diff --git a/modules/navier_stokes/test/tests/finite_element/ins/RZ_cone/gold/ad_rz_cone_by_parts_steady_stabilized_second_order_out.e b/modules/navier_stokes/test/tests/finite_element/ins/RZ_cone/gold/ad_rz_cone_by_parts_steady_stabilized_second_order_out.e
deleted file mode 100644
index 878cb3c7b3cf..000000000000
Binary files a/modules/navier_stokes/test/tests/finite_element/ins/RZ_cone/gold/ad_rz_cone_by_parts_steady_stabilized_second_order_out.e and /dev/null differ
diff --git a/modules/navier_stokes/test/tests/finite_element/ins/RZ_cone/gold/ad_rz_cone_by_parts_steady_stabilized_second_order_out.e b/modules/navier_stokes/test/tests/finite_element/ins/RZ_cone/gold/ad_rz_cone_by_parts_steady_stabilized_second_order_out.e
new file mode 120000
index 000000000000..3c944fec3c4e
--- /dev/null
+++ b/modules/navier_stokes/test/tests/finite_element/ins/RZ_cone/gold/ad_rz_cone_by_parts_steady_stabilized_second_order_out.e
@@ -0,0 +1 @@
+rz_cone_by_parts_steady_stabilized_second_order_out.e
\ No newline at end of file
diff --git a/modules/navier_stokes/test/tests/finite_element/ins/RZ_cone/gold/ad_rz_cone_no_parts_steady_stabilized_second_order_out.e b/modules/navier_stokes/test/tests/finite_element/ins/RZ_cone/gold/ad_rz_cone_no_parts_steady_stabilized_second_order_out.e
deleted file mode 100644
index a567e450ef74..000000000000
Binary files a/modules/navier_stokes/test/tests/finite_element/ins/RZ_cone/gold/ad_rz_cone_no_parts_steady_stabilized_second_order_out.e and /dev/null differ
diff --git a/modules/navier_stokes/test/tests/finite_element/ins/RZ_cone/gold/ad_rz_cone_no_parts_steady_stabilized_second_order_out.e b/modules/navier_stokes/test/tests/finite_element/ins/RZ_cone/gold/ad_rz_cone_no_parts_steady_stabilized_second_order_out.e
new file mode 120000
index 000000000000..f458bd4289e3
--- /dev/null
+++ b/modules/navier_stokes/test/tests/finite_element/ins/RZ_cone/gold/ad_rz_cone_no_parts_steady_stabilized_second_order_out.e
@@ -0,0 +1 @@
+rz_cone_no_parts_steady_stabilized_second_order_out.e
\ No newline at end of file
diff --git a/modules/navier_stokes/test/tests/finite_element/ins/RZ_cone/tests b/modules/navier_stokes/test/tests/finite_element/ins/RZ_cone/tests
index 1e2053191cef..41ab372aa64f 100644
--- a/modules/navier_stokes/test/tests/finite_element/ins/RZ_cone/tests
+++ b/modules/navier_stokes/test/tests/finite_element/ins/RZ_cone/tests
@@ -137,12 +137,12 @@
     custom_cmp = 'rz-cone-with-globals.cmp' # To ignore the vector variable components automatically generated by libMesh/ParaView
   []
   [ad_rz_cone_no_parts_steady_supg_pspg_second_order]
-    # TODO: update the gold file once second order derivatives are implemented in libMesh for TypeNTensors
     type = 'Exodiff'
     input = 'ad_rz_cone_no_parts_steady_stabilized_second_order.i'
     exodiff = 'ad_rz_cone_no_parts_steady_stabilized_second_order_out.e'
     issues = '#14901'
     requirement = 'The system shall be able to solve the steady incompressible Navier-Stokes equations with SUPG and PSPG stabilization and a second order velocity basis using an automatic differentiation, vector variable implementation in an RZ coordinate system while not integrating the pressure term by parts and applying a natural outflow boundary condition.'
+    custom_cmp = 'rz-cone-with-globals.cmp' # To ignore the vector variable components automatically generated by libMesh/ParaView
   []
   [rz_cone_no_parts_steady_supg_pspg_second_order]
     type = 'Exodiff'
@@ -152,12 +152,12 @@
     requirement = 'The system shall be able to solve the steady incompressible Navier-Stokes equations with SUPG and PSPG stabilization and a second order velocity basis using a hand-coded Jacobian, standard variable implementation in an RZ coordinate system while not integrating the pressure term by parts and applying a natural outflow boundary condition.'
   []
   [ad_rz_cone_by_parts_steady_supg_pspg_second_order]
-    # TODO: update the gold file once second order derivatives are implemented in libMesh for TypeNTensors
     type = 'Exodiff'
     input = 'ad_rz_cone_by_parts_steady_stabilized_second_order.i'
     exodiff = 'ad_rz_cone_by_parts_steady_stabilized_second_order_out.e'
     issues = '#14901'
     requirement = 'The system shall be able to solve the steady incompressible Navier-Stokes equations with SUPG and PSPG stabilization and a second order velocity basis using an automatic differentiation, vector variable implementation in an RZ coordinate system while integrating the pressure term by parts and applying a natural outflow boundary condition.'
+    custom_cmp = 'rz-cone-with-globals.cmp' # To ignore the vector variable components automatically generated by libMesh/ParaView
   []
   [rz_cone_by_parts_steady_supg_pspg_second_order]
     type = 'Exodiff'
diff --git a/modules/navier_stokes/test/tests/finite_element/ins/energy-conservation/gold/q2q1_out.csv b/modules/navier_stokes/test/tests/finite_element/ins/energy-conservation/gold/q2q1_out.csv
index 6d99624fe4ff..873ff9497b20 100644
--- a/modules/navier_stokes/test/tests/finite_element/ins/energy-conservation/gold/q2q1_out.csv
+++ b/modules/navier_stokes/test/tests/finite_element/ins/energy-conservation/gold/q2q1_out.csv
@@ -1,3 +1,3 @@
-time,advection,convective_heat_transfer,source,energy_balance
+time,advection,convective_heat_transfer,energy_balance,source
 0,0,0,0,0
-1,0.035399450358858,0.61909901913896,0.65449846949787,-5.9174887212521e-14
+1,0.035376853388243,0.61912161610963,-5.5511151231258e-16,0.65449846949787