Orszag-Tang Vortex#

The Orszag-Tang Vortex is a 2d non-dimensional MHD manufactured test.

The domain is $(x, y) = [0, 2 π]^{2}$ . The initial conditions of the velocity and the magnetic field are

u = \nabla \times φ and B = \nabla \times A,

where $φ = 2 \sin (y) - 2 \cos (x)$ and $A = \cos (2 y) - 2 \cos (x)$ . See Section 5.3 of [Michael Kraus and Omar Maj, Variational Integrators for Ideal Magnetohydrodynamics, 2021, arXiv]

These initial conditions are implemented. To initialize an ideal Orszag-Tang Vortex, for example, do

>>> from math import inf
>>> ph.samples.InitialConditionOrszagTangVortex()  
<tests.samples.iniCond_Orszag_Tang_vortex.InitialConditionOrszagTangVortex object at ...

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