Riemann Problem for a Two-Lane Traffic Model in Dusty Gas Flow
M. Manikandan
Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur, Tamil Nadu, India
Contribution: Writing - original draft, Methodology, Resources, Formal analysis, Validation, Investigation
Search for more papers by this authorSumita Jana
Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur, Tamil Nadu, India
Contribution: Writing - original draft, Conceptualization, Data curation, Resources, Formal analysis, Investigation, Software
Search for more papers by this authorCorresponding Author
Sahadeb Kuila
Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur, Tamil Nadu, India
Correspondence:
Sahadeb Kuila ([email protected])
Contribution: Writing - review & editing, Supervision, Project administration, Visualization, Investigation, Conceptualization
Search for more papers by this authorM. Manikandan
Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur, Tamil Nadu, India
Contribution: Writing - original draft, Methodology, Resources, Formal analysis, Validation, Investigation
Search for more papers by this authorSumita Jana
Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur, Tamil Nadu, India
Contribution: Writing - original draft, Conceptualization, Data curation, Resources, Formal analysis, Investigation, Software
Search for more papers by this authorCorresponding Author
Sahadeb Kuila
Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur, Tamil Nadu, India
Correspondence:
Sahadeb Kuila ([email protected])
Contribution: Writing - review & editing, Supervision, Project administration, Visualization, Investigation, Conceptualization
Search for more papers by this authorFunding: The authors received no specific funding for this work.
ABSTRACT
In this work, we deal with the Riemann solution for a 3 by 3 macroscopic two-lane traffic flow model of two distinct velocities and equal vehicle density in each lane, along with dust particles obeying the Mie–Grüneisen type equation of state. Based on the characteristic field analysis, we discuss the properties of rarefaction waves, shocks, and contact discontinuities elaborately. For every combination of elementary waves, we provide a solution strategy and derive the two nonlinear algebraic equations of two unknowns. Further, the existence-uniqueness of the Riemann solution is established locally for arbitrary initial data. Moreover, we apply the Newton–Raphson method for the nonlinear algebraic equations to obtain densities across the middle characteristic field. In the end, we have elaborately discussed the influence of the mass fraction and volume fraction of solid particles in physical quantities with a series of test cases.
Conflicts of Interest
The authors declare no conflicts of interest.
Open Research
Data Availability Statement
The data that support the findings of this study are available within the article.
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