diff --git a/tests/sa-model/channel_flow_short.i b/tests/sa-model/channel_flow_short.i
new file mode 100644
index 0000000000..9c3cacbcf8
--- /dev/null
+++ b/tests/sa-model/channel_flow_short.i
@@ -0,0 +1,307 @@
+Re = 1.375e4
+density = 1      # kg cm-3
+D = 1
+inlet = 1
+viscosity = '${fparse density * inlet * D / Re}'    # dynamic viscosity, mu = nu * rho, kg cm-1 s-1
+alpha = 0.33333           # INS SUPG and PSPG stabilization parameter
+
+[GlobalParams]
+  integrate_p_by_parts = false
+  viscous_form = 'traction'
+  pressure = p
+  velocity = vel
+[]
+
+[Mesh]
+  [channel]
+    type = CartesianMeshGenerator
+    dim = 2
+    dx = '0.05 0.2 19.75'
+    dy = '0.3 0.1 0.05 0.05'
+    ix = '20 1 79'
+    iy = '10 5 5 10'
+  []
+  [corner_node]
+    type = ExtraNodesetGenerator
+    input = channel
+    new_boundary = 'pinned_node'
+    coord = '20 0.5'
+  []
+[]
+
+[Problem]
+  type = FEProblem
+[]
+
+[Variables]
+  [vel]
+    family = LAGRANGE_VEC
+    order = FIRST
+  []
+  [p]
+  []
+  [mu_tilde]
+    initial_condition = '${fparse viscosity * 5}'
+  []
+[]
+
+[AuxVariables]
+  [mu_turbulence]
+  []
+  [wall_dist]
+  []
+  [velx]
+  []
+  [vely]
+  []
+  [wall_shear_stress]
+    family = MONOMIAL
+    order = CONSTANT
+  []
+  [turbulent_stress]
+    family = MONOMIAL
+    order = CONSTANT
+  []
+[]
+
+[Kernels]
+  [mass]
+    type = INSADMass
+    variable = p
+  []
+  [mass_pspg]
+    type = INSADMassPSPG
+    variable = p
+  []
+  [momentum_advection]
+    type = INSADMomentumAdvection
+    variable = vel
+  []
+  [momentum_viscous]
+    type = INSADMomentumViscous
+    variable = vel
+  []
+  [momentum_turbulent_viscous]
+    type = INSADMomentumTurbulentViscous
+    variable = vel
+    mu_tilde = mu_tilde
+  []
+  [momentum_pressure]
+    type = INSADMomentumPressure
+    variable = vel
+  []
+  [momentum_supg]
+    type = INSADMomentumSUPG
+    variable = vel
+  []
+  [momentum_time]
+    type = INSADMomentumTimeDerivative
+    variable = vel
+  []
+
+  [mu_tilde_time]
+    type = SATimeDerivative
+    variable = mu_tilde
+  []
+  [mu_tilde_space]
+    type = SATurbulentViscosity
+    variable = mu_tilde
+  []
+  [mu_tilde_supg]
+    type = SATurbulentViscositySUPG
+    variable = mu_tilde
+  []
+[]
+
+[AuxKernels]
+  [mu_space]
+    type = SATurbulentViscosityAux
+    variable = mu_turbulence
+    mu_tilde = mu_tilde
+  []
+  [wall_distance]
+    type = WallDistanceAux
+    variable = wall_dist
+    walls = 'top'
+    execute_on = initial
+  []
+  [velx]
+    type = VectorVariableComponentAux
+    variable = velx
+    vector_variable = vel
+    component = x
+  []
+  [vely]
+    type = VectorVariableComponentAux
+    variable = vely
+    vector_variable = vel
+    component = y
+  []
+  [wall_shear_stress]
+    type = WallShearStressAux
+    variable = wall_shear_stress
+    boundary = top
+  []
+  [turbulent_stress]
+    type = TurbulentStressAux
+    variable = turbulent_stress
+    mu_tilde = mu_tilde
+  []
+[]
+
+[Functions]
+  [xfunc]
+    type = ParsedFunction
+    expression = '${fparse inlet}'
+  []
+  [mu_func]
+    type = ParsedFunction
+    expression = 'if(y=0.5, 0, ${fparse viscosity * 5})'
+  []
+[]
+
+[ICs]
+  [velocity]
+    type = VectorFunctionIC
+    function_x = xfunc
+    function_y = 0
+    variable = vel
+  []
+[]
+
+[BCs]
+  [no_slip]
+    type = ADVectorFunctionDirichletBC
+    variable = vel
+    boundary = 'top'
+    function_x = 0
+    function_y = 0
+  []
+  [inlet]
+    type = ADVectorFunctionDirichletBC
+    variable = vel
+    boundary = 'left'
+    function_x = xfunc
+    function_y = 0
+  []
+  [outlet]
+    type = INSADMomentumTurbulentNoBCBC
+    variable = vel
+    boundary = 'right'
+    mu_tilde = mu_tilde
+  []
+  [outlet_supg]
+    type = INSADMomentumSUPGBC
+    variable = vel
+    boundary = 'right'
+  []
+  [outlet_pspg]
+    type = INSADMassPSPGBC
+    variable = p
+    boundary = 'right'
+  []
+  [symmetry]
+    type = ADVectorFunctionDirichletBC
+    variable = vel
+    boundary = 'bottom'
+    set_x_comp = false
+    function_y = 0
+  []
+
+  [pressure_pin]
+    type = DirichletBC
+    variable = p
+    boundary = 'pinned_node'
+    value = 0
+  []
+
+  [mu_inlet]
+    type = FunctionDirichletBC
+    variable = mu_tilde
+    boundary = 'left'
+    function = mu_func
+  []
+  [mu_wall]
+    type = DirichletBC
+    variable = mu_tilde
+    boundary = 'top'
+    value = 0
+  []
+  [mu_outlet]
+    type = SATurbulentViscosityNoBCBC
+    variable = mu_tilde
+    boundary = 'right'
+  []
+  [mu_outlet_supg]
+    type = SATurbulentViscositySUPGBC
+    variable = mu_tilde
+    boundary = 'right'
+  []
+[]
+
+[Materials]
+  [ad_mat]
+    type = ADGenericConstantMaterial
+    prop_names = 'rho mu'
+    prop_values = '${density} ${viscosity}'
+  []
+  [sa_mat]
+    type = SATauMaterial
+    alpha = ${alpha}
+    mu_tilde = mu_tilde
+    wall_distance_var = wall_dist
+    use_ft2_term = true
+  []
+[]
+
+[Executioner]
+  type = Transient
+
+  solve_type = 'NEWTON'
+  petsc_options = '-snes_converged_reason -ksp_converged_reason -snes_linesearch_monitor'
+  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_mat_solver_package'
+  petsc_options_value = 'lu       NONZERO               superlu_dist'
+  line_search = none
+
+  automatic_scaling = true
+  compute_scaling_once = false
+  resid_vs_jac_scaling_param = 0.1
+  scaling_group_variables = 'vel; p; mu_tilde'
+  off_diagonals_in_auto_scaling = true
+
+  nl_rel_tol = 1e-8
+  nl_abs_tol = 1e-14
+  nl_max_its = 10
+
+  start_time = 0.0
+  end_time = 6
+  dtmin = 1.0
+  dtmax = 10
+  [TimeStepper]
+    type = IterationAdaptiveDT
+    dt = 1e-0
+    cutback_factor = 0.9
+    growth_factor = 1.1
+    optimal_iterations = 6
+    iteration_window = 1
+    linear_iteration_ratio = 1000
+  []
+[]
+
+[Preconditioning]
+  [SMP]
+    type = SMP
+    full = true
+  []
+[]
+
+[Outputs]
+  [exodus]
+    type = Exodus
+    execute_on = final
+  []
+[]
+
+[Debug]
+  show_var_residual_norms = true
+[]
diff --git a/tests/sa-model/gold/channel_flow_short_exodus.e b/tests/sa-model/gold/channel_flow_short_exodus.e
new file mode 100644
index 0000000000..1997f8aad2
Binary files /dev/null and b/tests/sa-model/gold/channel_flow_short_exodus.e differ
diff --git a/tests/sa-model/tests b/tests/sa-model/tests
index c6bea0caac..56da41cafc 100644
--- a/tests/sa-model/tests
+++ b/tests/sa-model/tests
@@ -1,4 +1,9 @@
 [Tests]
+  [channel_flow_short]
+    type = 'Exodiff'
+    input = 'channel_flow_short.i'
+    exodiff = 'channel_flow_short_exodus.e'
+  []
   [channel_flow]
     type = 'Exodiff'
     input = 'channel_flow.i'