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Using a Combination of Roe and Rusanov Schemes for the Numerical Solution of the Equations of Magnetohydrodynamics in the Problems of Cosmic Plasma

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Abstract

The paper describes a new numerical method for solving the equations of ideal magnetohydrodynamics (MHD) based on the Godunov method, a combination of the Roe and Rusanov schemes, and a piecewise parabolic representation of the solution. The hybrid scheme for solving the Riemann problem is associated with the possibility to reproduce the numerical solution without singularities along the directions, which is especially important when the velocity and magnetic field components are reconstructed in the transverse direction. The numerical method is implemented as a software package for massively parallel supercomputers. Studies of parallel implementation and computational experiments were carried out on the NKS-1P cluster of the SSCC. A problem with an analytical solution was used as a test for the method verification. A numerical solution of the problem of the interaction of a molecular hydrogen cloud with the oncoming interstellar medium is considered.

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REFERENCES

  1. A. Fletcher, R. Beck, A. Shukurov, E. Berkhuijsen, and C. Horellou, “Magnetic fields and spiral arms in the galaxy M51,” Mon. Not. R. Astron. Soc. 412 (4), 2396–2416 (2011).

    Article  Google Scholar 

  2. R. Pakmor and V. Springel, “Simulations of magnetic fields in isolated disc galaxies,” Mon. Not. R. Astron. Soc. 432 (1), 176–193 (2013).

    Article  Google Scholar 

  3. E. Villaver, A. Manchado, and G. Garcia-Segura, “The interaction of asymptotic giant branch stars with the interstellar medium,” Astrophys. J. 748 (2), 94 (2012).

    Article  Google Scholar 

  4. I. Kulikov, I. Chernykh, and V. Protasov, “The numerical modelling of MHD astrophysical flows with chemistry,” J. Phys: Conf. Ser. 894, 012132 (2017).

    Google Scholar 

  5. J. Stone et al., “Athena: A new code for astrophysical MHD,” Astrophys. J. Suppl. Ser. 178, 137–177 (2008).

  6. A. Brandenburg and W. Dobler, “Hydromagnetic turbulence in computer simulations,” Comput. Phys. Comm. 147, 471–475 (2002).

    Article  MATH  Google Scholar 

  7. J. Hayes et al., “Simulating radiating and magnetized flows in multiple dimensions with ZEUS-MP,” Astrophys. J. Suppl. Ser. 165, 188–228 (2006).

  8. I. Kulikov, “A new code for the numerical simulation of relativistic flows on supercomputers by means of a low-dissipation scheme,” Comput. Phys. Comm. 257, 107532 (2020).

    Article  MathSciNet  Google Scholar 

  9. I. Kulikov, I. Chernykh, and A. Tutukov, “A new hydrodynamic code with explicit vectorization instructions optimizations that is dedicated to the numerical simulation of astrophysical gas flow. I. Numerical method, tests, and model problems,” Astrophys. J. Suppl. Ser. 243, 4 (2019).

    Article  Google Scholar 

  10. I. Kulikov and E. Vorobyov, “Using the PPML approach for constructing a low-dissipation, operator-splitting scheme for numerical simulations of hydrodynamic flows,” J. Comput. Phys. 317, 318–346 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  11. H. Nishikawa and K. Kitamura, “Very simple, carbuncle-free, boundary-layer-resolving, rotated-hybrid Riemann solvers,” J. Comput. Phys. 227, 2560–2581 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  12. R. Keppens, “Nonlinear magnetohydrodynamics: numerical concepts,” Fusion Sci. Technol. 45 (2), 107–114 (2004).

    Article  Google Scholar 

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Funding

The work was carried out within the framework of the state order for the Institute of Computational Mathematics and Mathematical Geophysics of the Siberian Branch of the Russian Academy of Sciences, project no. 0251-2022-0005.

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Authors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    M. A. Boronina, I. M. Kulikov, I. G. Chernykh & D. V. Vins

Authors
  1. M. A. Boronina
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  2. I. M. Kulikov
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  3. I. G. Chernykh
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  4. D. V. Vins
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Corresponding authors

Correspondence to M. A. Boronina, I. M. Kulikov, I. G. Chernykh or D. V. Vins.

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Translated by V. Potapchouck

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Boronina, M.A., Kulikov, I.M., Chernykh, I.G. et al. Using a Combination of Roe and Rusanov Schemes for the Numerical Solution of the Equations of Magnetohydrodynamics in the Problems of Cosmic Plasma. J. Appl. Ind. Math. 16, 596–605 (2022). https://doi.org/10.1134/S1990478922040020

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  • DOI: https://doi.org/10.1134/S1990478922040020

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