The Navier-Stokes equations model acceleration of a fluid by adding together all the active internal and external forces acting on the matter.
The advection term represents that in the grid simulation at a point the fluid that is flowing will move and be replaced by some other fluid. The replacement fluid could potentially have some different velocity than what was originally there so the advection term captures this effect. This is a change in apparent velocity that is not due to the actions of the active forces.
As an interesting side note, these equations are listed among the $1 million Millennium Problems for proving that a unique smooth solution exists (or doesn't exist) for any initial conditions.
LucasArmand
It seems very strange to me that equations like N-SE can even exist at all, considering how complex and chaotic fluid systems are. Just a simple system with water contains billions of billions of mostly independent atoms, yet we can predict their behavior with just a few terms of the macroscopic conditions.
rsha256
By definition, models are not perfect. I do not think N-SE actually predicts where fluid will go but instead shows an update which can be applied to a trajectory of a possible update. I think looking at a macro view of systems allows for us to view systems more coarsely and talk more generally about what we would expect by Newtonian physics.
The Navier-Stokes equations model acceleration of a fluid by adding together all the active internal and external forces acting on the matter.
The advection term represents that in the grid simulation at a point the fluid that is flowing will move and be replaced by some other fluid. The replacement fluid could potentially have some different velocity than what was originally there so the advection term captures this effect. This is a change in apparent velocity that is not due to the actions of the active forces.
As an interesting side note, these equations are listed among the $1 million Millennium Problems for proving that a unique smooth solution exists (or doesn't exist) for any initial conditions.
It seems very strange to me that equations like N-SE can even exist at all, considering how complex and chaotic fluid systems are. Just a simple system with water contains billions of billions of mostly independent atoms, yet we can predict their behavior with just a few terms of the macroscopic conditions.
By definition, models are not perfect. I do not think N-SE actually predicts where fluid will go but instead shows an update which can be applied to a trajectory of a possible update. I think looking at a macro view of systems allows for us to view systems more coarsely and talk more generally about what we would expect by Newtonian physics.