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A Constrained Transport Upwind Scheme for Divergence-free Advection

In: Hyperbolic Problems: Theory, Numerics, Applications

Author

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  • Michael Fey

    (ETH Zurich, Seminar for Applied Mathematics)

  • Manuel Torrilhon

    (ETH Zurich, Seminar for Applied Mathematics)

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 (1) $$ {{\partial }_{t}}u + curlF(u) = 0,\quad divu = const. $$ 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.

Suggested Citation

  • Michael Fey & Manuel Torrilhon, 2003. "A Constrained Transport Upwind Scheme for Divergence-free Advection," Springer Books, in: Thomas Y. Hou & Eitan Tadmor (ed.), Hyperbolic Problems: Theory, Numerics, Applications, pages 529-538, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-55711-8_49
    DOI: 10.1007/978-3-642-55711-8_49
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