JuliaFEM.Core: Seg2, Quad4, HeatProblem, assemble
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function test_one_element() # always start test function with name test_
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# volume element
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element = Quad4([1, 2, 3, 4])
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element["geometry"] = Vector[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 1.0]]
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element["temperature thermal conductivity"] = 6.0
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element["temperature load"] = [12.0, 12.0, 12.0, 12.0]
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element["density"] = 36.0
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# boundary element
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boundary_element = Seg2([1, 2])
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boundary_element["geometry"] = Vector[[0.0, 0.0], [1.0, 0.0]]
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# linear ramp from 0 to 6 in time 0 to 1
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boundary_element["temperature flux"] = (0.0 => 0.0, 1.0 => 6.0)
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problem = HeatProblem()
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push!(problem, element)
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push!(problem, boundary_element)
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# Set constant source f=12 with k=6. Accurate solution is
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# T=1 on free boundary, u(x,y) = -1/6*(1/2*f*x^2 - f*x)
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assembly = assemble(problem, 0.0)
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fdofs = [1, 2]
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A = full(assembly.stiffness_matrix)
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b = full(assembly.force_vector)
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@test isapprox(A, [
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4.0 -1.0 -2.0 -1.0
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-1.0 4.0 -1.0 -2.0
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-2.0 -1.0 4.0 -1.0
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-1.0 -2.0 -1.0 4.0
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])
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@test isapprox(A[fdofs, fdofs] \ b[fdofs], [1.0, 1.0])
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# Set constant flux g=6 on boundary. Accurate solution is
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# u(x,y) = x which equals T=1 on boundary.
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# at time t=1.0 all loads should be on.
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assembly = assemble(problem, 1.0)
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A = full(assembly.stiffness_matrix)
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b = full(assembly.force_vector)
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T = A[fdofs, fdofs] \ b[fdofs]
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info("T = $T")
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@test isapprox(T, [2.0, 2.0])
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end
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end
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