# This test solves a 1D transient heat equation
# The error is caclulated by comparing to the analytical solution
# The problem setup and analytical solution are taken from "Advanced Engineering
# Mathematics, 10th edition" by Erwin Kreyszig.
# http://www.amazon.com/Advanced-Engineering-Mathematics-Erwin-Kreyszig/dp/0470458364
# It is Example 1 in section 12.6 on page 561
[Mesh]
file = 3D.exo
[]
[Variables]
[./T]
[../]
[]
[ICs]
[./T_IC]
type = FunctionIC
variable = T
function = '100*sin(3.14159*x/80)*sin(3.14159*y/80)'
[../]
[]
[Kernels]
[./HeatDiff]
type = HeatConduction
variable = T
[../]
[./HeatTdot]
type = HeatConductionTimeDerivative
variable = T
[../]
[]
# [BCs]
# [./top]
# type = DirichletBC
# variable = T
# boundary = top
# value = 0
# [../]
# [./bottom]
# type = DirichletBC
# variable = T
# boundary = bottom
# value = 100
# [../]
# []
# [Materials]
# [./k]
# type = GenericConstantMaterial
# prop_names = 'thermal_conductivity'
# prop_values = '0.95' #copper in cal/(cm sec C)
# block = 0
# [../]
# [./cp]
# type = GenericConstantMaterial
# prop_names = 'specific_heat'
# prop_values = '0.092' #copper in cal/(g C)
# block = 0
# [../]
# [./rho]
# type = GenericConstantMaterial
# prop_names = 'density'
# prop_values = '8.92' #copper in g/(cm^3)
# block = 0
# [../]
# []
[Postprocessors]
[./error]
type = NodalL2Error
function = '100*sin(3.14159*x/80)*exp(-0.95/(0.092*8.92)*3.14159^2/80^2*t)' #T(x,t) = 100sin(pix/L)exp(-rho/(cp k) pi^2/L^2 t)
variable = T
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
nl_rel_tol = 1e-12
l_tol = 1e-6
dt = 2
end_time = 100
petsc_options_iname = '-pc_type -pc_hypre_type'
petsc_options_value = 'hypre boomeramg'
[]
[Outputs]
exodus = true
print_perf_log = true
[]