It might be very basic, but I am curious about the calculation of $(V\nabla V)\cdot n_{\rm out}$ where $V$ is defined on $\Omega$ and $n_{\rm out}$ is unit normal tangent vector on $\partial \Omega$.
- Like $\nabla \cdot (V\nabla V)=|\nabla V|^2+V\Delta V$, distribute the inner product and get $(V\nabla V)\cdot n_{\rm out}=(V\cdot n_{\rm out})\nabla V+V(\nabla V\cdot n_{\rm out})$.
- Simply write $V\nabla V\cdot n_{\rm out}$.
I know it is a very simple and easy question, but I am a little bit confused now.
Could you help me?