Shock-Fitting Versus Shock-Capturing Modeling of Strong Shocks in Nonequilibrium Plasmas

Pepe, Raffaele; Bonfiglioli, Aldo; D’Angola, A.; Colonna, G.; Paciorri, Renato

doi:10.1109/tps.2014.2324493

Cited by 8 publications

(6 citation statements)

References 10 publications

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“…The correlation of γ 2 and T 2 , respectively plotted in figures 11(b) and 11(d), clearly shows the same hump located at the same place ( figure 17). Therefore, the hump is nothing other that the resonance of the dissociation of oxygen and nitrogen molecules in air in the range 3500−4500 K. This behaviour, due to the real gas effect resulting from air dissociation (γ 1 ≠ γ 2 ), points out the algorithmic complexity noticed in shock-fitting in argon flow (Pepe et al 2014). Moreover, we checked that this feature is present even in the non-magnetic case, and in the variation of γ 2 and ρ 2 /ρ 1 at constant χ 1 = 0 as the incident Mach number M 1 varies from 5 to 30.…”

Section: Discussionmentioning

confidence: 90%

“…Therefore, the analytic approach of the present paper, extending the classical Rankine−Hugoniot relations (Rankine 1870;Hugoniot 1889), opens a prospect towards MHD shock fitting as an alternative to the shock-capturing approach broadly used in the many numerical models published and in progress. The respective advantages and drawbacks of shock fitting over shock capturing have been recently pointed out in aerodynamic applications (Moretti 2002;Bonfiglioli & Paciorri 2010;Pepe et al 2014).…”

Section: Introductionmentioning

confidence: 99%

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Analytic model of a resistive magnetohydrodynamic shock without Hall effect

Berton

2018

J. Fluid Mech.

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An analytic model of a stationary hypersonic magnetohydrodynamic (MHD) shock with an externally applied magnetic field is proposed. Basically, original jump conditions at a plane oblique shock, analogous to the Rankine–Hugoniot formulae, with a moderately resistive air plasma downstream are derived. Viscous, thermal and Hall effects are neglected, but the plasma dissociation behind the shock causing a jump of isentropic exponent is also a major input of the model. Then, a shock-fitting procedure with ambient atmospheric conditions is worked out by the coupling of these MHD jumps with thermodynamic correlations and an electric conductivity model. For an application to atmospheric entry problems, the flow behind an axisymmetric blunt-body shock is modelled with a stream function satisfying these MHD jump conditions as boundary conditions. An important feature put into evidence is a similarity rule involving the hypersonic parameter$M_{1}\cos \unicode[STIX]{x1D712}_{1}$, which shows an aerodynamic correspondence between the upstream Mach number$M_{1}$and the velocity angle$\unicode[STIX]{x1D712}_{1}$. It also emerges that curvature effects become important past$30^{\circ }$and the assumption of a spherical shock also becomes untenable past$50^{\circ }$; therefore, we limit the model of shock thickness used in the MHD fitting to$\unicode[STIX]{x1D712}_{1}<50^{\circ }$.

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Section: Discussionmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Analytic model of a resistive magnetohydrodynamic shock without Hall effect

Berton

2018

J. Fluid Mech.

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“…An order-of-accuracy analysis of the steady, two-dimensional scheme has been conducted in [23] showing that shock-fitting allows to preserve the design order of the spatial discretization scheme within the entire shock-downstream region. The unstructured, shockfitting algorithm was also used to simulate real-gas effects in hypersonic, two-dimensional steady flows [24,25], whereas time-accurate simulations of two-dimensional, unsteady flows are reported in [26,27]. Finally, the technique has been recently used to simulate twodimensional, laminar and turbulent viscous flows featuring shock-wave/boundary-layer interactions [28].…”

Section: Introductionmentioning

confidence: 99%

UnDiFi-2D: an Unstructured Discontinuity Fitting code for 2D grids

Campoli,

Assonitis,

Ciallella

et al. 2021

Preprint

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UnDiFi-2D, an open source (free software) Unstructured-grid, Di scontinuity Fi tting code, is presented. The aim of UnDiFi-2D is to model gas-dynamic discontinuities in twodimensional (2D) flows as if they were true discontinuities of null thickness that bound regions of the flow-field where a smooth solution to the governing PDEs exists. UnDiFi-2D therefore needs to be coupled with an unstructured CFD solver that is used to discretize the governing PDEs within the smooth regions of the flow-field. Two different, in-house developed, CFD solvers are also included in the current distribution.The main features of the UnDiFi-2D software can be summarized as follows:Programming Language UnDiFi-2D is written in standard Fortran 77/95; its design is highly modular in order to enhance simplicity of use, maintenance and allow coupling with virtually any existing CFD solver;Usability, Maintenance and Enhancement In order to improve the usability, maintenance and enhancement of the code also the documentation has been carefully taken into account. The git distributed versioning system has been adopted to facilitate collaborative maintenance and code development;Copyrights UnDiFi-2D is a free software that anyone can use, copy, distribute, change and improve under the GNU Public License version 3.The present paper is a manifesto of the first public release of the UnDiFi-2D code. It describes the currently implemented features, which are the result of more than a decade of still ongoing CFD developments. This work is focused on the computational techniques adopted and a detailed description of the main characteristics is reported. UnDiFi-2D capabilities are demonstrated by means of examples test cases. The design of the code allows to easily include existing CFD codes and is aimed at ease code reuse and readability.

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“…Owing to the advantage of fast convergence, shock-capturing procedures are widely used in computational fluid dynamics (CFD), but they have the drawback of lesser accuracy [38]. Conversely, fitting procedures are more accurate, but they are also more time-consuming [33] [34] [43].…”

Section: Introductionmentioning

confidence: 99%

Analytic model of a plane resistive magnetohydrodynamic shock with Hall effect

Berton

2020

CEAS Space J

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In the present work, our formerly published analytical model of resistive magnetohydrodynamic (MHD) shock without Hall effect has been extended to include the Hall effect. Original jump conditions at a plane oblique shock, analogous to the Rankine-Hugoniot formulas, with a moderately resistive air plasma downstream are derived. Viscous and Ohmic dissipations are neglected, but the jump of isentropic exponent, caused by molecular dissociations behind the shock, is also included in the model. Then, for an application to atmospheric entry problems, a shock fitting procedure with realistic geometrical configurations and ambient conditions at two altitudes is worked out by the coupling of these MHD jumps with thermodynamic correlations at equilibrium and an electrical conductivity model. Fundamental features put into evidence are the reduction and saturation of the MHD interaction by the Hall effect as the magnetic field increases, and the crucial role played by the ion slip factor in the phenomenon. Paradoxically, the Hall effect arises because of the dominance of the magnetic field over collisions, and eventually it counters the MHD interaction. The validity of the assumption of plasma equilibrium and possible validation experiments for the flight conditions considered are also discussed.

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Shock-Fitting Versus Shock-Capturing Modeling of Strong Shocks in Nonequilibrium Plasmas

Cited by 8 publications

References 10 publications

Analytic model of a resistive magnetohydrodynamic shock without Hall effect

Analytic model of a resistive magnetohydrodynamic shock without Hall effect

UnDiFi-2D: an Unstructured Discontinuity Fitting code for 2D grids

Analytic model of a plane resistive magnetohydrodynamic shock with Hall effect

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