To move in some direction (as a fluid does in a pipe). Often contrasted with diffusion, which is a spreading out without necessarily having any movement of the field as a whole.

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### Attempt on 2d Advection with FDM - With Code

I tried to implement the 2d advection problem with a velocity field, that is not constant in space. My problem is, that the "mass" of my shifted density gets "eroded" or just ...
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### Global reconstruction defined elementwise in a-posteriori error estimator

This question is a follow-up of this previous one. In "Error Control for Discontinuous Galerkin Methods for First Order Hyperbolic Problems" by Georgoulis et al., an error estimator is ...
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### TVD Lax-Wendroff with non-constant velocity

I am dealing with a linear advection equation with a non-constant velocity, where I would like to apply a TVD Lax-Wendroff scheme in 1D. The equation is the following: \begin{equation} \frac{\...
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### Why the numerical solution of advection-dominant problem is challenging

In many CFD text books, usually there is a dedicated chapter for advection term discretization. Why discretization of such term in advection-dominated problems and near the discontinuities is ...
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### Efects from the boundary in advection equation [duplicate]

I am implementing the advection equation $u_x+(1/c)u_t=0$ following a Crank-Nicholson finite difference scheme. The equation for this is \begin{eqnarray*} -\frac{\gamma}{4} w_{n-3 j+1} + w_{n-2 j+1} ...
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### Inflow and outflow boundary conditions for advection-diffusion equation

I'm trying to solve this advection-diffusion equation (ADE): $$\frac{\partial \phi}{\partial t} + \nabla \cdot (-D \nabla \phi + \mathbf{u} \phi) = 0$$ In fact, this ADE framework is coupled to a ...
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### Deposition model in laminar flow

I have a chamber full with a fluid flowing horizontally in laminar regime from one side to the other. It carries a suspension with concentration $c$. This suspension also falls to the bottom of the ...
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### Numerical diffusion in during advection of a free surface in an FE context

I am currently working on a project where a two-phase flow is considered. The phases are described using a level set approach and a signed distance function from the interface between the phases where ...
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### When is it safe to ignore the diffusion term in an advection-diffusion equation?

Given the one dimensional equation: $\epsilon\frac{\partial^2u}{\partial x^2} +\frac{\partial u}{\partial x} = 0$ with $0\le\epsilon \ll1$ with boundary conditions $u(0) = 0$ and $u(1) = 2$, we ...
I have a 2D (x,y) scalar advection problem that describes net blowing snow ($q$) transport at a point. This takes the form $$q = A - F*\nabla\cdot(q {\bf \hat u}),$$ where A ($kg\cdot m^{-2}\cdot s^{... 1answer 411 views ### Upwind difference for velocity in staggered grid I am reading the paper, http://math.mit.edu/~gs/cse/codes/mit18086_navierstokes.pdf In the paper, the nonlinear term is treated as mix of central central difference and upwind difference using a ... 2answers 114 views ### How to support or contradict a hypothesis on unconditional stability using numerical optimization The main motivation behind my next question is that I think I derived a higher order numerical scheme for linear advection equation that is unconditionally stable using Von Neumann stability analysis. ... 0answers 201 views ### Spherical Advection Discretization (boundary nodes) Consider the spherical advection problem: describing the conservation of a property$u$in a closed spherical domain. $$\frac{\partial u}{\partial t}+\frac{1}{r^2}\frac{\partial }{\partial r}\left(r^... 0answers 74 views ### Direction-splitting for SSP-RK schemes What are the implications of applying a direction-splitting within each stage of an SSP-RK scheme? For instance, given a standard advective transport type equation:$$ \partial_{t}Q + \operatorname{... 1answer 687 views ### More Smearing with decreasing timestep in advection problems I find it kind of counter intuitive, that the result of an advection gets more smeared out at the borders when decreasing the timestep (which should make it more accurate). Let there be a equally ... 0answers 348 views ### Corner Transport Upwind for Linear Advection in Arbitrary Velocity Field I need to implement a 3D version of the Corner Transport Upwind (CTU) finite volume method (in python); and so I've been reading Leveque, "Finite Volume Methods for Hyperbolic Problems" which I think ... 0answers 263 views ### Numerical solution of non-linear advection equation other than inviscid burgers I am solving a non-linear advection equation of the form$u_t + f(u)_x = 0$where$f(u)$is a complicated function of$u$. I am solving this equation using a first order fully implicit scheme (... 1answer 873 views ### Numerically computing the advection equation I am trying to write a program to compute the advection equation. $$u_t +u_x = 0$$ I use the spectral method for the spatial derivative$u_x$and the leapfrog method for the time derivative$u_t\$. ...
Given the advection equation for an incompressible flow field $$\frac{\partial c}{\partial t} + \mathrm{Pe} \frac{\partial c}{\partial x} = 0$$ what would the best method be for discretizing this ...