Add charge conservative MHD implementation & fixes to build issues (netgen, jinja2)

examples/mhd/charge_conserving/development/step1_NavierStokes_elementTypes/2d_INSAD.i

@@ -0,0 +1,176 @@
+# Note: if this is run on 1 core only, ILU is not used
+# And instead a method requiring more iterations is applied.
+
+N_X = 200
+N_Y_half = 10
+U_AVG = 1
+element_type = 'QUAD9'
+
+[Mesh]
+  [meshTop]
+    type = GeneratedMeshGenerator
+    dim = 2
+    nx = ${N_X}
+    ny = ${N_Y_half}
+    xmin = 0
+    xmax = 20
+    ymin = 0
+    ymax = 1
+    bias_y = 0.8
+    boundary_name_prefix = 'meshTop'
+    elem_type = ${element_type}
+  []
+  [meshBottom]
+    type = GeneratedMeshGenerator
+    dim = 2
+    nx = ${N_X}
+    ny = ${N_Y_half}
+    xmin = 0
+    xmax = 20
+    ymin = -1
+    ymax = 0
+    bias_y = 1.25
+    boundary_name_prefix = 'meshBottom'
+    elem_type = ${element_type}
+  []
+  [meshComplete]
+    type = StitchedMeshGenerator
+    inputs = 'meshTop meshBottom'
+    clear_stitched_boundary_ids = true
+    stitch_boundaries_pairs = 'meshTop_bottom meshBottom_top'
+  []
+  [meshRename]
+    type = RenameBoundaryGenerator
+    input = meshComplete
+    old_boundary = '
+      meshTop_right meshBottom_right
+      meshTop_left meshBottom_left
+      meshTop_top
+      meshBottom_bottom
+    '
+    new_boundary = '
+      right right
+      left left
+      top
+      bottom
+    '
+  []
+[]
+
+[Variables]
+  [velocity]
+    family = LAGRANGE_VEC
+    order = SECOND
+  []
+  [pressure]
+    family = MONOMIAL
+    order = FIRST
+  []
+[]
+
+# [ICs]
+#   [velocity]
+#     type = VectorFunctionIC
+#     variable = velocity
+#     function = velocityInlet
+#   []
+# []
+
+[Functions]
+  [velocityInlet]
+    type = ParsedVectorFunction
+    symbol_names = 'y_max'
+    symbol_values = '1'
+    expression_x = '(3/2) * ${U_AVG} * (1 - (y * y) / (y_max * y_max))'
+    expression_y = '0'
+  []
+[]
+
+[BCs]
+  [inlet]
+    type = VectorFunctionDirichletBC
+    variable = velocity
+    boundary = left
+    function = velocityInlet
+  []
+  [no_slip]
+    type = VectorDirichletBC
+    variable = velocity
+    boundary = 'top bottom'
+    values = '0 0 0'
+  []
+  [pressure_set]
+    type = PenaltyDirichletBC
+    variable = pressure
+    value = 0
+    boundary = 'right'
+    penalty = 1e5
+  []
+  # [pressure_set]
+  #   type = DirichletBC
+  #   variable = pressure
+  #   boundary = 'right'
+  #   value = 0
+  # []
+[]
+
+[Materials]
+  [const]
+    type = ADGenericConstantMaterial
+    prop_names = 'rho mu'
+    prop_values = '1  1'
+  []
+  [ins_mat]
+    type = INSADTauMaterial
+    velocity = velocity
+    pressure = pressure
+  []
+[]
+
+[Kernels]
+  [mass]
+    type = INSADMass
+    variable = pressure
+  []
+
+  [momentum_convection]
+    type = INSADMomentumAdvection
+    variable = velocity
+  []
+
+  [momentum_viscous]
+    type = INSADMomentumViscous
+    variable = velocity
+  []
+
+  [momentum_pressure]
+    type = INSADMomentumPressure
+    variable = velocity
+    pressure = pressure
+    integrate_p_by_parts = true
+  []
+[]
+
+[Problem]
+  type = FEProblem
+[]
+
+[Preconditioning]
+  [SMP]
+    type = SMP
+    full = true
+  []
+[]
+
+[Executioner]
+  type = Steady
+  solve_type = NEWTON
+  l_max_its = 100
+  nl_max_its = 1000
+  petsc_options_iname = '-pc_type'
+  petsc_options_value = 'ilu'
+[]
+
+[Outputs]
+  exodus = true
+[]