Magnetohydrodynamic and gasdynamic theories for planetary bow waves

The observed properties of bow waves and the associated plasma flows are outlined, along with those features identified that can be described by a continuum magnetohydrodynamic flow theory as opposed to a more detailed multicomponent particle and field plasma theory. The primary objectives are to provide an account of the fundamental concepts and current status of the magnetohydrodynamic and gas dynamic theories for solar wind flow past planetary bodies. This includes a critical examination of: (1) the fundamental assumptions of the theories; (2) the various simplifying approximations introduced to obtain tractable mathematical problems; (3) the limitations they impose on the results; and (4) the relationship between the results of the simpler gas dynamic-frozen field theory and the more accurate but less completely worked out magnetohydrodynamic theory. Representative results of the various theories are presented and compared. A number of deficiencies, ambiguities, and suggestions for improvements are discussed, and several significant extensions of the theory required to provide comparable results for all planets, their satellites, and comets are noted

Magnetohydrodynamic and gasdynamic theories for planetary bow waves

A bow wave was previously observed in the solar wind upstream of each of the first six planets. The observed properties of these bow waves and the associated plasma flows are outlined, and those features identified that can be described by a continuum magnetohydrodynamic flow theory. An account of the fundamental concepts and current status of the magnetohydrodynamic and gas dynamic theories for solar wind flow past planetary bodies is provided. This includes a critical examination of: (1) the fundamental assumptions of the theories; (2) the various simplifying approximations introduced to obtain tractable mathematical problems; (3) the limitations they impose on the results; and (4) the relationship between the results of the simpler gas dynamic-frozen field theory and the more accurate but less completely worked out magnetohydrodynamic theory. Representative results of the various theories are presented and compared

Interface conditions for domain decomposition with radical grid refinement

Interface conditions for coupling the domains in a physically motivated domain decomposition method are discussed. The domain decomposition is based on an asymptotic-induced method for the numerical solution of hyperbolic conservation laws with small viscosity. The method consists of multiple stages. The first stage is to obtain a first approximation using a first-order method, such as the Godunov scheme. Subsequent stages of the method involve solving internal-layer problem via a domain decomposition. The method is derived and justified via singular perturbation techniques

Admissibility Region for Rarefaction Shock Waves in Dense Gases

In the vapour phase and close to the liquid–vapour saturation curve, fluids made of complex molecules are expected to exhibit a thermodynamic region in which the fundamental derivative of gasdynamic G is negative. In this region, non-classical gasdynamic phenomena such as rarefaction shock waves are physically admissible, namely they obey the second law of thermodynamics and fulfil the speed-orienting condition for mechanical stability. Previous studies have demonstrated that the thermodynamic states for which rarefaction shock waves are admissible are however not limited to the G <0 region. In this paper, the conditions for admissibility of rarefaction shocks are investigated. This results in the definition of a new thermodynamic region – the rarefaction shocks region – which embeds the G <0 region. The rarefaction shocks region is bounded by the saturation curve and by the locus of the states connecting double-sonic rarefaction shocks, i.e. shock waves in which both the pre-shock and post-shock states are sonic. Only one double-sonic shock is shown to be admissible along a given isentrope, therefore the double-sonic states can be connected by a single curve in the volume–pressure plane. This curve is named the double sonic locus. The influence of molecular complexity on the shape and size of the rarefaction shocks region is also illustrated by using the van der Waals model; these results are confirmed by very accurate multi-parameter thermodynamic models applied to siloxane fluids and are therefore of practical importance in experiments aimed at proving the existence of rarefaction shock waves in the single-phase vapour region as well as in future industrial applications operating in the non-classical regime

Some Gasdynamic Problems in the Flow of Condensing Vapors

Some Gasdynamic Problems in the Flow of Condensing Vapors. The general problem of the flow of a wet vapor, with or without an inert diluent is formulated under the assumption that the liquid phase is finely divided and dispersed throughout the gaseous component in droplets whose radii are nearly constant in any local region. The processes of momentum transfer, heat transfer between phases are assumed to take place according to Stokes law and Nusselt number of unity, respectively. The mass transfer process is treated as diffusion governed in the presence of an inert diluent and kinetic governed for two phases of a pure substance. The physical understanding of such problems, in contrast with those of conventional gas dynamics, rests largely in the role played by the relaxation times or equilibration lengths associated with these three processes. Consequently, both simple and coupled relaxation processes are examined rather carefully by specific examples. Subsequently, the problem of near-equilibrium flow in a nozzle with phase change is solved under the small-slip approximation. The structure of the normal shock in a pure substance is investigated and reveals three rather distinct zones: the gasdynamic shock, the vapor relaxation zone, and the thermal and velocity equilibration zone. The three-dimensional steady flow of the two-phase condensing continuum is formulated according to first order perturbation theory, and the structure of waves in such supersonic flow is examined. Finally, the attenuation of sound in fogs is formulated and solved accounting for the important effects of phase change as well as the viscous damping and heat transfer which have been included in previous analyses

Hybrid Entropy Stable HLL-Type Riemann Solvers for Hyperbolic Conservation Laws

It is known that HLL-type schemes are more dissipative than schemes based on characteristic decompositions. However, HLL-type methods offer greater flexibility to large systems of hyperbolic conservation laws because the eigenstructure of the flux Jacobian is not needed. We demonstrate in the present work that several HLL-type Riemann solvers are provably entropy stable. Further, we provide convex combinations of standard dissipation terms to create hybrid HLL-type methods that have less dissipation while retaining entropy stability. The decrease in dissipation is demonstrated for the ideal MHD equations with a numerical example.Comment: 6 page

Hydromagnetic waves - Theory and applications Scientific report

Magnetohydrodynamic wave influence on various physical phenomen

Gasdynamic shock waves

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