Magnetic Field Loop Advection
The advection of magnetic field loop is an important test of the code's ability to maintain a divergenceless field. The field loop is initialized using a numerical curl of a vector potential. The vector potential is given by: A = α * MAX( R - r), where R = 0.3 and α = 0.001. α is chosen to be small enough so that the gas pressure is larger than the magnetic pressure. Initial pressure and density are both set to 1.0.
In 2 dimensions velocities are set as: Vx = COS (θ) , Vy = SIN (θ), where θ = 60. The cfl condition should be set to lower than 0.4. The movie below shows the time evolution of the field loop at a resolution of 800 x 400 in a physical domain of -1x1 in x and -0.5x0.5 in y.