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cfdmarkus September 24, 2008 05:25

Hi I believe that the gradi

I believe that the gradient of a vector field grad() is not computed consistent with the common definition.
The definition of grad() in OF follows equation 2.3 in the programmers guide. The correct definition of the velocity gradient tensor is V_ij=grad(U)=du_i/dx_j. OF defines the gradient as V_ij=du_j/dx_i, which is the transpose of the correct definition.

The wrong definition of grad(U) result for example in a wrong definition of the skew symmetric part in OF: W_ij=0.5(grad(U) - grad(U).T())=0.5(du_j/dx_i - du_i/dx_j) which should actually be W_ij=0.5(du_i/dx_j - du_j/dx_i).

Is there any reason why OF uses a different definition of grad(). Does this mean that the user alwasy needs to use grad().T() in OF to get the correct definition of the gradient?

I am somewhat confused about this issue.

henry September 24, 2008 05:47

The "definition" of grad in Op
The "definition" of grad in OpenFOAM is not a definition but simply the result of the grad vector operator operating from the left of the field as it is written, i.e. it is entirely consistent with the definition of the vector multiply operator.


sven July 16, 2009 18:54

Definition of skew symmetric part

Where in OpenFOAM (e.g. in which file) can I find the above mentioned skew symmetric part W_ij=0.5(grad(U) - grad(U).T())??

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