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One Dimensional Ideal MHD Equation


In this example we use CentPack's one-dimensional second order fully-discrete formulation, centpack_1d_FD2, to evolve the solution of the equations of Ideal Magnetohydrodynamics


stands for the total pressure, and the the pressure, p, is related to the conserved quantities through the equation of state

with . The solution is calculated over the domain , from , to . The initial conditions are those of the Brio-Wu shock tube

and Dirichlet boundary conditions (i.e., the conserved quantities take on the values specified by the initial conditions at either boundary). Solution computed with 400 cells and cfl number 0.475.

The images below display, from top to bottom and left to right, the profiles of density, x-velocity, y-velocity, y-magnetic field, and pressure at . Click on the individual images to see an animation from to

Click on the images to see an animation


The files implementing this example 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