Roe Linearization for the van der Waals Gas

Guardone, Alberto; Vigevano, Luigi

doi:10.1006/jcph.2001.6915

Cited by 53 publications

(61 citation statements)

References 30 publications

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“…It represents a powerful analytical model that allows thermodynamic phase change and therefore complex wave dynamics 1,12,28,30,33,39 .…”

Section: A the Van Der Waals Model For Dense Fluids Under The Influementioning

confidence: 99%

“…We consider three Riemann problems proposed for Euler equations in references 28,30 . The initial data for the dense gas are defined in the interval [0, 1] as two constant states at both sides of 0.5, u L (left) and u R (right).…”

Section: A the Van Der Waals Model For Dense Fluids Under The Influementioning

confidence: 99%

“…The analysis of the wave structure in the evolution of classical hydrodynamics described by Euler equations closed with a non-ideal EOS has been widely studied in the literature 1,13,14,[28][29][30][31][32] . It is well known that the structure and dynamics of waves are deter-mined by the properties of the material through a thermodynamic magnitude, the funda-…”

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confidence: 99%

“…The acoustic waves in classical hydrodynamics are genuinely nonlinear when the fundamental derivative is positive 12,30,33 . This implies that the only possible waves allowed in the solution are linear waves (contacts), compression shock waves and expansion fans.…”

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confidence: 99%

“…We illustrate our analytical approach considering the MHD system and two non-convex EOS that exhibit anomalous behavior. We analyze a van der Waals model that exhibits phase transition 28,30 and a Mie-Grüneisen type EOS 1,41,42 which is considered as representative of real liquids and solids for which the fundamental derivative changes sign. In both cases we analyze the structure and behavior of wave curves determined by the nonlinearity factor.…”

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confidence: 99%

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Anomalous wave structure in magnetized materials described by non-convex equations of state

Serna

Marquina

2014

Physics of Fluids

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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.

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“…It represents a powerful analytical model that allows thermodynamic phase change and therefore complex wave dynamics 1,12,28,30,33,39 .…”

Section: A the Van Der Waals Model For Dense Fluids Under The Influementioning

confidence: 99%

Section: A the Van Der Waals Model For Dense Fluids Under The Influementioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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confidence: 99%

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Anomalous wave structure in magnetized materials described by non-convex equations of state

Serna

Marquina

2014

Physics of Fluids

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Equivalence conditions between linear Lagrangian finite element and node‐centred finite volume schemes for conservation laws in cylindrical coordinates

Santis

Geraci

Guardone

2013

Numerical Methods in Fluids

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SUMMARYA complete set of equivalence conditions, relating the mass‐lumped Bubnov–Galerkin finite element (FE) scheme for Lagrangian linear elements to node‐centred finite volume (FV) schemes, is derived for the first time for conservation laws in a three‐dimensional cylindrical reference. Equivalence conditions are used to devise a class of FV schemes, in which all grid‐dependent quantities are defined in terms of FE integrals. Moreover, all relevant differential operators in the FV framework are consistent with their FE counterparts, thus opening the way to the development of consistent hybrid FV/FE schemes for conservation laws in a three‐dimensional cylindrical coordinate system. The two‐dimensional schemes for the polar and the axisymmetrical cases are also explicitly derived. Numerical experiments for compressible unsteady flows, including expanding and converging shock problems and the interaction of a converging shock waves with obstacles, are carried out using the new approach. The results agree fairly well with one‐dimensional simulations and simplified models. Copyright © 2013 John Wiley & Sons, Ltd.

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Roe‐type Riemann solvers for general hyperbolic systems

Castro

Toro

2014

Numerical Methods in Fluids

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SUMMARYWe present a Roe‐type weak formulation Riemann solver where the average coefficient matrix is computed numerically. The novelty of this approach is that it is general enough that can be applied to any hyperbolic system while retaining the accuracy of the original Roe solver. We show applications to the compressible Euler equations with general equation of state. An alternative version of the method uses directly the eigenvectors in the averaging process, simplifying the algorithm. These new solvers are applied in conservative and path‐conservative schemes with high‐order accuracy and on unstructured meshes. Copyright © 2014 John Wiley & Sons, Ltd.

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Roe Linearization for the van der Waals Gas

Cited by 53 publications

References 30 publications

Anomalous wave structure in magnetized materials described by non-convex equations of state

Anomalous wave structure in magnetized materials described by non-convex equations of state

Equivalence conditions between linear Lagrangian finite element and node‐centred finite volume schemes for conservation laws in cylindrical coordinates

Roe‐type Riemann solvers for general hyperbolic systems

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