diff --git a/modules/navier_stokes/test/tests/finite_volume/cns/mms/1d-with-bcs/wpcnsfv.i b/modules/navier_stokes/test/tests/finite_volume/cns/mms/1d-with-bcs/wpcnsfv.i
new file mode 100644
index 000000000000..e979f27d8933
--- /dev/null
+++ b/modules/navier_stokes/test/tests/finite_volume/cns/mms/1d-with-bcs/wpcnsfv.i
@@ -0,0 +1,317 @@
+mu=1e-15
+rho='rho'
+advected_interp_method='average'
+velocity_interp_method='rc'
+gamma=1.4
+R=8.3145
+molar_mass=29.0e-3
+R_specific=${fparse R/molar_mass}
+cp=${fparse gamma*R_specific/(gamma-1)}
+
+[GlobalParams]
+  two_term_boundary_expansion = true
+[]
+
+[Mesh]
+  [cartesian]
+    type = GeneratedMeshGenerator
+    dim = 1
+    xmin = .1
+    xmax = .6
+    nx = 100
+  []
+[]
+
+[Modules]
+  [FluidProperties]
+    [fp]
+      type = IdealGasFluidProperties
+    []
+  []
+[]
+
+[Problem]
+  fv_bcs_integrity_check = false
+[]
+
+[Variables]
+  [pressure]
+    type = INSFVPressureVariable
+  []
+  [sup_vel_x]
+    type = PINSFVSuperficialVelocityVariable
+  []
+  [T_fluid]
+    type = INSFVEnergyVariable
+  []
+[]
+
+[AuxVariables]
+  [porosity]
+    type = MooseVariableFVReal
+  []
+[]
+
+[ICs]
+  [pressure]
+    type = FunctionIC
+    variable = pressure
+    function = 'exact_p'
+  []
+  [sup_vel_x]
+    type = FunctionIC
+    variable = sup_vel_x
+    function = 'exact_sup_vel_x'
+  []
+  [T_fluid]
+    type = FunctionIC
+    variable = T_fluid
+    function = 'exact_T'
+  []
+  [eps]
+    type = FunctionIC
+    variable = porosity
+    function = 'eps'
+  []
+[]
+
+[FVKernels]
+  [mass_advection]
+    type = PINSFVMassAdvection
+    variable = pressure
+    advected_interp_method = ${advected_interp_method}
+    velocity_interp_method = ${velocity_interp_method}
+    vel = 'velocity'
+    pressure = pressure
+    u = sup_vel_x
+    mu = ${mu}
+    rho = ${rho}
+    porosity = porosity
+  []
+  [mass_fn]
+    type = FVBodyForce
+    variable = pressure
+    function = 'forcing_rho'
+  []
+
+  [u_advection]
+    type = PINSFVMomentumAdvection
+    variable = sup_vel_x
+    advected_quantity = 'rhou'
+    vel = 'velocity'
+    advected_interp_method = ${advected_interp_method}
+    velocity_interp_method = ${velocity_interp_method}
+    pressure = pressure
+    u = sup_vel_x
+    mu = ${mu}
+    rho = ${rho}
+    porosity = porosity
+  []
+  [u_pressure]
+    type = PINSFVMomentumPressureFlux
+    variable = sup_vel_x
+    pressure = pressure
+    porosity = porosity
+    momentum_component = 'x'
+  []
+  [momentum_fn]
+    type = FVBodyForce
+    variable = sup_vel_x
+    function = 'forcing_rho_ud'
+  []
+
+  [temp_advection]
+    type = PINSFVEnergyAdvection
+    variable = T_fluid
+    vel = 'velocity'
+    velocity_interp_method = ${velocity_interp_method}
+    advected_interp_method = ${advected_interp_method}
+    pressure = pressure
+    u = sup_vel_x
+    mu = ${mu}
+    rho = ${rho}
+    porosity = porosity
+  []
+  [energy_fn]
+    type = FVBodyForce
+    variable = T_fluid
+    function = 'forcing_rho_et'
+  []
+[]
+
+[FVBCs]
+  [mass]
+    variable = pressure
+    type = PWCNSFVStrongBC
+    boundary = 'left right'
+    T_fluid = T_fluid
+    superficial_vel_x = sup_vel_x
+    pressure = pressure
+    eqn = 'mass'
+    porosity = porosity
+  []
+  [momentum]
+    variable = sup_vel_x
+    type = PWCNSFVStrongBC
+    boundary = 'left right'
+    T_fluid = T_fluid
+    superficial_vel_x = sup_vel_x
+    pressure = pressure
+    eqn = 'momentum'
+    momentum_component = 'x'
+    porosity = porosity
+  []
+  [energy]
+    variable = T_fluid
+    type = PWCNSFVStrongBC
+    boundary = 'left right'
+    T_fluid = T_fluid
+    superficial_vel_x = sup_vel_x
+    pressure = pressure
+    eqn = 'energy'
+    porosity = porosity
+  []
+
+  # help gradient reconstruction *and* create Dirichlet values for use in PWCNSFVStrongBC
+  [pressure_right]
+    type = FVFunctionDirichletBC
+    variable = pressure
+    function = exact_p
+    boundary = 'right'
+  []
+  [sup_vel_x_left]
+    type = FVFunctionDirichletBC
+    variable = sup_vel_x
+    function = exact_sup_vel_x
+    boundary = 'left'
+  []
+  [T_fluid_left]
+    type = FVFunctionDirichletBC
+    variable = T_fluid
+    function = exact_T
+    boundary = 'left'
+  []
+[]
+
+[Materials]
+  [const_functor]
+    type = ADGenericConstantFunctorMaterial
+    prop_names = 'cp'
+    prop_values = '${cp}'
+  []
+  [rho]
+    type = RhoFromPTFunctorMaterial
+    fp = fp
+    temperature = T_fluid
+    pressure = pressure
+  []
+  [ins_fv]
+    type = INSFVMaterial
+    u = sup_vel_x
+    pressure = pressure
+    temperature = T_fluid
+    rho = ${rho}
+  []
+[]
+
+[Functions]
+[exact_rho]
+  type = ParsedFunction
+  value = '3.48788261470924*cos(x)'
+[]
+[forcing_rho]
+  type = ParsedFunction
+  value = '-3.45300378856215*sin(1.1*x)'
+[]
+[exact_rho_ud]
+  type = ParsedFunction
+  value = '3.13909435323832*cos(1.1*x)'
+[]
+[forcing_rho_ud]
+  type = ParsedFunction
+  value = '-0.9*(10.6975765229419*cos(1.2*x)/cos(x) - 0.697576522941849*cos(1.1*x)^2/cos(x)^2)*sin(x) + 0.9*(10.6975765229419*sin(x)*cos(1.2*x)/cos(x)^2 - 1.3951530458837*sin(x)*cos(1.1*x)^2/cos(x)^3 + 1.53466835047207*sin(1.1*x)*cos(1.1*x)/cos(x)^2 - 12.8370918275302*sin(1.2*x)/cos(x))*cos(x) + 3.13909435323832*sin(x)*cos(1.1*x)^2/cos(x)^2 - 6.9060075771243*sin(1.1*x)*cos(1.1*x)/cos(x)'
+[]
+[exact_rho_et]
+  type = ParsedFunction
+  value = '26.7439413073546*cos(1.2*x)'
+[]
+[forcing_rho_et]
+  type = ParsedFunction
+  value = '0.9*(3.48788261470924*(3.06706896551724*cos(1.2*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.2*x))*sin(x)*cos(1.1*x)/cos(x)^2 - 0.99*(3.48788261470924*(3.06706896551724*cos(1.2*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x) + 26.7439413073546*cos(1.2*x))*sin(1.1*x)/cos(x) + 0.9*(-(10.6975765229419*cos(1.2*x)/cos(x) - 0.697576522941849*cos(1.1*x)^2/cos(x)^2)*sin(x) + (10.6975765229419*sin(x)*cos(1.2*x)/cos(x)^2 - 1.3951530458837*sin(x)*cos(1.1*x)^2/cos(x)^3 + 1.53466835047207*sin(1.1*x)*cos(1.1*x)/cos(x)^2 - 12.8370918275302*sin(1.2*x)/cos(x))*cos(x) - 32.0927295688256*sin(1.2*x))*cos(1.1*x)/cos(x)'
+[]
+[exact_T]
+  type = ParsedFunction
+  value = '0.0106975765229418*cos(1.2*x)/cos(x) - 0.000697576522941848*cos(1.1*x)^2/cos(x)^2'
+[]
+[exact_eps_p]
+  type = ParsedFunction
+  value = '3.13909435323832*(3.06706896551724*cos(1.2*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x)'
+[]
+[exact_p]
+  type = ParsedFunction
+  value = '3.48788261470924*(3.06706896551724*cos(1.2*x)/cos(x) - 0.2*cos(1.1*x)^2/cos(x)^2)*cos(x)'
+[]
+[exact_sup_vel_x]
+  type = ParsedFunction
+  value = '0.9*cos(1.1*x)/cos(x)'
+[]
+[exact_superficial_velocity]
+  type = ParsedVectorFunction
+  value_x = '0.9*cos(1.1*x)/cos(x)'
+[]
+[eps]
+  type = ParsedFunction
+  value = '0.9'
+[]
+[]
+
+[Executioner]
+  solve_type = NEWTON
+  type = Transient
+  num_steps = 1
+  dtmin = 1
+  petsc_options_iname = '-pc_type'
+  petsc_options_value = 'lu'
+  nl_max_its = 50
+  line_search = bt
+  nl_rel_tol = 1e-12
+  nl_abs_tol = 1e-12
+[]
+
+[Outputs]
+  exodus = true
+  csv = true
+[]
+
+[Debug]
+  show_var_residual_norms = true
+[]
+
+[Postprocessors]
+  [h]
+    type = AverageElementSize
+    outputs = 'console csv'
+    execute_on = 'timestep_end'
+  []
+  [L2pressure]
+    type = ElementL2Error
+    variable = pressure
+    function = exact_p
+    outputs = 'console csv'
+    execute_on = 'timestep_end'
+  []
+  [L2sup_vel_x]
+    variable = sup_vel_x
+    function = exact_sup_vel_x
+    type = ElementL2Error
+    outputs = 'console csv'
+    execute_on = 'timestep_end'
+  []
+  [L2T_fluid]
+    variable = T_fluid
+    function = exact_T
+    type = ElementL2Error
+    outputs = 'console csv'
+    execute_on = 'timestep_end'
+  []
+[]