A Constrained Transport Upwind Scheme for Divergence-free Advection

Michael Fey () and Manuel Torrilhon ()
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Michael Fey: ETH Zurich, Seminar for Applied Mathematics
Manuel Torrilhon: ETH Zurich, Seminar for Applied Mathematics

A chapter in Hyperbolic Problems: Theory, Numerics, Applications, 2003, pp 529-538 from Springer

Abstract: 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.

Keywords: Order Scheme; Divergence Constraint; Upwind Direction; Magnetohydrodynamic Flow; Vorticity Transport (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-55711-8_49

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DOI: 10.1007/978-3-642-55711-8_49

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