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The modified Rusanov scheme for solving the phonon-Bose model

  • Kamel Mohamed und Mahmoud A. E. Abdelrahman EMAIL logo
Veröffentlicht/Copyright: 26. Mai 2022
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International Journal of Nonlinear Sciences and Numerical Simulation
Aus der Zeitschrift International Journal of Nonlinear Sciences and Numerical Simulation Band 24 Heft 8

Abstract

This paper considers the one-dimensional model of heat conduction in solids at low temperature, the so called phonon-Bose model. The nonlinear model consists of a conservation equation for the energy density e and the heat flux Q with ∣Q∣ < e. We present a simple and accurate class of finite volume schemes for numerical simulation of heat flow in arteries. This scheme consists of predictor and corrector steps, the predictor step contains a parameter of control of the numerical diffusion of the scheme, which modulate by using limiter theory and Riemann invariant, the corrector step recovers the balance conservation equation, the scheme can compute the numerical flux corresponding the real state of solution without relying on Riemann problem solvers and it can thus be turned to order 1 in the regions where the flow has a strong variation and to order 2 in the regions where the flow is regular. The numerical test cases demonstrate high resolution of the proposed finite volume scheme (modified Rusanov) and confirm its capability to provide accurate simulations for heat flow under flow regimes with strong shocks.

Keywords: conservation laws; entropy shocks; modified Rusanov scheme; phonon-Bose model; rarefaction waves; Riemann solutions
Mathematics Subject Classification (2010): 35L45; 35L65; 35L67; 76P05; 76M12; 80M12
Corresponding author: Mahmoud A. E. Abdelrahman, Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia; and Department of Mathematics, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt, E-mail:

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2021-07-26
Revised: 2022-04-09
Accepted: 2022-04-26
Published Online: 2022-05-26

© 2022 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. Original Research Articles
  3. Testing of logarithmic-law for the slip with friction boundary condition
  4. A new clique polynomial approach for fractional partial differential equations
  5. The modified Rusanov scheme for solving the phonon-Bose model
  6. Delta-shock for a class of strictly hyperbolic systems of conservation laws
  7. The Cădariu–Radu method for existence, uniqueness and Gauss Hypergeometric stability of a class of Ξ-Hilfer fractional differential equations
  8. Novel periodic and optical soliton solutions for Davey–Stewartson system by generalized Jacobi elliptic expansion method
  9. The simulation of two-dimensional plane problems using ordinary state-based peridynamics
  10. Reduced basis method for the nonlinear Poisson–Boltzmann equation regularized by the range-separated canonical tensor format
  11. Simulation of the crystallization processes by population balance model using a linear separation method
  12. PS and GW optimization of variable sliding gains mode control to stabilize a wind energy conversion system under the real wind in Adrar, Algeria
  13. Characteristics of internal flow of nozzle integrated with aircraft under transonic flow
  14. Magnetogasdynamic shock wave propagation using the method of group invariance in rotating medium with the flux of monochromatic radiation and azimuthal magnetic field
  15. The influence pulse-like near-field earthquakes on repairability index of reversible in mid-and short-rise buildings
  16. Intelligent controller for maximum power extraction of wind generation systems using ANN
  17. A new self-adaptive inertial CQ-algorithm for solving convex feasibility and monotone inclusion problems
  18. Existence and Hyers–Ulam stability of solutions for nonlinear three fractional sequential differential equations with nonlocal boundary conditions
  19. A study on solvability of the fourth-order nonlinear boundary value problems
  20. Adaptive control for position and force tracking of uncertain teleoperation with actuators saturation and asymmetric varying time delays
  21. Framing the hydrothermal significance of water-based hybrid nanofluid flow over a revolving disk
  22. Catalytic surface reaction on a vertical wavy surface placed in a non-Darcy porous medium
  23. Carleman framework filtering of nonlinear noisy phase-locked loop system
  24. Corrigendum
  25. Corrigendum to: numerical modeling of thermal influence to pollutant dispersion and dynamics of particles motion with various sizes in idealized street canyon
https://doi.org/10.1515/ijnsns-2021-0305
Schlagwörter für diesen Artikel
conservation laws; entropy shocks; modified Rusanov scheme; phonon-Bose model; rarefaction waves; Riemann solutions

Artikel in diesem Heft

  1. Frontmatter
  2. Original Research Articles
  3. Testing of logarithmic-law for the slip with friction boundary condition
  4. A new clique polynomial approach for fractional partial differential equations
  5. The modified Rusanov scheme for solving the phonon-Bose model
  6. Delta-shock for a class of strictly hyperbolic systems of conservation laws
  7. The Cădariu–Radu method for existence, uniqueness and Gauss Hypergeometric stability of a class of Ξ-Hilfer fractional differential equations
  8. Novel periodic and optical soliton solutions for Davey–Stewartson system by generalized Jacobi elliptic expansion method
  9. The simulation of two-dimensional plane problems using ordinary state-based peridynamics
  10. Reduced basis method for the nonlinear Poisson–Boltzmann equation regularized by the range-separated canonical tensor format
  11. Simulation of the crystallization processes by population balance model using a linear separation method
  12. PS and GW optimization of variable sliding gains mode control to stabilize a wind energy conversion system under the real wind in Adrar, Algeria
  13. Characteristics of internal flow of nozzle integrated with aircraft under transonic flow
  14. Magnetogasdynamic shock wave propagation using the method of group invariance in rotating medium with the flux of monochromatic radiation and azimuthal magnetic field
  15. The influence pulse-like near-field earthquakes on repairability index of reversible in mid-and short-rise buildings
  16. Intelligent controller for maximum power extraction of wind generation systems using ANN
  17. A new self-adaptive inertial CQ-algorithm for solving convex feasibility and monotone inclusion problems
  18. Existence and Hyers–Ulam stability of solutions for nonlinear three fractional sequential differential equations with nonlocal boundary conditions
  19. A study on solvability of the fourth-order nonlinear boundary value problems
  20. Adaptive control for position and force tracking of uncertain teleoperation with actuators saturation and asymmetric varying time delays
  21. Framing the hydrothermal significance of water-based hybrid nanofluid flow over a revolving disk
  22. Catalytic surface reaction on a vertical wavy surface placed in a non-Darcy porous medium
  23. Carleman framework filtering of nonlinear noisy phase-locked loop system
  24. Corrigendum
  25. Corrigendum to: numerical modeling of thermal influence to pollutant dispersion and dynamics of particles motion with various sizes in idealized street canyon
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