heat problem

2026-09-28 20:46:58 +00:00 · 2016-07-01 02:55:56 +03:00
parent ce9eb715ec
commit 9f4eface6c
11 changed files with 328 additions and 33 deletions
@@ -22,23 +22,59 @@ where
    f = temperature load                    defined on volume elements
    g = temperature flux                    defined on boundary elements

+Parameters
+----------
+temperature thermal conductivity
+temperature load
+temperature flux
+
+thermal conductivity
+heat source
+heat flux
+heat transfer coefficient
+external temperature
+
+
+Formulations
+------------
+1D, 2D, 3D
+
 References
 ----------
 https://en.wikipedia.org/wiki/Heat_equation
-
+https://en.wikipedia.org/wiki/Heat_capacity
+https://en.wikipedia.org/wiki/Thermal_conduction
+https://en.wikipedia.org/wiki/Thermal_conductivity
+https://en.wikipedia.org/wiki/Thermal_diffusivity
+https://en.wikipedia.org/wiki/Volumetric_heat_capacity
 """
 type Heat <: FieldProblem
+    formulation :: ASCIIString
+end
+
+function Heat()
+    return Heat("3D")
 end

 function get_unknown_field_name(problem::Problem{Heat})
    return "temperature"
 end

-function get_unknown_field_type(problem::Problem{Heat})
-    return Float64
+function assemble!(assembly::Assembly, problem::Problem{Heat}, element::Element, time=0.0)
+    formulation = Val{Symbol(problem.properties.formulation)}
+    assemble!(assembly, problem, element, time, formulation)
 end

-function assemble!(assembly::Assembly, problem::Problem{Heat}, element::Element, time=0.0)
+# 3d heat problems
+
+function assemble!{E}(assembly::Assembly, problem::Problem{Heat}, element::Element{E}, time, ::Type{Val{Symbol("3D")}})
+    info("Unknown element type $E for 3d heat problem!")
+end
+
+typealias Heat3DVolumeElements Union{Tet4, Tet10, Hex8}
+typealias Heat3DSurfaceElements Union{Tri3, Tri6, Quad4}
+
+function assemble!{E<:Heat3DVolumeElements}(assembly::Assembly, problem::Problem{Heat}, element::Element{E}, time, ::Type{Val{Symbol("3D")}})
    gdofs = get_gdofs(problem, element)
    field_name = get_unknown_field_name(problem)
    nnodes = length(element)
@@ -57,6 +93,85 @@ function assemble!(assembly::Assembly, problem::Problem{Heat}, element::Element,
            f = element("$field_name load", ip, time)
            fq += w*N'*f
        end
+    end
+    T = vec(element[field_name](time))
+    fq -= K*T
+    add!(assembly.K, gdofs, gdofs, K)
+    add!(assembly.f, gdofs, fq)
+end
+
+function assemble!{E<:Heat3DSurfaceElements}(assembly::Assembly, problem::Problem{Heat}, element::Element{E}, time, ::Type{Val{Symbol("3D")}})
+    gdofs = get_gdofs(problem, element)
+    field_name = get_unknown_field_name(problem)
+    nnodes = length(element)
+    K = zeros(nnodes, nnodes)
+    fq = zeros(nnodes)
+    for ip in get_integration_points(element)
+        detJ = element(ip, time, Val{:detJ})
+        w = ip.weight*detJ
+        N = element(ip, time)
+        if haskey(element, "$field_name flux")
+            q = element("$field_name flux", ip, time)
+            fq += w*N'*q
+        end
+        if haskey(element, "$field_name heat transfer coefficient")
+            h = element("$field_name heat transfer coefficient", ip, time)
+            Tu = element("$field_name external temperature", ip, time)
+            K += w*h*N'*N
+            fq += w*N'*h*Tu
+        end
+    end
+    T = vec(element[field_name](time))
+    fq -= K*T
+    add!(assembly.K, gdofs, gdofs, K)
+    add!(assembly.f, gdofs, fq)
+end
+
+# 2d heat problems
+
+function assemble!{E}(assembly::Assembly, problem::Problem{Heat}, element::Element{E}, time, ::Type{Val{Symbol("2D")}})
+    info("Unknown element type $E for 2d heat problem!")
+end
+
+typealias Heat2DVolumeElements Union{Tri3, Tri6, Quad4}
+typealias Heat2DSurfaceElements Union{Seg2, Seg3}
+
+function assemble!{E<:Heat2DVolumeElements}(assembly::Assembly, problem::Problem{Heat}, element::Element{E}, time, ::Type{Val{Symbol("2D")}})
+    gdofs = get_gdofs(problem, element)
+    field_name = get_unknown_field_name(problem)
+    nnodes = length(element)
+    K = zeros(nnodes, nnodes)
+    fq = zeros(nnodes)
+    for ip in get_integration_points(element)
+        detJ = element(ip, time, Val{:detJ})
+        w = ip.weight*detJ
+        N = element(ip, time)
+        if haskey(element, "$field_name thermal conductivity")
+            dN = element(ip, time, Val{:Grad})
+            k = element("$field_name thermal conductivity", ip, time)
+            K += w*k*dN'*dN
+        end
+        if haskey(element, "$field_name load")
+            f = element("$field_name load", ip, time)
+            fq += w*N'*f
+        end
+    end
+    T = vec(element[field_name](time))
+    fq -= K*T
+    add!(assembly.K, gdofs, gdofs, K)
+    add!(assembly.f, gdofs, fq)
+end
+
+function assemble!{E<:Heat2DSurfaceElements}(assembly::Assembly, problem::Problem{Heat}, element::Element{E}, time, ::Type{Val{Symbol("2D")}})
+    gdofs = get_gdofs(problem, element)
+    field_name = get_unknown_field_name(problem)
+    nnodes = length(element)
+    K = zeros(nnodes, nnodes)
+    fq = zeros(nnodes)
+    for ip in get_integration_points(element)
+        detJ = element(ip, time, Val{:detJ})
+        w = ip.weight*detJ
+        N = element(ip, time)
        if haskey(element, "$field_name flux")
            g = element("$field_name flux", ip, time)
            fq += w*N'*g