Sahadeb Kuila

@srmist.edu.in

Assistant Professor and Mathematics
SRM Institute of Science and Technology Kattankulathur

Sahadeb Kuila


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https://researchid.co/sahadeb

RESEARCH INTERESTS

Hyperbolic Conservation Laws
Fluid Dynamics
Shock Waves
Riemann Problem
18

Scopus Publications

263

Scholar Citations

9

Scholar h-index

9

Scholar i10-index

Scopus Publications

  • Collision between weak shock waves for a two-layer blood flow model
    M. Manikandan, M. Venkateshprasath, Sahadeb Kuila, T. Raja Sekhar
    Indian Journal of Pure and Applied Mathematics, 2026
  • Nonlinear wave interactions for a flux perturbed model in non-ideal gas dynamics
    Sumita Jana, Sahadeb Kuila
    Journal of Mathematical Physics, 2025
    This work explores the Riemann problem for a pressureless gas dynamics Cargo–LeRoux model with constant gravity governing a 3 by 3 system of conservation laws in the absence of external forces of Euler equations. Introducing flux perturbation of a van der Waals isothermal gas, the elementary waves of the Riemann problem are derived and establish the existence-uniqueness of the Riemann solution for arbitrary initial data locally. We develop a series of test cases to design these waves, where the Newton-Raphson method of two variables is used to determine the unknown densities. Moreover, the influence of van der Waals excluded volume on physical quantities such as density, potential, velocity and total pressure is analyzed and illustrated graphically using MATLAB. Finally, we extensively study the elementary wave interactions with and without involving contact discontinuity and the possible combination of waves is demonstrated thoroughly.
  • Riemann Problem for a Two-Lane Traffic Model in Dusty Gas Flow
    M. Manikandan, Sumita Jana, Sahadeb Kuila
    Mathematical Methods in the Applied Sciences, 2025
    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.
  • Riemann solutions and shock wave interactions for a two-velocity isentropic traffic flow
    M Venkateshprasath, Sahadeb Kuila
    Physica Scripta, 2025
    The study explores the Riemann problem and wave interactions for a two-lane two velocities traffic flow model with ideal isentropic pressure governing 3 × 3 system of hyperbolic conservation laws. Utilizing the method of characteristics, we construct the elementary waves, namely shock waves, rarefaction waves, and contact discontinuities of the Riemann problem in one-parameter family of curves. A condition for the existence of a unique solution is proved on arbitrary initial data which is not necessarily closed. Also, we establish a necessary and sufficient condition to determine whether a shock wave or a rarefaction wave exist of the solution in one-family and three-family of characteristic fields. Further, we analyze the combination of two shocks originating from the same family. Moreover, we solve the Riemann problem in a qualitative manner by considering the projections of the elementary waves in phase plane. At the end, the conditions on initial data are demonstrated to the waves structure of the Riemann problem along with the vacuum state.
  • Nonlinear wave interactions of the Riemann problem for a two-lane traffic flow model
    Sahadeb Kuila, Sumita Jana, T. Raja Sekhar
    Physics of Fluids, 2025
    In this work, we analyze all possible nonlinear wave interactions within a macroscopic traffic flow model for a two-lane system with a van der Waals gas pressure, two distinct velocities, and equal vehicle density in each lane. The Riemann solution is derived constructively by exploiting the characteristic analysis approach. Properties of possible elementary waves, namely, shock, rarefaction, and contact discontinuity waves, are thoroughly investigated. With respect to arbitrary initial data, we also prove that the exact solution to the Riemann problem uniquely exists. Furthermore, we explore in detail about the elementary wave interactions that occur between rarefaction and shock waves with and without involving contact discontinuity. At the end, following each wave interaction the global structure of the Riemann solution is explicitly established with an evident graphic illustration using MATHEMATICA software. Here, nonlinear wave interaction finds that the local solution of the initial value problem produces a unique result, where a shock wave can travel in the same direction or the opposite direction while a rarefaction wave also can be generated in either directions. Additionally, the contact discontinuity wave may or may not be developed following the interaction.
  • On the Riemann problem and interaction of elementary waves for two-layered blood flow model through arteries
    Sumita Jana, Sahadeb Kuila
    Mathematical Methods in the Applied Sciences, 2024
    In this paper, we focus on the Riemann problem for two‐layered blood flow model, which is represented by a system of quasi‐linear hyperbolic partial differential equations (PDEs) derived from the Euler equations by vertical averaging across each layer. We consider the Riemann problem with varying velocities and equal constant density through arteries. For instance, the flow layer close to the wall of vessel has a slower average speed than the layer far from the vessel because of the viscous effect of the blood vessel. We first establish the existence and uniqueness of the corresponding Riemann solution by a thorough investigation of the properties of elementary waves, namely, shock wave, rarefaction wave, and contact discontinuity wave. Further, we extensively analyze the elementary wave interaction between rarefaction wave and shock wave with contact discontinuity and rarefaction wave and shock wave. The global structure of the Riemann solutions after each wave interaction is explicitly constructed and graphically illustrated towards the end.
  • Riemann solutions of two-layered blood flow model in arteries
    Sumita Jana, Sahadeb Kuila
    International Journal of Non Linear Mechanics, 2023
  • Solution to the Riemann problem for drift-flux model with modified Chaplygin two-phase flows
    Dia Zeidan, Sumita Jana, Sahadeb Kuila, T. Raja Sekhar
    International Journal for Numerical Methods in Fluids, 2023
    Abstract In this paper, we concern about the Riemann problem for compressible no‐slip drift‐flux model which represents a system of quasi‐linear partial differential equations derived by averaging the mass and momentum conservation laws with modified Chaplygin two‐phase flows. We obtain the exact solution of Riemann problem by elaborately analyzing characteristic fields and discuss the elementary waves namely, shock wave, rarefaction wave and contact discontinuity wave. By employing the equality of pressure and velocity across the middle characteristic field, two nonlinear algebraic equations with two unknowns as gas density ahead and behind the middle wave are formed. The Newton–Raphson method of two variables is applied to find the unknowns with a series of initial data from the literature. Finally, the exact solution for the physical quantities such as gas density, liquid density, velocity, and pressure are illustrated graphically.
  • Exact solution of the flux perturbed Riemann problem for Cargo-LeRoux model in a van der Waals gas
    Sumita Jana, Sahadeb Kuila
    Chaos Solitons and Fractals, 2022
  • Weak shock wave interactions in isentropic Cargo-LeRoux model of flux perturbation
    Sahadeb Kuila, Dia Zeidan, T. Raja Sekhar
    Mathematical Methods in the Applied Sciences, 2022
    In this paper, we explore the weak shock wave interactions in isentropic Cargo‐LeRoux model of flux perturbation which describes strictly hyperbolic quasilinear system of conservation laws. For the Riemann problem, we provide a global existence and uniqueness result of exact solution. Further, we establish the exact solution explicitly in terms of one parameter family of elementary wave curves. We devise a necessary and sufficient condition on initial data for which the solution of the Riemann problem consists of either a shock wave or a simple wave according to one and three family of characteristic curves. Lastly, we analyze the Von Neumann result related to collision of weak shock waves of same family.
  • Interaction of weak shocks in drift-flux model of compressible two-phase flows
    S. Kuila, T. Raja Sekhar
    Chaos Solitons and Fractals, 2018
  • Wave Interactions in Non-ideal Isentropic Magnetogasdynamics
    Sahadeb Kuila, T. Raja Sekhar
    International Journal of Applied and Computational Mathematics, 2017
  • Solution to the Riemann problem for a five-equation model of multiphase flows in non-conservative form
    Sahadeb Kuila, T Raja Sekhar, G C Shit
    Sadhana Academy Proceedings in Engineering Sciences, 2016
  • The Riemann problem for non-ideal isentropic compressible two phase flows
    Sahadeb Kuila, T. Raja Sekhar, G.C. Shit
    International Journal of Non Linear Mechanics, 2016
  • Riemann solution for one dimensional non-ideal isentropic magnetogasdynamics
    Sahadeb Kuila, T. Raja Sekhar
    Computational and Applied Mathematics, 2016
  • On the Riemann Problem Simulation for the Drift-Flux Equations of Two-Phase Flows
    S. Kuila, T. Raja Sekhar, D. Zeidan
    International Journal of Computational Methods, 2016
  • A Robust and accurate Riemann solver for a compressible two-phase flow model
    Sahadeb Kuila, T. Raja Sekhar, D. Zeidan
    Applied Mathematics and Computation, 2015
  • Riemann solution for ideal isentropic magnetogasdynamics
    Sahadeb Kuila, T. Raja Sekhar
    Meccanica, 2014

RECENT SCHOLAR PUBLICATIONS

  • Collision between weak shock waves for a two-layer blood flow model: M. Manikandan et al.
    M Manikandan, M Venkateshprasath, S Kuila, T Raja Sekhar
    Indian Journal of Pure and Applied Mathematics 57 (2), 679-691 , 2026
    2026
  • Nonlinear wave interactions for a flux perturbed model in non-ideal gas dynamics
    S Jana, S Kuila
    Journal of Mathematical Physics 66 (10) , 2025
    2025
  • Riemann Problem for a Two‐Lane Traffic Model in Dusty Gas Flow
    M Manikandan, S Jana, S Kuila
    Mathematical Methods in the Applied Sciences 48 (12), 12463-12478 , 2025
    2025
    Citations: 2
  • Riemann solutions and shock wave interactions for a two-velocity isentropic traffic flow
    M Venkateshprasath, S Kuila
    Physica Scripta 100 (7), 075246 , 2025
    2025
    Citations: 1
  • Nonlinear wave interactions of the Riemann problem for a two-lane traffic flow model
    S Kuila, S Jana, T Raja Sekhar
    Physics of Fluids 37 (3) , 2025
    2025
    Citations: 3
  • On the Riemann problem and interaction of elementary waves for two‐layered blood flow model through arteries
    S Jana, S Kuila
    Mathematical Methods in the Applied Sciences 47 (1), 27-46 , 2024
    2024
    Citations: 4
  • Riemann solutions of two-layered blood flow model in arteries
    S Jana, S Kuila
    International Journal of Non-Linear Mechanics 156, 104485 , 2023
    2023
    Citations: 9
  • Solution to the Riemann problem for drift‐flux model with modified Chaplygin two‐phase flows
    D Zeidan, S Jana, S Kuila, TR Sekhar
    International Journal for Numerical Methods in Fluids 95 (2), 242-261 , 2023
    2023
    Citations: 26
  • Exact solution of the flux perturbed Riemann problem for Cargo-LeRoux model in a van der Waals gas
    S Jana, S Kuila
    Chaos, Solitons & Fractals 161, 112369 , 2022
    2022
    Citations: 12
  • Weak shock wave interactions in isentropic Cargo‐LeRoux model of flux perturbation
    S Kuila, D Zeidan, T Raja Sekhar
    Mathematical Methods in the Applied Sciences 45 (12), 7526-7537 , 2022
    2022
    Citations: 11
  • Interaction of weak shocks in drift-flux model of compressible two-phase flows
    S Kuila, TR Sekhar
    Chaos, Solitons & Fractals 107, 222-227 , 2018
    2018
    Citations: 22
  • Wave interactions in non-ideal isentropic magnetogasdynamics
    S Kuila, T Raja Sekhar
    International Journal of Applied and Computational Mathematics 3 (3), 1809-1831 , 2017
    2017
    Citations: 14
  • Solution to the Riemann problem for a five-equation model of multiphase flows in non-conservative form
    S Kuila, TR Sekhar, GC Shit
    Sādhanā 41 (9), 1099-1109 , 2016
    2016
    Citations: 2
  • The Riemann problem for non-ideal isentropic compressible two phase flows
    S Kuila, TR Sekhar, GC Shit
    International Journal of Non-Linear Mechanics 81, 197-206 , 2016
    2016
    Citations: 6
  • Riemann solution for one dimensional non-ideal isentropic magnetogasdynamics
    S Kuila, T Raja Sekhar
    Computational and Applied Mathematics 35 (1), 119-133 , 2016
    2016
    Citations: 22
  • On the Riemann problem simulation for the drift-flux equations of two-phase flows
    S Kuila, T Raja Sekhar, D Zeidan
    International Journal of Computational Methods 13 (01), 1650009 , 2016
    2016
    Citations: 49
  • A Robust and accurate Riemann solver for a compressible two-phase flow model
    S Kuila, TR Sekhar, D Zeidan
    Applied Mathematics and Computation 265, 681-695 , 2015
    2015
    Citations: 56
  • Riemann solution for ideal isentropic magnetogasdynamics
    S Kuila, TR Sekhar
    Meccanica 49 (10), 2453-2465 , 2014
    2014
    Citations: 24

MOST CITED SCHOLAR PUBLICATIONS

  • A Robust and accurate Riemann solver for a compressible two-phase flow model
    S Kuila, TR Sekhar, D Zeidan
    Applied Mathematics and Computation 265, 681-695 , 2015
    2015
    Citations: 56
  • On the Riemann problem simulation for the drift-flux equations of two-phase flows
    S Kuila, T Raja Sekhar, D Zeidan
    International Journal of Computational Methods 13 (01), 1650009 , 2016
    2016
    Citations: 49
  • Solution to the Riemann problem for drift‐flux model with modified Chaplygin two‐phase flows
    D Zeidan, S Jana, S Kuila, TR Sekhar
    International Journal for Numerical Methods in Fluids 95 (2), 242-261 , 2023
    2023
    Citations: 26
  • Riemann solution for ideal isentropic magnetogasdynamics
    S Kuila, TR Sekhar
    Meccanica 49 (10), 2453-2465 , 2014
    2014
    Citations: 24
  • Interaction of weak shocks in drift-flux model of compressible two-phase flows
    S Kuila, TR Sekhar
    Chaos, Solitons & Fractals 107, 222-227 , 2018
    2018
    Citations: 22
  • Riemann solution for one dimensional non-ideal isentropic magnetogasdynamics
    S Kuila, T Raja Sekhar
    Computational and Applied Mathematics 35 (1), 119-133 , 2016
    2016
    Citations: 22
  • Wave interactions in non-ideal isentropic magnetogasdynamics
    S Kuila, T Raja Sekhar
    International Journal of Applied and Computational Mathematics 3 (3), 1809-1831 , 2017
    2017
    Citations: 14
  • Exact solution of the flux perturbed Riemann problem for Cargo-LeRoux model in a van der Waals gas
    S Jana, S Kuila
    Chaos, Solitons & Fractals 161, 112369 , 2022
    2022
    Citations: 12
  • Weak shock wave interactions in isentropic Cargo‐LeRoux model of flux perturbation
    S Kuila, D Zeidan, T Raja Sekhar
    Mathematical Methods in the Applied Sciences 45 (12), 7526-7537 , 2022
    2022
    Citations: 11
  • Riemann solutions of two-layered blood flow model in arteries
    S Jana, S Kuila
    International Journal of Non-Linear Mechanics 156, 104485 , 2023
    2023
    Citations: 9
  • The Riemann problem for non-ideal isentropic compressible two phase flows
    S Kuila, TR Sekhar, GC Shit
    International Journal of Non-Linear Mechanics 81, 197-206 , 2016
    2016
    Citations: 6
  • On the Riemann problem and interaction of elementary waves for two‐layered blood flow model through arteries
    S Jana, S Kuila
    Mathematical Methods in the Applied Sciences 47 (1), 27-46 , 2024
    2024
    Citations: 4
  • Nonlinear wave interactions of the Riemann problem for a two-lane traffic flow model
    S Kuila, S Jana, T Raja Sekhar
    Physics of Fluids 37 (3) , 2025
    2025
    Citations: 3
  • Riemann Problem for a Two‐Lane Traffic Model in Dusty Gas Flow
    M Manikandan, S Jana, S Kuila
    Mathematical Methods in the Applied Sciences 48 (12), 12463-12478 , 2025
    2025
    Citations: 2
  • Solution to the Riemann problem for a five-equation model of multiphase flows in non-conservative form
    S Kuila, TR Sekhar, GC Shit
    Sādhanā 41 (9), 1099-1109 , 2016
    2016
    Citations: 2
  • Riemann solutions and shock wave interactions for a two-velocity isentropic traffic flow
    M Venkateshprasath, S Kuila
    Physica Scripta 100 (7), 075246 , 2025
    2025
    Citations: 1
  • Collision between weak shock waves for a two-layer blood flow model: M. Manikandan et al.
    M Manikandan, M Venkateshprasath, S Kuila, T Raja Sekhar
    Indian Journal of Pure and Applied Mathematics 57 (2), 679-691 , 2026
    2026
  • Nonlinear wave interactions for a flux perturbed model in non-ideal gas dynamics
    S Jana, S Kuila
    Journal of Mathematical Physics 66 (10) , 2025
    2025