Orszag-Tang Vortex

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

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

\[\boldsymbol{u} = \nabla\times \varphi \quad \text{and} \quad \boldsymbol{B} = \nabla\times A,\]

where \(\varphi = 2\sin(y) - 2\cos(x)\) and \(A=\cos(2y) - 2 \cos(x)\). 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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