Inviscid Burgers's Equation

Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
Burgers's equation is one of the simplest cases of a nonlinear, hyperbolic partial differential equation. It is useful as a test problem in computational fluid dynamics. The one-dimensional, inviscid (i.e., zero viscosity) form of the equation is given by
[more]
Contributed by: Garrett Neske (March 2011)
Open content licensed under CC BY-NC-SA
Snapshots
Details
The inviscid Burgers's equation is a flux-conservative partial differential equation, and is thus amenable to finite-volume methods, which are often used for numerically solving nonlinear, hyperbolic partial differential equations. Hyperbolic problems are represented in the flux-conserving form
,
where is the flux function for some conserved quantity
. The inviscid Burgers's equation is easily represented in this form if the flux function is considered to be
The finite-volume method takes the following form with forward-Euler time-stepping
,
where is the space index,
is the time index,
is the flux at the right boundary enclosing the volume around point
, and
is the flux at the left boundary enclosing the volume around point
. There are several different finite-volume methods, which differ in their determination of
and
In this Demonstration, the Harten-Lax-van Leer (HLL) method is used because it is good at capturing shocks in an evolving waveform, which is a feature often found in solutions to Burgers's equation.
Reference: R. J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge, UK: Cambridge University Press, 2002.
Permanent Citation