The terms advection and convection have different meanings depending on in which context they are used. Fluid dynamics. In fluid dynamics, advection is a type of convection, with the other type of convection being diffusion. Both advection and diffusion act to move around various intensive properties of a fluid.

Let me try to give you a visual picture of these terms in the advection -diffusion equation(ADE): Coffee cream mixing Advection (1st term in ADE): It is the mechanical motion of the fluid. For example, stirring a coffee cream by spoon. Diffusion(2nd term in ADE): After this mechanical/spoon action, cream will stretch and fold and form thin ...

Apr 1, 2018 · Advection is the part of convection due to a net force acting on all the particles of one substance, causing them to drift as if they're a point mass. (By "particles" of a "substance" I could also mean quasiparticles, such as phonons of heat, which convect in a mathematically similar way; a container with only one fluid material in it will ...

Jan 20, 2015 · The problem is in the way you wrote your last equation as a matrix multiplication. You have $$ [ \textbf u \cdot ( \nabla \textbf u) ]_i = u_j (\partial_i u_j) = (\partial_i u_j) u_j, $$ so if you want to write this in matrix form you have to multiply the vector $\textbf u$ at the right, as a column vector, i.e.

Apr 13, 2021 · For a 3D flow, the advection term in the x-momentum equation is $-\\nabla \\cdot (\\rho u \\vec{u})$. How does momentum flow in the y and z directions contribute to the momentum flux in the x direction?

She is struggling to find a good way to introduce the reader to diffusion using an everyday example. We do not like the canonical example of propagation of kitchen smells or perfume, because it is not obvious how to rule out spreading by air convection (i.e. advection of …

Jul 19, 2020 · Question: Any idea or reference about the diffusion-advection equation in periodic boundary conditions (in particular about the steady-state)? Which is the "Gibbs-like solution" in this case? Which is the "Gibbs-like solution" in this case?

My question has 2 parts: I just followed the derivation of Navier Stokes (for Control Volume CFD analysis) and was able to understand most parts. However, the book I use (by Versteeg) does not deri...

$\begingroup$ Well you don't adjust the advection equation, you derive a new one. In the case of the magnetic field, the temporal evolution of the $\mathbf B$ field depends on the electric field, you then can use the Lorentz force law (assuming no forces) to get that $\mathbf E=\mathbf v\times\mathbf B$, thus $\partial_t\mathbf B=\nabla\times ...

Oct 30, 2021 · In this Wikipedia article, specifically in the section "Mathematics of advection", the following general equation for advection is given as: \begin{equation} \dfrac{\partial\psi}{\partial t}+\nabla\cdot(\psi u)=\sigma \end{equation} Being a continuity equation, it's not hard to understand what it's saying. But I want know how to derive it ...