Abstract
Many transport equations in physics and engineering come along with intrinsic constraints. A standard example for an evolution equation with intrinsic constraint is given by
where u is a space vector. The divergence constraint is intrinsic since it follows from the evolution equation and must not be viewed as an additional equation. There are several areas where equations like (1) arise: Maxwells equations, the transport of the magnetic field inmagnetohydrodynamics (MHD), or the vorticity transport in case of incompressible flows. One can easily think of other constrained transport equations. In [8] a system that conserves vorticity is investigated.
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Fey, M., Torrilhon, M. (2003). A Constrained Transport Upwind Scheme for Divergence-free Advection. In: Hou, T.Y., Tadmor, E. (eds) Hyperbolic Problems: Theory, Numerics, Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55711-8_49
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DOI: https://doi.org/10.1007/978-3-642-55711-8_49
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