Anomalous wave structure in magnetized materials described by non-convex equations of state
Serna, Susana (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Marquina, Antonio (Universitat de València. Departament de Matemàtiques)

Data:	2014
Resum:	We analyze the anomalous wave structure appearing in flow dynamics under the influence of magnetic field in materials described by non-ideal equations of state. We consider the system of magnetohydrodynamics equations closed by a general equation of state (EOS) and propose a complete spectral decomposition of the fluxes that allows us to derive an expression of the nonlinearity factor as the mathematical tool to determine the nature of the wave phenomena. We prove that the possible formation of non-classical wave structure is determined by both the thermodynamic properties of the material and the magnetic field as well as its possible rotation. We demonstrate that phase transitions induced by material properties do not necessarily imply the loss of genuine nonlinearity of the wavefields as is the case in classical hydrodynamics. The analytical expression of the nonlinearity factor allows us to determine the specific amount of magnetic field necessary to prevent formation of complex structure induced by phase transition in the material. We illustrate our analytical approach by considering two non-convex EOS that exhibit phase transitions and anomalous behavior in the evolution. We present numerical experiments validating the analysis performed through a set of one-dimensional Riemann problems. In the examples we show how to determine the appropriate amount of magnetic field in the initial conditions of the Riemann problem to transform a thermodynamic composite wave into a simple nonlinear wave.
Ajuts:	Ministerio de Ciencia e Innovación MTM2011-28043 Ministerio de Ciencia e Innovación MTM2011-26995-C02-01
Nota:	Agraïments: Institute for Pure and Applied Mathematics (UCLA) 2012 program on "Computational Methods in High Energy Density Plasmas.
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Matèria:	Magnetohydrodynamics ; Non-convex equation of state ; Phase transitions ; Complex wave structure ; Composite waves
Publicat a:	Physics of Fluids, Vol. 26 (2014) , p. 16101, ISSN 1089-7666

DOI: 10.1063/1.4851415

Postprint 44 p, 3.4 MB

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