Both are correct and depends on the problem under investigation. To have a better grasp of this aspect use tensor notation and learn about the derivation of Lame's parameters. 

https://en.wikipedia.org/wiki/Lam%C3%A9_parameters

The factor "2" comes from the symmetric aspect of the problem, see page 58 in

https://pangea.stanford.edu/courses/gp262/Notes/5.Elasticity.pdf

Also see Eqns 3.16 to 3.21 in 

http://web.mit.edu/16.20/homepage/3_Constitutive/Constitutive_files/module_3_no_solutions.pdf

I agree with the response above, the correct definition of the deviatoric part of the stress tensor is 2*mu*D0, being the latter term the simmetric part of the velocity gradients having zero trace.

For incompressible flow, Div(2*mu*D0) = mu * Lap v