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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### 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 ...
113 views

### 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 ...
147 views

### what do positive real parts of eigenvalues mean?

I am solving a 1D advection problem of the the form $$d{Q}/dt = [A]{Q}$$ where {Q} is the vector of unknowns and [A] is the matrix of coefficients of spatial discretisation. I have worked out the ...
113 views

### Calculating theoretical order of accuracy of least squares fit advection scheme

I'm familiar with finding the order of accuracy using von Neumann analysis for finite difference schemes formulated using Taylor series expansions. But is there a similar technique for finding the ...
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### Comparison of convection time - theoretical value vs computed

This is a follow up to my previous post here, I'm solving for convection in 1D $$\frac{\partial C}{\partial t} = - v\frac{\partial C}{\partial x}$$ The discretization of the above equation is ...
225 views

### 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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### Extrapolating to non-fluid cells (for Shallow Water Equations), for a shore/beach?

The water height $h$ and 2d velocity field $(u,w)$ are "extrapolated to non-fluid-cells, i.e., setting $h$ equal to the value in the nearest fluid cell." [Bridson] I'm using finite differences. ...
255 views

### Crank-Nicolson scheme in space for advection equation

Consider the equation $$\frac{\partial}{\partial t}v(t,x)=\frac{\partial}{\partial x}v(t,x)$$, for $t,x\in\mathbb{R}$. I'd like to solve this equation forward in space and backward in time, ...
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### Why can I not solve the negative advection equation (backwards in time)?

Suppose we have the negative, inhomogeneous advection equation: $$\left(\frac{\partial}{\partial x}-\frac{1}{c}\frac{\partial}{\partial t}\right)v(t,x)=u(t,x)\qquad(t\in\mathbb{R}_{+},x\in\mathbb{R})$$...
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### 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{...
241 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 (...
500 views

### How to solve advection equation using semi-lagrangian method?

I am working on something that involves solving an advection equation $\partial{x}/\partial{t}+\vec{u}\cdot\nabla{x}=0$ in 3D. I discretized the space into 3d cartesian grid and used the Semi-...
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### Concept of Hermite WENO scheme

Hermite WENO schemes (HWENO, paper2004 and paper2015) are said to be known extension of WENO schemes evolves slopes, so two variables $\{\overline{u}_i,\,\overline{v}_i\}$ are updated in time. ...