hi my thesis is about simulation metal casting flow with ale method(finite volume) please give me some refrence when we use lagrangian method why the convective terms neglected? thanks111111fsfs

I hope this is not what you are refering to...

DA/Dt = dA/dt + u dA/dx

Maybe you use moving mesh technique.

Case1 : Nodal point and material point move together. (This is the same case of Lagrangian description.)

The two points have the same position throught the simulation. So there is no convection through the mesh surface.

Case2 : The speed of flow through the control volume surface is very small.

You can neglect the convection term. Diffusion term is more important.