mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-09-23 02:59:52 +00:00
Jukka Aho
78 lines
2.3 KiB
Julia
78 lines
2.3 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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using JuliaFEM
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using JuliaFEM.Test
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@testset "test one element heat problem" begin
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X = Dict{Int, Vector{Float64}}(
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1 => [0.0,0.0],
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2 => [1.0,0.0],
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3 => [1.0,1.0],
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4 => [0.0,1.0])
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# define volume element
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el1 = Element(Quad4, [1, 2, 3, 4])
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update!(el1, "geometry", X)
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update!(el1, "temperature thermal conductivity", 6.0)
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update!(el1, "temperature load", 12.0)
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update!(el1, "density", 36.0)
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# define boundary element for flux
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el2 = Element(Seg2, [1, 2])
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update!(el2, "geometry", X)
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# linear ramp from 0 -> 6 in time 0 -> 1
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update!(el2, "temperature flux", 0.0 => 0.0, 1.0 => 6.0)
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# define heat problem and push elements to problem
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problem = Problem(Heat, "one element heat problem", 1)
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push!(problem, el1, el2)
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# define boundary element for dirichlet boundary condition
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el3 = Element(Seg2, [3, 4])
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update!(el3, "geometry", X)
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update!(el3, "temperature 1", 0.0)
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boundary_condition = Problem(Dirichlet, "T=0 on top", 1, "temperature")
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push!(boundary_condition, el3)
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# manual assembling of problem + solution:
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assemble!(problem, 0.0)
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A = full(problem.assembly.K)
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b = full(problem.assembly.f)
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A_expected = [
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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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free_dofs = [1, 2]
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@test isapprox(A, A_expected)
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@test isapprox(A[free_dofs, free_dofs] \ b[free_dofs], [1.0, 1.0])
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# using Solver
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solver = Solver("solve heat problem")
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solver.is_linear_system = true
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push!(solver, problem, boundary_condition)
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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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# when boundary flux not active (at t=0)
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solver.time = 0.0
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call(solver)
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# interpolate temperature at middle of element 2 (flux boundary) at time t=0:
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T = el2("temperature", [0.0], 0.0)
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@test isapprox(T[1], 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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solver.time = 1.0
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call(solver)
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T = el2("temperature", [0.0], 1.0)
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@test isapprox(T[1], 2.0)
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end
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