CentPack Logo Center for Scientific Computation and Mathematical Modeling


Two Dimensional Euler's Equations of Gas Dynamics


In this example we use CentPack's two-dimensional second order fully-discrete formulation, centpack_2d_FD2, to evolve the solution of Euler's equations of gas dynamics

where the pressure, p, is related to the conserved quantities through the equation of state

with . We solve a two-d Riemann problem over the computational domain , with initial conditions given by

and Dirichlet boundary conditions (i.e., the conserved quantities take on the values specified by the initial conditions at either boundary). The solution is evolved up to , using a 200 x 200 mesh and cfl number 0.75.

The images below display the contour lines of density, and pressure (top) and the velocity field (bottom) at ,. Click on the individual images to see an animation from to .

Click on the images above to see an animation


The files implementing this exaple are included in the current CentPack distribution, CP-1.0. Read here how to run and compile this example.

One dimensional examples

Burgers equation
Euler equations of gas dynamics
MHD equations

Two dimensional examples

Scalar example
Euler equations of gas dynamics
MHD equations


User's guide

Jorge Balbas and Eitan Tadmor
University of Maryland    

Maintained by CSCAMM. CSCAMM is part of the
College of Computer, Mathematical & Natural Sciences (CMNS).
Direct questions and comments to webmaster@cscamm.umd.edu