Recent content by Kastenfrosch

what do you mean with "the first one" and "the last one"? 1. = (\nabla \cdot \bold{v})\bold{v} 2. = (\bold{v} \cdot \nabla)\bold{v} ? i can see my mistake, that i wrote a \cdot between (\nabla \cdot \bold{v}) and \bold{v}, which is no dot- but a scalar multiplication... But what i meant...

OK, then i still didn't get it... in http://en.wikipedia.org/wiki/Advection they say, that \bold{v}\cdot\nabla is a scalar. And if i use (\bold{v} \cdot \nabla) = \left( \frac{v_x \partial }{\partial x} + \frac{v_y \partial }{\partial y} + \frac{v_z \partial }{\partial z}...

Ah, ok, if i got you right, you mean that (\nabla \cdot \bold{v}) = \left( \frac{\partial v_x}{\partial x} + \frac{\partial v_y}{\partial y} + \frac{\partial v_z}{\partial z} \right) whereas (\bold{v} \cdot \nabla) = \left( \frac{v_x \partial }{\partial x} +...

Sorry, perhaps i get you wrong because I'm from germany... So (\nabla \cdot \bold{v})\cdot \bold{v} = \left( \frac{\partial v_x}{\partial x} + \frac{\partial v_y}{\partial y} + \frac{\partial v_z}{\partial z} \right) \bold{v} = \left(v_x\frac{\partial v_x}{\partial x}+v_x\frac{\partial...

Hello and Thanks for your answer! ... but i think i still don't know what to do... in the linked PDF i saw that there are many definitions, but i didn't find a definition for v \cdot\nabla encouraged by your post i searched for "abuse of nabla", and i found that it's not right to always treat...

Hello! The incompressible Navier Stokes equation consists of the two equations and Why can't i insert the 2nd one into the first one so that the advection term drops out?! \nabla\cdotv = v\cdot\nabla = 0 => (v\cdot\nabla)\cdotv = 0