heat problem

test/test_heat.jl

@@ -3,7 +3,7 @@
 
 using JuliaFEM
 using JuliaFEM.Test
-
+using JuliaFEM.Preprocess
 
 @testset "test one element heat problem" begin
 
@@ -19,7 +19,6 @@ using JuliaFEM.Test
     update!(el1, "geometry", X)
     update!(el1, "temperature thermal conductivity", 6.0)
     update!(el1, "temperature load", 12.0)
-    update!(el1, "density", 36.0)
 
     # define boundary element for flux
     el2 = Element(Seg2, [1, 2])
@@ -29,6 +28,7 @@ using JuliaFEM.Test
 
     # define heat problem and push elements to problem
     problem = Problem(Heat, "one element heat problem", 1)
+    problem.properties.formulation = "2D"
     push!(problem, el1, el2)
 
     # define boundary element for dirichlet boundary condition
@@ -53,8 +53,7 @@ using JuliaFEM.Test
     @test isapprox(A[free_dofs, free_dofs] \ b[free_dofs], [1.0, 1.0])
 
     # using Solver
-    solver = Solver("solve heat problem")
-    solver.is_linear_system = true
+    solver = LinearSolver("solve heat problem")
     push!(solver, problem, boundary_condition)
 
     # Set constant source f=12 with k=6. Accurate solution is
@@ -75,3 +74,87 @@ using JuliaFEM.Test
     @test isapprox(T[1], 2.0)
 end
 
+function T_acc(x)
+    # accurate solution
+    a = 0.01
+    L = 0.20
+    k = 50.0
+    Tᵤ = 20.0
+    h = 10.0
+    P = 4*a
+    A = a^2
+    α = h
+    β = sqrt((h*P)/(k*A))
+    T̂ = 100.0
+    C = [1.0 1.0; (α+k*β)*exp(β*L) (α-k*β)*exp(-β*L)] \ [T̂-Tᵤ, 0.0]
+    return dot(C, [exp(β*x), exp(-β*x)]) + Tᵤ
+end
+
+#=
+@testset "test 1d heat problem" begin
+    X = Dict{Int, Vector{Float64}}(
+        1 => [0.0, 0.0, 0.0],
+        2 => [0.1, 0.0, 0.0],
+        3 => [0.2, 0.0, 0.0])
+    e1 = Element(Seg2, [1, 2])
+    e2 = Element(Seg2, [2, 3])
+    e3 = Element(Poi1, [3])
+
+    p1 = Problem(Heat, "1d heat problem", 1)
+    p1.properties.formulation = "1D"
+    push!(p1, e1, e2, e3)
+    update!(p1, "geometry", X)
+    a = 0.010
+    update!(p1, "cross-section area", a^2)
+    update!(p1, "cross-section perimeter", 4*a)
+    update!(p1, "temperature thermal conductivity", 50.0) # k [W/(m∘C)]
+    update!(p1, "temperature heat transfer coefficient", 10.0) # h [W/(m²∘C)]
+    update!(p1, "temperature external temperature", 20.0)
+
+    p2 = Problem(Dirichlet, "left boundary", 1, "temperature")
+    e3 = Element(Poi1, [1])
+    update!(e3, "geometry", X)
+    update!(e3, "temperature 1", 100.0)
+    push!(p2, e3)
+
+    solver = LinearSolver(p1, p2)
+    call(solver)
+    T_min = minimum(p1.assembly.u)
+    @test isapprox(T_max, T_acc(0.2); rtol=4.5e-2)
+end
+=#
+
+@testset "test 3d heat problem" begin
+    fn = Pkg.dir("JuliaFEM") * "/test/testdata/rod_short.med"
+    mesh = aster_read_mesh(fn, "SHORT_ROD_RECTANGLE_HEX8")
+
+    p1 = Problem(Heat, "rod", 1)
+    push!(p1, create_elements(mesh, "ROD"))
+    push!(p1, create_elements(mesh, "SIDES"))
+    push!(p1, create_elements(mesh, "RIGHT"))
+    update!(p1, "temperature thermal conductivity", 50.0)
+    update!(p1, "temperature external temperature", 20.0)
+    update!(p1, "temperature heat transfer coefficient", 10.0)
+
+    p2 = Problem(Dirichlet, "left support T=100", 1, "temperature")
+    push!(p2, create_elements(mesh, "LEFT"))
+    update!(p2, "temperature 1", 100.0)
+
+    solver = LinearSolver(p1, p2)
+    call(solver)
+
+    T_min = minimum(p1.assembly.u)
+
+    # Code Aster solution
+    T_CA_HEX20 = 4.58158267950429E+01
+    T_CA_HEX8 = 3.77215189873436E+01
+    info("T_min = $T_min")
+    info("T_acc = $(T_acc(0.2))")
+    rtol1 = norm(T_min-T_CA_HEX8)/max(T_min,T_CA_HEX8)*100.0
+    rtol2 = norm(T_min-T_acc(0.2))/max(T_min,T_acc(0.2))*100.0
+    info("rel. tol to CA solution: $rtol1 %")
+    info("rel. tol to accurate solution: $rtol2 %")
+
+    @test isapprox(T_min, T_acc(0.2); rtol=18.0e-2)
+    @test isapprox(T_min, T_CA_HEX8; rtol=1.0e-9)
+end