A general existence result for isothermal two-phase flows with phase transition

Hantke, Maren; Thein, Ferdinand

doi:10.1142/s0219891619500206

Cited by 8 publications

(4 citation statements)

References 25 publications

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“…From (8), we may then obtain a kinetic relation depending on

(e.g., directly proportional) which has desired thermodynamic properties, cf. [ 4 , 16 ]. We want to emphasize that the previous results generalize the statements given in [ 6 ] in the case where a single set of equations, together with a kinetic relation, is used to describe the two-phase flow.…”

Section: Discussionmentioning

confidence: 99%

“…Moreover, due to the explicit character of the kinetic relation, it may be possible to construct exact solutions for Riemann initial data. For example, for the system of isothermal Euler equations equipped with a kinetic relation, exact solutions for Riemann problems were constructed by Hantke et al [ 4 , 5 ]. Also, existence and uniqueness of the solution was proven.…”

Section: Introductionmentioning

confidence: 99%

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On the Impossibility of First-Order Phase Transitions in Systems Modeled by the Full Euler Equations

Hantke

Thein

2019

Entropy

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Liquid-vapor flows exhibiting phase transition, including phase creation in single-phase flows, are of high interest in mathematics, as well as in the engineering sciences. In two preceding articles the authors showed on the one hand the capability of the isothermal Euler equations to describe such phenomena (Hantke and Thein, arXiv, 2017, arXiv:1703.09431). On the other hand they proved the nonexistence of certain phase creation phenomena in flows governed by the full system of Euler equations, see Hantke and Thein, Quart. Appl. Math. 2015, 73, 575-591. In this note, the authors close the gap for two-phase flows by showing that the two-phase flows considered are not possible when the flow is governed by the full Euler equations, together with the regular Rankine-Hugoniot conditions. The arguments rely on the fact that for (regular) fluids, the differences of the entropy and the enthalpy between the liquid and the vapor phase of a single substance have a strict sign below the critical point.

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“…From (8), we may then obtain a kinetic relation depending on

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Impossibility of First-Order Phase Transitions in Systems Modeled by the Full Euler Equations

Hantke

Thein

2019

Entropy

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“…In particular the inequality for the isothermal case is perfectly analogous to the one used in [37].…”

Section: Entropy Inequalitymentioning

confidence: 92%

Exact and Numerical Solutions of the Riemann Problem for a Conservative Model of Compressible Two-Phase Flows

2022

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In this work we study the solution of the Riemann problem for the barotropic version of the conservative symmetric hyperbolic and thermodynamically compatible (SHTC) two-phase flow model introduced in Romenski et al. (J Sci Comput 42(1):68, 2009, Quart Appl Math 65(2):259–279, 2007). All characteristic fields are carefully studied and explicit expressions are derived for the Riemann invariants and the Rankine–Hugoniot conditions. Due to the presence of multiple characteristics in the system under consideration, non-standard wave phenomena can occur. Therefore we briefly review admissibility conditions for discontinuities and then discuss possible wave interactions. In particular we will show that overlapping rarefaction waves are possible and moreover we may have shocks that lie inside a rarefaction wave. In contrast to nonconservative two phase flow models, such as the Baer–Nunziato system, we can use the advantage of the conservative form of the model under consideration. Furthermore, we show the relation between the considered conservative SHTC system and the corresponding barotropic version of the nonconservative Baer–Nunziato model. Additionally, we derive the reduced four equation Kapila system for the case of instantaneous relaxation, which is the common limit system of both, the conservative SHTC model and the non-conservative Baer–Nunziato model. Finally, we compare exact solutions of the Riemann problem with numerical results obtained for the conservative two-phase flow model under consideration, for the non-conservative Baer–Nunziato system and for the Kapila limit. The examples underline the previous analysis of the different wave phenomena, as well as differences and similarities of the three systems.

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“…In particular the inequality for the isothermal case is perfectly analogous to the one used in [34].…”

Section: Entropy Inequalitymentioning

confidence: 92%

Exact and numerical solutions of the Riemann problem for a conservative model of compressible two-phase flows

Thein¹,

Romenski²,

Dumbser³

2022

Preprint

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In this work we study the solution of the Riemann problem for the barotropic version of the conservative symmetric hyperbolic and thermodynamically compatible (SHTC) two-phase flow model introduced in [63,58]. All characteristic fields are carefully studied and explicit expressions are derived for the Riemann invariants and the Rankine-Hugoniot conditions. Due to the presence of multiple characteristics in the system under consideration, non-standard wave phenomena can occur. Therefore we briefly review admissibility conditions for discontinuities and then discuss possible wave interactions. In particular we will show that overlapping rarefaction waves are possible and moreover we may have shocks that lie inside a rarefaction wave. In contrast to nonconservative two phase flow models, such as the Baer-Nunziato system, we can use the advantage of the conservative form of the model under consideration. Furthermore, we show the relation between the considered conservative SHTC system and the corresponding barotropic version of the nonconservative Baer-Nunziato model. Additionally, we derive the reduced four equation Kapila system for the case of instantaneous relaxation, which is the common limit system of both, the conservative SHTC model and the non-conservative Baer-Nunziato model. Finally, we compare exact solutions of the Riemann problem with numerical results obtained for the conservative two-phase flow model under consideration, for the non-conservative Baer-Nunziato system and for the Kapila limit. The examples underline the previous analysis of the different wave phenomena, as well as differences and similarities of the three systems.

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A general existence result for isothermal two-phase flows with phase transition

Cited by 8 publications

References 25 publications

On the Impossibility of First-Order Phase Transitions in Systems Modeled by the Full Euler Equations

On the Impossibility of First-Order Phase Transitions in Systems Modeled by the Full Euler Equations

Exact and Numerical Solutions of the Riemann Problem for a Conservative Model of Compressible Two-Phase Flows

Exact and numerical solutions of the Riemann problem for a conservative model of compressible two-phase flows

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