I'm currently trying to apply the Finite Volume method to the momentum equation in CFD and I came across an integral which I cannot solve. The integral is as follows:
$ \int_{w}^{e} \frac{\partial (uu)}{\partial x} dx + \int_{w}^{e} \frac{\partial (uv)}{\partial y} dx + \int_{w}^{e} \frac{\partial (uw)}{\partial z} dx $ where $ u=u(x,y,z,t); v=v(x,y,z,t) ; w=(x,y,z,t) $ are the $x,y,z$ components of velocity $\vec v$ respectively.
How do I solve each of the above integrals?
This occurs in the conservative form the momentum equations and I do not want to split the differential using product rule to make it into a non-conservative form.
I searched the internet but I am did not get a satisfactory answer. it would be of great help if someone could help me in this.