Non-strictly Hyperbolic Systems, Singularity and Bifurcation

Li, Xuefeng; Saxton, Katarzyna

doi:10.1007/s10915-014-9876-3

Cited by 2 publications

(2 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…systems with multiple eigenvalues, naturally arise in multi dimensions [15]. Specific cases of non-strictly hyperbolic systems where studied in [3,42,48] and recently by Freistühler and Pellhammer [25]. Subject of study in the aforementioned references are mostly systems of two equations where the coincidence of eigenvalues often occurred in points where also the character of the related field changes from genuinely nonlinear to linearly degenerated.…”

Section: Introductionmentioning

confidence: 99%

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

2022

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

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

2022

View full text Add to dashboard Cite

show abstract

“…systems with multiple eigenvalues, naturally arise in multi dimensions [15]. Specific cases of non-strictly hyperbolic systems where studied in [38,3,44] and recently by Freistühler and Pellhammer [24]. There mostly systems of two equations where studied and the coincidence of eigenvalues often occurred in points where also the character of the related field changed from genuine nonlinear to linearly degenerated.…”

Section: Introductionmentioning

confidence: 99%

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

Thein¹,

Romenski²,

Dumbser³

2022

Preprint

View full text Add to dashboard Cite

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.

show abstract

Non-strictly Hyperbolic Systems, Singularity and Bifurcation

Cited by 2 publications

References 7 publications

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

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

Contact Info

Product

Resources

About