# Search Results

Results tagged with Search options answers only user 123
7 results

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.

You have discretized an advection equation using a forward difference in time and centered differences in space. You have correctly deduced that this is an unstable discretization; in fact it is … unstable even for constant-coefficient advection in one dimension. There are many stable discretizations you could use; the most common (and simplest) is to switch to a centered difference in time. To …
answered Oct 17 '14 by David Ketcheson
Linear finite difference discretization of a 1D problem with periodic boundaries leads to a discretization of the form $$U^{n+1} = LU^n$$ where $L$ is a circulant matrix. The eigenvectors of any cir …
answered May 28 '12 by David Ketcheson
It's quite common in computational fluid dynamics to use implicit schemes similar to what you propose. The ones I know of are based on compact finite difference formulas (not simply on replacing $n$ …
answered May 5 '12 by David Ketcheson
There are multiple questions here, but let's start with the basics. You have written two hyperbolic PDEs; (1) is the continuity equation, which is conservative and (2) is the color equation, which is …
answered Mar 11 '15 by David Ketcheson
This is a well-framed question and a very useful thing to understand. Korrok is correct to refer you to von Neumann analysis and LeVeque's book. I can add a bit more to that. I'd like to write a de …
answered Mar 3 '13 by David Ketcheson
The equation you're solving does not permit right-going solutions, so there is no such thing as a reflecting boundary condition for this equation. If you consider the characteristics, you'll realize …
answered Mar 4 '13 by David Ketcheson
In the time-dependent nonlinear case, if you drop the diffusive term then you have a nonlinear hyperbolic problem. Solutions will naturally generate singularities (discontinuities) in finite time. T …
answered Feb 16 '17 by David Ketcheson