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.

70 questions
Filter by
Sorted by
Tagged with
30 views

### discretizing advection equation with variable wave speed + stability

I currently have a code that solves $u_t+ cu_x=0$ with periodic boundary conditions, and constant $c$ (using an upwind method). I'm wondering how I would alter this code to solve something of the form ...
43 views

### numerical solution to pde on an ellipse

Looking for advice on discretization (preferably finite difference) schemes for pdes on curves in general, but in this case it is an ellipse (so given by $(a\cos(r), b\sin(r)$). The problem is the ...
71 views

### 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. ...
196 views

### Order of Accuracy Measurements on 1D Advection Methods

I am trying to learn about basics of computational fluid dynamics, at the moment on the simple example of linear advection in 1D. I am am currently testing the theoretical predictions of the order of ...
41 views

### 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 ...
82 views

360 views

### Advection equation in 2D using finite differences - the scheme works, but the pulse loses “energy”

I am trying to solve the following equation $\partial_t g(x,y,t) = - v\left(\partial_x + \partial_y\right) g(x,y,t)$ using finite differences (here $v>0$). The equation is also solvable ...
496 views

### Is there a general analytic solution to 1D advection of velocity, $u_t=-uu_x$?

This is to help me relate continuous and discrete, predict what my scheme should be doing, and move toward using the method of manufactured solutions. There's a solution for constant velocity $c$ ...
293 views

### Solving the Advection Equation with Forcing using the Discontinuous Galerkin Method

I've been learning about the Discontinous Galkerin Method by reading the book by Hesthaven and Warburton and have ran into a problem with the advection equation with forcing $u_t + u_x = g(x,t)$ ...