Navier stokes Definition and 63 Threads

Hello! :smile: I am going over an example in my fluid mechanics text and I am confused about a few lines. My question is more about the math then the fluid mechanics. In fact, I doubt you need to understand the FM at all; if you understand Diff eqs, you can probably answer my question. I am...

I am curious about what insight people might have as to the statistics of Navier Stokes equation. I thought of the following way someone might try to calculate these. 1) Choose a bais (Basis A) 2) Pick a discrete number of points to constrain the solution of stokes equation. 3) Find the...

Please can anyone tell me how to set this up? I know how to do the required settings in the Physics/Period Conditions. However, to fully implement it, I'm also required to choose boundary conditions in the 2D incompressible navier stokes solver (e.g. wall, inlet, outflow, open boundary...

I wasn't sure whether to put this in Aerospace, but decided on physics in the end. 1.) How do you factor a chemical reaction into the solution for the Navier Stokes equations? More precisely, how can you include the affects of a heat absorbing (endothermic), or heat releasing (exothermic)...

Hi, I've been doing some work with the NS equations. I've read a few papers by fellow undergrads that imply a relationship between the helmholtz-hodge decomposition and the pressure equation. As far as I can see, they're both separate ways of resolving the problem of keeping the flow...

(This is from the perspective of Geophysical Fluid Dynamics) In the Navier Stokes equations I am confused as to why there is both a pressure term and a gravity term. Is this pressure resulting from differences in densities and temperature differences alone? I would think that the gravity term...

Hello, I want, for obscur reasons which would lead us too far to explain, to split my flow into two component, one steady and another one non-steadyv = v_0 + v' I'm looking for a simple equation governing the evolution of this non steady components. The complete momentum equation gives...

Hello, I haven't studied PDEs much yet, but checked out what the Navier Stokes equations are. I think I understood meaning of the terms in Navier Stokes equations, and what is their purpose in defining the time evolution of velocity of the fluid, but I couldn't see any conditions for the...

I've seen several examples of using Navier Stokes in a rotating container where gravity is purely in the Z direction. These solutions generally used cylindircal coordinate systems. I wanted to attempt this problem where the gravity vector does not point purely in the Z direction. (ie...

Consider a stationary body within the flow of some fluid. I want to calculate pressure on the surface of the body. From the Navier Stokes (incompressible, stationary, no volume forces) equations, you would get something like: dp/dx=-rho(u du/dx+v du/dy+w du/dz)+eta(d²u/dx²+d²u/dy²+d²u/dz²)...

Hello, I need the Navier Stokes equations for compressible flow (Newtonian fluid would be ok) in cylinder coordinates. Can anybody help? Thanks

Hi, I'm trying to understand how to convert the cartesian form of the N-S equation to cylinderical/spherical form. Rather than re-derive the equation for spherical/cylindrical systems, I am trying to directly convert the cartesian PDE. I'm ok with converting the d/dx and d2/dx2 terms. What...

I recently came across the vector version of the Navier Stokes equations for fluid flow. \displaystyle{\frac{\partial \mathbf{u}}{\partial \mathbf{t}}} + ( \mathbf{u} \cdot \bigtriangledown) \mathbf{u} = v \bigtriangleup \mathbf{u} - grad \ p Ok, all is well until \bigtriangleup. I know...