JuliaFEM.jl/test/test_heat.jl

# This file is a part of JuliaFEM.
# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md

# unit tests for heat equations

module HeatTests  # always wrap tests to module ending with "Tests"

using JuliaFEM.Test  # always use JuliaFEM.Test, not Base.Test

using JuliaFEM.Core: Seg2, Quad4, HeatProblem, assemble

function test_one_element()  # always start test function with name test_

    # volume element
    element = Quad4([1, 2, 3, 4])

    element["geometry"] = Vector[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 1.0]]
    element["temperature thermal conductivity"] = 6.0
    element["temperature load"] = [12.0, 12.0, 12.0, 12.0]
    element["density"] = 36.0

    # boundary element 
    boundary_element = Seg2([1, 2])
    boundary_element["geometry"] = Vector[[0.0, 0.0], [1.0, 0.0]]
    # linear ramp from 0 to 6 in time 0 to 1
    boundary_element["temperature flux"] = (0.0 => 0.0, 1.0 => 6.0)

    problem = HeatProblem()
    push!(problem, element)
    push!(problem, boundary_element)

    # Set constant source f=12 with k=6. Accurate solution is
    # T=1 on free boundary, u(x,y) = -1/6*(1/2*f*x^2 - f*x)
    assembly = assemble(problem, 0.0)
    fdofs = [1, 2]
    A = full(assembly.stiffness_matrix)
    b = full(assembly.force_vector)

    info("stiffness matrix = \n$(round(A, 3))")

    @test isapprox(A, [
         4.0 -1.0 -2.0 -1.0
        -1.0  4.0 -1.0 -2.0
        -2.0 -1.0  4.0 -1.0
        -1.0 -2.0 -1.0  4.0
    ])

    @test isapprox(A[fdofs, fdofs] \ b[fdofs], [1.0, 1.0])

    # Set constant flux g=6 on boundary. Accurate solution is
    # u(x,y) = x which equals T=1 on boundary.
    # at time t=1.0 all loads should be on.
    assembly = assemble(problem, 1.0)
    A = full(assembly.stiffness_matrix)
    b = full(assembly.force_vector)
    T = A[fdofs, fdofs] \ b[fdofs]
    info("T = $T")
    @test isapprox(T, [2.0, 2.0])

end

end