Dear Vikram,

I just deal with product between tensors and vectors as a whole for these 
force/moment components together, not separating them before.

If I properly understand your suggestion, do you think there's something wrong 
with the tensor
computation? Anyway, I will tell you whether that's OK or not later for terms 
like \int{tau*normal }.

Now, the results with only viscous shear stress are as follows
NACA0012 airfoil, AOA=0., Re=68.8,
1) np=1
step 9, forces: (-1.634845e+00 -2.619208e-07 0.000000e+00 )
step 9, moments: (0.000000e+00 0.000000e+00 8.167970e-09 )
// Obviously the drag should NEVER be negative ! Lift and pitching moments are 
small enough yet.
The full log is attached as result_np1.log.
2) np=4
step 9, forces: (-1.634845e+00 1.288435e-07 0.000000e+00 )
step 9, moments: (0.000000e+00 0.000000e+00 2.282703e-08 )
still negative drag
The full screen output are attached as from stdout.processor.0 to 
stdout.processor.3 here.

In fact, my doubt comes from two points:
1) I may misused  face quadrature for the boundary integral, esp. psi_face for 
p and q_face for velocity.
could you please have a look at the code in my last email?
2) when running parallel with -np 4, the big wrong result I got before (AOA>=4. 
) always comes from a single node, rank 1 or 2,  but this does not appear when 
AOA=0.0 with only viscous stress.

Many thanks,

Zhenyu
### ####### ./icaruslm starts ###################
### casename: naca0012
### paramfile: ../cases/naca0012/naca0012.param
### ../cases/naca0012/naca0012.bc found.
### ../cases/naca0012/naca0012.ic found.
### ../cases/naca0012/naca0012.post found.
###------- Input Parameters------------------------
Re:           68.8
dt:           0.001
nstep:        10
vel_order:    2
pres_order:   1
lag_multiplier: false
pin_pressure: false
Dirichlet penalty: 1e+08
bc-file:      ../cases/naca0012/naca0012.bc
ic-file:      ../cases/naca0012/naca0012.ic
post-file:    ../cases/naca0012/naca0012.post
##############################################
*** Warning, AutoPtr is deprecated and will be removed in a future library 
version! ./include/libmesh/auto_ptr.h, line 256, compiled Apr  1 2015 at 
08:24:46 ***
### read ../cases/naca0012/naca0012.exo
### boundary numbers in bmap: 5
### Name:        inlet , index= 1
### Name:    lowerwing , index= 4
### Name:       outlet , index= 2
### Name: trailingedge , index= 5
### Name:    upperwing , index= 3
### ---------------------------------------
 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=3
  n_nodes()=58708
    n_local_nodes()=58708
  n_elem()=14536
    n_local_elem()=14536
    n_active_elem()=14536
  n_subdomains()=5
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0

###########################################
0
### system: ns_0; type: forces; names: normal axial none; console output: true
### boundary names: upperwing lowerwing trailingedge
### file_name: ../cases/naca0012/post/force.dat
### ---------------------------------------
### system: ns_0; type: moments; names: none none pitching; console output: true
### center: (0.25, 0, 0)
### boundary names: upperwing lowerwing trailingedge
### file_name: ../cases/naca0012/post/moment.dat
### ---------------------------------------
###########################################
**********************

Side Boundary conditions:
-------------------------
  (ID, number of sides)   
  (1, 340)
  (2, 70)
  (3, 74)
  (4, 74)
  (5, 6)
**********************
### Loading Boundary Condition file ../cases/naca0012/naca0012.bc
### ../cases/naca0012/naca0012.bc loaded.
#### BoundaryConditions::print_info head @ rank 0 ##########
field: pressure
 - type Dirichlet
  . boundary        outlet; components: 1; expr :                      0.0, id: 
2, bcfunc_type:        const, get_func: 0x23ea280
--------------------------
field: velocity
 - type Dirichlet
  . boundary         inlet; components: 2; expr :               {1.0}{0.0}, id: 
1, bcfunc_type:         expr, get_func: 0x181f610
--------------------------
  . boundary     lowerwing; components: 2; expr :                      0.0, id: 
4, bcfunc_type:        const, get_func: 0x24d9f10
--------------------------
  . boundary  trailingedge; components: 2; expr :                      0.0, id: 
5, bcfunc_type:        const, get_func: 0x23eb870
--------------------------
  . boundary     upperwing; components: 2; expr :                      0.0, id: 
3, bcfunc_type:        const, get_func: 0x24d7cb0
--------------------------
#### BoundaryConditions::print_info tail @ rank 0 ##########
### Loading Initial Condition file ../cases/naca0012/naca0012.ic
### ../cases/naca0012/naca0012.ic loaded.
### InitConditions::print_info -- start-------------- ##########
### 1 systems
 system: ns_0
 - variable p
    components: 1; expr :                       0., ic_type:        const, 
get_func: 0x24019e0
--------------------------
 - variable u
    components: 1; expr :                      1.0, ic_type:         expr, 
get_func: 0x28d40d0
--------------------------
 - variable v
    components: 1; expr :                      0.0, ic_type:         expr, 
get_func: 0x28d6740
--------------------------
### InitConditions::print_info -- tails-------------- ##########
init_sys called by ns_0
 EquationSystems
  n_systems()=1
   System #0, "ns_0"
    Type "TransientNonlinearImplicit"
    Variables={ "u" "v" } "p" 
    Finite Element Types="LAGRANGE", "JACOBI_20_00" "LAGRANGE", "JACOBI_20_00" 
    Infinite Element Mapping="CARTESIAN" "CARTESIAN" 
    Approximation Orders="SECOND", "THIRD" "FIRST", "THIRD" 
    n_dofs()=132234
    n_local_dofs()=132234
    n_constrained_dofs()=2049
    n_local_constrained_dofs()=2049
    n_vectors()=3
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 40.2404
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 73
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 2049
      Number of Heterogenous Constraints= 681
      Average DoF Constraint Length= 0
      Number of Node Constraints = 0

file_name: ../cases/naca0012/output/init_test.e
Warning:  This MeshOutput subclass only supports meshes which have been 
serialized!
Warning:  This MeshOutput subclass only supports meshes which have been 
serialized!
Solution Initialized in init_test.e


*** Solving time step 0, time = 0.001 ***
  NL step  0, |residual|_2 = 3.364858e-02
  NL step  1, |residual|_2 = 8.721472e-06
After 1 nonlinear iterations,   convergence: ||u - u_old|| = 3.005974e+03, 
final_nonlinear_residual: 8.721472e-06
file_name: ../cases/naca0012/output/out_Re_68_001.e
nelem=: 154; _values: -8.383427e+00,3.457312e-05,0.000000e+00
nelem=: 154; _values: 0.000000e+00,0.000000e+00,1.736603e-06
step 0, forces: (-8.383427e+00 3.457312e-05 0.000000e+00 )
step 0, moments: (0.000000e+00 0.000000e+00 1.736603e-06 )


*** Solving time step 1, time = 2.000000e-03 ***
  NL step  0, |residual|_2 = 2.174039e-03
  NL step  1, |residual|_2 = 3.410028e-08
After 1 nonlinear iterations,   convergence: ||u - u_old|| = 2.842638e+03, 
final_nonlinear_residual: 3.410028e-08
file_name: ../cases/naca0012/output/out_Re_68_002.e
nelem=: 154; _values: -4.251007e+00,-1.284619e-05,0.000000e+00
nelem=: 154; _values: 0.000000e+00,0.000000e+00,2.991758e-07
step 1, forces: (-4.251007e+00 -1.284619e-05 0.000000e+00 )
step 1, moments: (0.000000e+00 0.000000e+00 2.991758e-07 )


*** Solving time step 2, time = 3.000000e-03 ***
  NL step  0, |residual|_2 = 1.937317e-04
  NL step  1, |residual|_2 = 1.219620e-08
After 1 nonlinear iterations,   convergence: ||u - u_old|| = 1.320741e+02, 
final_nonlinear_residual: 1.219620e-08
file_name: ../cases/naca0012/output/out_Re_68_003.e
nelem=: 154; _values: -3.211936e+00,-2.928710e-06,0.000000e+00
nelem=: 154; _values: 0.000000e+00,0.000000e+00,1.521435e-07
step 2, forces: (-3.211936e+00 -2.928710e-06 0.000000e+00 )
step 2, moments: (0.000000e+00 0.000000e+00 1.521435e-07 )


*** Solving time step 3, time = 4.000000e-03 ***
  NL step  0, |residual|_2 = 9.430067e-05
  NL step  1, |residual|_2 = 6.970001e-09
After 1 nonlinear iterations,   convergence: ||u - u_old|| = 1.857992e+01, 
final_nonlinear_residual: 6.970001e-09
file_name: ../cases/naca0012/output/out_Re_68_004.e
nelem=: 154; _values: -2.692333e+00,-1.612411e-06,0.000000e+00
nelem=: 154; _values: 0.000000e+00,0.000000e+00,1.012821e-07
step 3, forces: (-2.692333e+00 -1.612411e-06 0.000000e+00 )
step 3, moments: (0.000000e+00 0.000000e+00 1.012821e-07 )


*** Solving time step 4, time = 5.000000e-03 ***
  NL step  0, |residual|_2 = 7.980746e-05
  NL step  1, |residual|_2 = 4.658918e-09
After 1 nonlinear iterations,   convergence: ||u - u_old|| = 1.187731e+01, 
final_nonlinear_residual: 4.658918e-09
file_name: ../cases/naca0012/output/out_Re_68_005.e
nelem=: 154; _values: -2.367414e+00,-1.104939e-06,0.000000e+00
nelem=: 154; _values: 0.000000e+00,0.000000e+00,6.901615e-08
step 4, forces: (-2.367414e+00 -1.104939e-06 0.000000e+00 )
step 4, moments: (0.000000e+00 0.000000e+00 6.901615e-08 )


*** Solving time step 5, time = 6.000000e-03 ***
  NL step  0, |residual|_2 = 7.022237e-05
  NL step  1, |residual|_2 = 3.415680e-09
After 1 nonlinear iterations,   convergence: ||u - u_old|| = 8.479603e+00, 
final_nonlinear_residual: 3.415680e-09
file_name: ../cases/naca0012/output/out_Re_68_006.e
nelem=: 154; _values: -2.139854e+00,-7.685668e-07,0.000000e+00
nelem=: 154; _values: 0.000000e+00,0.000000e+00,5.440303e-08
step 5, forces: (-2.139854e+00 -7.685668e-07 0.000000e+00 )
step 5, moments: (0.000000e+00 0.000000e+00 5.440303e-08 )


*** Solving time step 6, time = 7.000000e-03 ***
  NL step  0, |residual|_2 = 6.335432e-05
  NL step  1, |residual|_2 = 2.639653e-09
After 1 nonlinear iterations,   convergence: ||u - u_old|| = 6.418179e+00, 
final_nonlinear_residual: 2.639653e-09
file_name: ../cases/naca0012/output/out_Re_68_007.e
nelem=: 154; _values: -1.969107e+00,-5.753260e-07,0.000000e+00
nelem=: 154; _values: 0.000000e+00,0.000000e+00,4.397925e-08
step 6, forces: (-1.969107e+00 -5.753260e-07 0.000000e+00 )
step 6, moments: (0.000000e+00 0.000000e+00 4.397925e-08 )


*** Solving time step 7, time = 8.000000e-03 ***
  NL step  0, |residual|_2 = 5.818830e-05
  NL step  1, |residual|_2 = 2.129185e-09
After 1 nonlinear iterations,   convergence: ||u - u_old|| = 5.104349e+00, 
final_nonlinear_residual: 2.129185e-09
file_name: ../cases/naca0012/output/out_Re_68_008.e
nelem=: 154; _values: -1.834889e+00,-4.557370e-07,0.000000e+00
nelem=: 154; _values: 0.000000e+00,0.000000e+00,3.293668e-08
step 7, forces: (-1.834889e+00 -4.557370e-07 0.000000e+00 )
step 7, moments: (0.000000e+00 0.000000e+00 3.293668e-08 )


*** Solving time step 8, time = 9.000000e-03 ***
  NL step  0, |residual|_2 = 5.410796e-05
  NL step  1, |residual|_2 = 1.749671e-09
After 1 nonlinear iterations,   convergence: ||u - u_old|| = 4.195181e+00, 
final_nonlinear_residual: 1.749671e-09
file_name: ../cases/naca0012/output/out_Re_68_009.e
nelem=: 154; _values: -1.725793e+00,-3.283791e-07,0.000000e+00
nelem=: 154; _values: 0.000000e+00,0.000000e+00,1.563776e-08
step 8, forces: (-1.725793e+00 -3.283791e-07 0.000000e+00 )
step 8, moments: (0.000000e+00 0.000000e+00 1.563776e-08 )


*** Solving time step 9, time = 1.000000e-02 ***
  NL step  0, |residual|_2 = 5.078198e-05
  NL step  1, |residual|_2 = 1.485509e-09
After 1 nonlinear iterations,   convergence: ||u - u_old|| = 3.536478e+00, 
final_nonlinear_residual: 1.485509e-09
file_name: ../cases/naca0012/output/out_Re_68_010.e
nelem=: 154; _values: -1.634845e+00,-2.619208e-07,0.000000e+00
nelem=: 154; _values: 0.000000e+00,0.000000e+00,8.167970e-09
step 9, forces: (-1.634845e+00 -2.619208e-07 0.000000e+00 )
step 9, moments: (0.000000e+00 0.000000e+00 8.167970e-09 )

 --------------------------------------------------------------
| Time:           Mon Apr 27 10:04:35 2015                     |
| OS:             Linux                                        |
| HostName:       hp820g1                                      |
| OS Release:     3.16.0-36-generic                            |
| OS Version:     #48-Ubuntu SMP Tue Apr 14 20:08:31 UTC 2015  |
| Machine:        x86_64                                       |
| Username:       zhenyu                                       |
| Configuration:  ./configure  '--prefix=/home/zhenyu/deps/libmesh'|
|  '--enable-everything'                                       |
|  '--enable-parmesh'                                          |
|  '--enable-ifem'                                             |
|  '--enable-nodeconstraint'                                   |
|  '--enable-perflog'                                          |
|  '--enable-blocked-storage'                                  |
|  '--with-fparser=release'                                    |
|  'PETSC_DIR=/usr/lib/petsc'                                  |
|  'VTK_INCLUDE=/usr/include/vtk-5.8'                          |
|  'VTK_DIR=/usr/lib/vtk-5.8'                                  |
|  'HDF5_DIR=/usr/lib/x86_64-linux-gnu'                        |
|  '--disable-testsets'                                        |
|  'CXX=mpicxx'                                                |
|  'CC=mpicc'                                                  |
|  'F77=mpif77'                                                |
|  'FC=mpif90'                                                 |
|  'CPPFLAGS= '                                                |
|  'LIBS= '                                                    |
 --------------------------------------------------------------
 
-------------------------------------------------------------------------------------------------------------------------
| libMesh Performance: Alive time=181.326, Active time=179.93                   
                                          |
 
-------------------------------------------------------------------------------------------------------------------------
| Event                                      nCalls     Total Time  Avg Time    
Total Time  Avg Time    % of Active Time  |
|                                                       w/o Sub     w/o Sub     
With Sub    With Sub    w/o S    With S   |
|-------------------------------------------------------------------------------------------------------------------------|
|                                                                               
                                          |
|                                                                               
                                          |
| DofMap                                                                        
                                          |
|   add_neighbors_to_send_list()             1          0.0178      0.017841    
0.0178      0.017841    0.01     0.01     |
|   build_constraint_matrix()                436080     0.6879      0.000002    
0.6879      0.000002    0.38     0.38     |
|   build_sparsity()                         1          0.1531      0.153107    
0.1733      0.173324    0.09     0.10     |
|   constrain_elem_matrix()                  145360     0.1524      0.000001    
0.1524      0.000001    0.08     0.08     |
|   constrain_elem_vector()                  290720     0.5602      0.000002    
0.5602      0.000002    0.31     0.31     |
|   create_dof_constraints()                 1          0.1717      0.171662    
0.3020      0.302035    0.10     0.17     |
|   distribute_dofs()                        1          0.0492      0.049202    
0.1208      0.120754    0.03     0.07     |
|   dof_indices()                            3299672    3.5297      0.000001    
3.5297      0.000001    1.96     1.96     |
|   enforce_constraints_exactly()            31         0.0597      0.001925    
0.0597      0.001925    0.03     0.03     |
|   prepare_send_list()                      1          0.0000      0.000001    
0.0000      0.000001    0.00     0.00     |
|   reinit()                                 1          0.0715      0.071548    
0.0715      0.071548    0.04     0.04     |
|                                                                               
                                          |
| EquationSystems                                                               
                                          |
|   build_solution_vector()                  11         0.9630      0.087546    
1.5801      0.143646    0.54     0.88     |
|                                                                               
                                          |
| ExodusII_IO                                                                   
                                          |
|   write_nodal_data()                       11         0.4939      0.044902    
0.4939      0.044902    0.27     0.27     |
|                                                                               
                                          |
| FE                                                                            
                                          |
|   compute_shape_functions()                1170028    3.4516      0.000003    
3.4516      0.000003    1.92     1.92     |
|   init_shape_functions()                   239786     0.1115      0.000000    
0.1115      0.000000    0.06     0.06     |
|   inverse_map()                            716092     1.3363      0.000002    
1.3363      0.000002    0.74     0.74     |
|                                                                               
                                          |
| FEMap                                                                         
                                          |
|   compute_face_map()                       239724     0.6320      0.000003    
2.0125      0.000008    0.35     1.12     |
|   compute_map()                            1170028    2.6920      0.000002    
2.6920      0.000002    1.50     1.50     |
|   init_face_shape_functions()              1030       0.0008      0.000001    
0.0008      0.000001    0.00     0.00     |
|   init_reference_to_physical_map()         239786     0.8027      0.000003    
0.8027      0.000003    0.45     0.45     |
|                                                                               
                                          |
| GenericProjector                                                              
                                          |
|   operator()                               1          1.2562      1.256243    
4.7947      4.794731    0.70     2.66     |
|                                                                               
                                          |
| Mesh                                                                          
                                          |
|   all_second_order()                       1          0.0673      0.067264    
0.0673      0.067264    0.04     0.04     |
|   find_neighbors()                         2          0.0673      0.033666    
0.0673      0.033666    0.04     0.04     |
|                                                                               
                                          |
| MeshCommunication                                                             
                                          |
|   delete_remote_elements()                 13         0.1632      0.012556    
0.1632      0.012556    0.09     0.09     |
|   make_node_ids_parallel_consistent()      1          0.0050      0.005014    
0.0050      0.005014    0.00     0.00     |
|   make_node_proc_ids_parallel_consistent() 2          0.0100      0.005012    
0.0100      0.005012    0.01     0.01     |
|                                                                               
                                          |
| MeshOutput                                                                    
                                          |
|   write_equation_systems()                 11         0.0004      0.000035    
2.0744      0.188584    0.00     1.15     |
|                                                                               
                                          |
| Parallel                                                                      
                                          |
|   allgather()                              9          0.0000      0.000002    
0.0000      0.000002    0.00     0.00     |
|                                                                               
                                          |
| ParallelMesh                                                                  
                                          |
|   renumber_nodes_and_elements()            4          0.1883      0.047080    
0.1883      0.047084    0.10     0.10     |
|                                                                               
                                          |
| Partitioner                                                                   
                                          |
|   set_node_processor_ids()                 1          0.0133      0.013328    
0.0133      0.013328    0.01     0.01     |
|   single_partition()                       1          0.0014      0.001371    
0.0014      0.001371    0.00     0.00     |
|                                                                               
                                          |
| PetscNonlinearSolver                                                          
                                          |
|   jacobian()                               10         10.1162     1.011616    
12.4029     1.240294    5.62     6.89     |
|   residual()                               20         5.6422      0.282112    
12.9523     0.647616    3.14     7.20     |
|   solve()                                  10         146.4412    14.644124   
171.7965    17.179650   81.39    95.48    |
|                                                                               
                                          |
| System                                                                        
                                          |
|   project_fem_vector()                     1          0.0016      0.001642    
4.7978      4.797779    0.00     2.67     |
|   project_vector()                         1          0.0000      0.000008    
4.7978      4.797787    0.00     2.67     |
|   solve()                                  10         0.0193      0.001927    
171.8158    17.181578   0.01     95.49    |
 
-------------------------------------------------------------------------------------------------------------------------
| Totals:                                    7948463    179.9301                
                        100.00            |
 
-------------------------------------------------------------------------------------------------------------------------

 
------------------------------------------------------------------------------------------------------------
| IcarusLM Performance: Alive time=181.329, Active time=171.818                 
                             |
 
------------------------------------------------------------------------------------------------------------
| Event                         nCalls     Total Time  Avg Time    Total Time  
Avg Time    % of Active Time  |
|                                          w/o Sub     w/o Sub     With Sub    
With Sub    w/o S    With S   |
|------------------------------------------------------------------------------------------------------------|
|                                                                               
                             |
| nonlinear solve               10         171.8179    17.181786   171.8179    
17.181786   100.00   100.00   |
 
------------------------------------------------------------------------------------------------------------
| Totals:                       10         171.8179                             
           100.00            |
 
------------------------------------------------------------------------------------------------------------

--------------------------------------------------------------------------
mpirun noticed that process rank 0 with PID 6984 on node hp820g1 exited on 
signal 11 (Segmentation fault).
--------------------------------------------------------------------------
------------------------------------------------------------------------------
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