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Erschienen in: Journal of Applied and Industrial Mathematics 3/2020

01.08.2020

On a Modification of the Rusanov Solver for the Equations of Special Relativistic Magnetic Hydrodynamics

verfasst von: I. M. Kulikov

Erschienen in: Journal of Applied and Industrial Mathematics | Ausgabe 3/2020

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Abstract

We describe the implementation of a modification of the Rusanov solver for the equations of special relativistic magnetic hydrodynamics. The particularity of the relativistic hydrodynamics equations, including a magnetic field, is a natural constraint on the admissible wave propagation velocity, which allows us to construct a fairly simple modification of the Rusanov solver using the maximum wave propagation velocity equal to the speed of light.

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Literatur
1.
Zurück zum Zitat P. Wang, T. Abel, and W. Zhang, “Relativistic Hydrodynamic Flows Using Spatial and Temporal Adaptive Structured Mesh Refinement,” Astrophys. J. Suppl. Ser.176, 467–483 (2008).CrossRef P. Wang, T. Abel, and W. Zhang, “Relativistic Hydrodynamic Flows Using Spatial and Temporal Adaptive Structured Mesh Refinement,” Astrophys. J. Suppl. Ser.176, 467–483 (2008).CrossRef
2.
Zurück zum Zitat H.-Y. Karen Yang and C. S. Reynolds, “How AGN Jets Heat the Intracluster Medium: Insights from Hydrodynamic Simulations,” Astrophys. J. 829, Article No 90 (2016). H.-Y. Karen Yang and C. S. Reynolds, “How AGN Jets Heat the Intracluster Medium: Insights from Hydrodynamic Simulations,” Astrophys. J. 829, Article No 90 (2016).
3.
Zurück zum Zitat S. Khoperskov, Yu. Venichenko, S. Khrapov, and E. Vasiliev, “High Performance Computing of Magnetized Galactic Disks,” Supercomputing Frontiers and Innovations 5, 103–106 (2018). S. Khoperskov, Yu. Venichenko, S. Khrapov, and E. Vasiliev, “High Performance Computing of Magnetized Galactic Disks,” Supercomputing Frontiers and Innovations 5, 103–106 (2018).
4.
Zurück zum Zitat V. Bosch-Ramon and D. Khangulyan, “Understanding the Very-High-Energy Emission from Microquasars,” Internat. J. Modern Physics D, 18 (3), 347–387 (2009).CrossRef V. Bosch-Ramon and D. Khangulyan, “Understanding the Very-High-Energy Emission from Microquasars,” Internat. J. Modern Physics D, 18 (3), 347–387 (2009).CrossRef
5.
Zurück zum Zitat C. M. Fromm, M. Perucho, P. Mimica, and E. Ros, “Spectral Evolution of Flaring Blazars from Numerical Simulations,” Astronomy and Astrophysics 588, Article No. A101 (2016). C. M. Fromm, M. Perucho, P. Mimica, and E. Ros, “Spectral Evolution of Flaring Blazars from Numerical Simulations,” Astronomy and Astrophysics 588, Article No. A101 (2016).
6.
Zurück zum Zitat A. Janiuk, K. Sapountzis, J. Mortier, and I. Janiuk, “Numerical Simulations of Black Hole Accretion Flows,” Supercomputing Frontiers and Innovations 5, 86–102 (2018). A. Janiuk, K. Sapountzis, J. Mortier, and I. Janiuk, “Numerical Simulations of Black Hole Accretion Flows,” Supercomputing Frontiers and Innovations 5, 86–102 (2018).
7.
Zurück zum Zitat H. Nagakura, H. Ito, K. Kiuchi, S. Yamada, “Jet Propagations, Breakouts, and Photospheric Emissions in Collapsing Massive Progenitors of Long-Duration Gamma-Ray Bursts,” Astrophys. J. 731, Article No. 80 (2011). H. Nagakura, H. Ito, K. Kiuchi, S. Yamada, “Jet Propagations, Breakouts, and Photospheric Emissions in Collapsing Massive Progenitors of Long-Duration Gamma-Ray Bursts,” Astrophys. J. 731, Article No. 80 (2011).
8.
Zurück zum Zitat P. Hughes, M. Miller, and G. Duncan, “Three-Dimensional Hydrodynamic Simulations of Relativistic Extragalactic Jets,” Astrophys. J. 572, 713–728 (2002).CrossRef P. Hughes, M. Miller, and G. Duncan, “Three-Dimensional Hydrodynamic Simulations of Relativistic Extragalactic Jets,” Astrophys. J. 572, 713–728 (2002).CrossRef
9.
Zurück zum Zitat H. Nagakura, K. Sumiyoshi, and S. Yamada, “Three-Dimensional Boltzmann Hydro Code for Core Collapse in Massive Stars. I. Special Relativistic Treatments,” Astrophys. J.Suppl. Ser. 214, Article No. 16 (2014). H. Nagakura, K. Sumiyoshi, and S. Yamada, “Three-Dimensional Boltzmann Hydro Code for Core Collapse in Massive Stars. I. Special Relativistic Treatments,” Astrophys. J.Suppl. Ser. 214, Article No. 16 (2014).
10.
Zurück zum Zitat E. O’Connor and C. Ott, “A New Open-Source Code for Spherically Symmetric Stellar Collapse to Neutron Stars and Black Holes,” Classical and Quantum Gravity27, Article No. 114103 (2010). E. O’Connor and C. Ott, “A New Open-Source Code for Spherically Symmetric Stellar Collapse to Neutron Stars and Black Holes,” Classical and Quantum Gravity27, Article No. 114103 (2010).
11.
Zurück zum Zitat S. Komissarov, “Electrodynamics of Black Hole Magnetospheres,” Monthly Notices Royal Astronom. Soc. 350 (2), 427–448 (2004).CrossRef S. Komissarov, “Electrodynamics of Black Hole Magnetospheres,” Monthly Notices Royal Astronom. Soc. 350 (2), 427–448 (2004).CrossRef
12.
Zurück zum Zitat S. Komissarov, “Observations of the Blandford–Znajek Process and the Magnetohydrodynamic Penrose Process in Computer Simulations of Black Hole Magnetospheres,” Monthly Notices Royal Astronom. Soc. 359 (3), 801–808 (2005).CrossRef S. Komissarov, “Observations of the Blandford–Znajek Process and the Magnetohydrodynamic Penrose Process in Computer Simulations of Black Hole Magnetospheres,” Monthly Notices Royal Astronom. Soc. 359 (3), 801–808 (2005).CrossRef
13.
Zurück zum Zitat C. Palenzuela, T. Garrett, L. Lehner, and S. Liebling, “Magnetospheres of Black Hole Systems in Force-Free Plasma,” Physics Review D, 82, Article No. 044045 (2010). C. Palenzuela, T. Garrett, L. Lehner, and S. Liebling, “Magnetospheres of Black Hole Systems in Force-Free Plasma,” Physics Review D, 82, Article No. 044045 (2010).
14.
Zurück zum Zitat C. Palenzuela, C. Bona, L. Lehner, and O. Reula, “Robustness of the Blandford–Znajek Mechanism,” Classical and Quantum Gravity 28, Article No. 4007 (2011). C. Palenzuela, C. Bona, L. Lehner, and O. Reula, “Robustness of the Blandford–Znajek Mechanism,” Classical and Quantum Gravity 28, Article No. 4007 (2011).
15.
Zurück zum Zitat C. Palenzuela, L. Lehner, and S. Liebling, “Dual Jets from Binary Black Holes,” Science 329, 927–930 (2010).CrossRef C. Palenzuela, L. Lehner, and S. Liebling, “Dual Jets from Binary Black Holes,” Science 329, 927–930 (2010).CrossRef
16.
Zurück zum Zitat S. Komissarov, “Simulations of the Axisymmetric Magnetospheres of Neutron Stars,” Monthly Notices Royal Astronom. Soc. 367 (1), 19–31 (2006).CrossRef S. Komissarov, “Simulations of the Axisymmetric Magnetospheres of Neutron Stars,” Monthly Notices Royal Astronom. Soc. 367 (1), 19–31 (2006).CrossRef
17.
Zurück zum Zitat M. D. Duez, Y. T. Liu, S. L. Shapiro, M. Shibata, and B.C. Stephens, “Collapse of Magnetized Hypermassive Neutron Stars in General Relativity,” Phys. Review Lett.96, Article No. 031101 (2006). M. D. Duez, Y. T. Liu, S. L. Shapiro, M. Shibata, and B.C. Stephens, “Collapse of Magnetized Hypermassive Neutron Stars in General Relativity,” Phys. Review Lett.96, Article No. 031101 (2006).
18.
Zurück zum Zitat M. D. Duez , Y. T. Liu, S. L. Shapiro, M. Shibata, and B. C. Stephens, “Evolution of Magnetized, Differentially Rotating Neutron Stars: Simulations in Full General Relativity,” Phys. Review D, 73, Article No. 104015 (2006). M. D. Duez , Y. T. Liu, S. L. Shapiro, M. Shibata, and B. C. Stephens, “Evolution of Magnetized, Differentially Rotating Neutron Stars: Simulations in Full General Relativity,” Phys. Review D, 73, Article No. 104015 (2006).
19.
Zurück zum Zitat M. Shibata, M. D. Duez, Y. T. Liu, S. L. Shapiro, and B. C. Stephens, “Magnetized Hypermassive Neutron-Star Collapse: A Central Engine for Short Gamma-Ray Bursts,” Phys. Review Lett. 96, Article No. 031102 (2006). M. Shibata, M. D. Duez, Y. T. Liu, S. L. Shapiro, and B. C. Stephens, “Magnetized Hypermassive Neutron-Star Collapse: A Central Engine for Short Gamma-Ray Bursts,” Phys. Review Lett. 96, Article No. 031102 (2006).
20.
Zurück zum Zitat T. Marsh, et al., “A Radio-Pulsing White Dwarf Binary Star,” Nature537, 374–377 (2016).CrossRef T. Marsh, et al., “A Radio-Pulsing White Dwarf Binary Star,” Nature537, 374–377 (2016).CrossRef
21.
Zurück zum Zitat M. Coleman Miller and N. Yunes, “The New Frontier of Gravitational Waves,” Nature 568, 469–476 (2019).CrossRef M. Coleman Miller and N. Yunes, “The New Frontier of Gravitational Waves,” Nature 568, 469–476 (2019).CrossRef
22.
Zurück zum Zitat F. Lora-Clavijo, A. Cruz-Osorio, and F. Guzman, “CAFE: A New Relativistic MHD Code,” Astrophys. J. Suppl. Ser. 218 (2), Article No. 24 (2015). F. Lora-Clavijo, A. Cruz-Osorio, and F. Guzman, “CAFE: A New Relativistic MHD Code,” Astrophys. J. Suppl. Ser. 218 (2), Article No. 24 (2015).
23.
Zurück zum Zitat J. Stone, et al., “Athena: A New Code for Astrophysical MHD,” Astrophys. J. Suppl. Ser. 178, 137–177 (2008).CrossRef J. Stone, et al., “Athena: A New Code for Astrophysical MHD,” Astrophys. J. Suppl. Ser. 178, 137–177 (2008).CrossRef
24.
Zurück zum Zitat Z. Etienne, M. Wan, M. Babiuc, S. McWilliams, and A. Choudhary, “GiRaFFE: An Open-Source General Relativistic Force-Free Electrodynamics Code,” Classical and Quantum Gravity 34, Article No. 215001 (2017). Z. Etienne, M. Wan, M. Babiuc, S. McWilliams, and A. Choudhary, “GiRaFFE: An Open-Source General Relativistic Force-Free Electrodynamics Code,” Classical and Quantum Gravity 34, Article No. 215001 (2017).
25.
Zurück zum Zitat Z. Etienne, V. Paschalidis, R. Haas, P. Mosta, and S. Shapiro, “IllinoisGRMHD: An Open-Source, User-Friendly GRMHD Code for Dynamical Spacetimes,” Classical and Quantum Gravity 32, Article No. 175009 (2015). Z. Etienne, V. Paschalidis, R. Haas, P. Mosta, and S. Shapiro, “IllinoisGRMHD: An Open-Source, User-Friendly GRMHD Code for Dynamical Spacetimes,” Classical and Quantum Gravity 32, Article No. 175009 (2015).
26.
Zurück zum Zitat M. Rempel, “Extension of the MURAM Radiative MHD Code for Coronal Simulations,” Astrophys. J. 834, Article No. 10 (2017). M. Rempel, “Extension of the MURAM Radiative MHD Code for Coronal Simulations,” Astrophys. J. 834, Article No. 10 (2017).
27.
Zurück zum Zitat B. Giacomazzo and L. Rezzolla, “WhiskyMHD: A New Numerical Code for General Relativistic Magnetohydrodynamics,” Classical and Quantum Gravity 24, Article No. S235 (2007). B. Giacomazzo and L. Rezzolla, “WhiskyMHD: A New Numerical Code for General Relativistic Magnetohydrodynamics,” Classical and Quantum Gravity 24, Article No. S235 (2007).
28.
Zurück zum Zitat V. V. Rusanov, “The Calculation of the Interaction of Nonstationary Shock Waves with Barriers,” Comput. Math. Math. Phys. 1, 267–279 (1961). V. V. Rusanov, “The Calculation of the Interaction of Nonstationary Shock Waves with Barriers,” Comput. Math. Math. Phys. 1, 267–279 (1961).
29.
Zurück zum Zitat S. Chen, C. Yan, and X. Xiang, “Effective Low-Mach Number Improvement for Upwind Schemes,” Computers and Math. with Appl. 75 (10), 3737–3755 (2018).MathSciNetCrossRef S. Chen, C. Yan, and X. Xiang, “Effective Low-Mach Number Improvement for Upwind Schemes,” Computers and Math. with Appl. 75 (10), 3737–3755 (2018).MathSciNetCrossRef
30.
Zurück zum Zitat T. Ohwada, Y. Shibata, T. Kato, and T. Nakamura, “A Simple, Robust and Efficient High-Order Accurate Shock-Capturing Scheme for Compressible Flows: Towards Minimalism,” J. Comput. Phys. 362, 131–162 (2018).MathSciNetCrossRef T. Ohwada, Y. Shibata, T. Kato, and T. Nakamura, “A Simple, Robust and Efficient High-Order Accurate Shock-Capturing Scheme for Compressible Flows: Towards Minimalism,” J. Comput. Phys. 362, 131–162 (2018).MathSciNetCrossRef
31.
Zurück zum Zitat M. Edwards, “The Dominant Wave-Capturing Flux: A Finite-Volume Scheme Without Decomposition for Systems of Hyperbolic Conservation Laws,” J. Comput. Phys.218 (1), 275–294 (2006).MathSciNetCrossRef M. Edwards, “The Dominant Wave-Capturing Flux: A Finite-Volume Scheme Without Decomposition for Systems of Hyperbolic Conservation Laws,” J. Comput. Phys.218 (1), 275–294 (2006).MathSciNetCrossRef
32.
Zurück zum Zitat 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, Article No. 4 (2019). 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, Article No. 4 (2019).
33.
Zurück zum Zitat I. M. Kulikov, I. G. Chernykh, and A. V. Tutukov, “A New Parallel Intel Xeon Phi Hydrodynamics Code for Massively Parallel Supercomputers ,” Lobachevskii J. Math.39 (9), 1207–1216 (2018).MathSciNetCrossRef I. M. Kulikov, I. G. Chernykh, and A. V. Tutukov, “A New Parallel Intel Xeon Phi Hydrodynamics Code for Massively Parallel Supercomputers ,” Lobachevskii J. Math.39 (9), 1207–1216 (2018).MathSciNetCrossRef
34.
Zurück zum Zitat Z. Huang, G. Toth, B. der Holst, Y. Chen, and T. Gombosi, “A Six-Moment Multi-Fluid Plasma Model,” J. Comput. Phys. 387, 134–153 (2019).MathSciNetCrossRef Z. Huang, G. Toth, B. der Holst, Y. Chen, and T. Gombosi, “A Six-Moment Multi-Fluid Plasma Model,” J. Comput. Phys. 387, 134–153 (2019).MathSciNetCrossRef
35.
Zurück zum Zitat F. Coquel, J.-M. Herard, and K. Saleh, “A Positive and Entropy-Satisfying Finite Volume Scheme for the Baer–Nunziato Model,” J. Comput. Phys. 330, 401–435 (2017).MathSciNetCrossRef F. Coquel, J.-M. Herard, and K. Saleh, “A Positive and Entropy-Satisfying Finite Volume Scheme for the Baer–Nunziato Model,” J. Comput. Phys. 330, 401–435 (2017).MathSciNetCrossRef
36.
Zurück zum Zitat M. H. Abbasi, S. Naderi Lordejani, N. Velmurugan, et al., “A Godunov-Type Scheme for the Drift Flux Model with Variable Cross Section,” J. Petroleum Science and Engineering. 179, 796–813 (2019).CrossRef M. H. Abbasi, S. Naderi Lordejani, N. Velmurugan, et al., “A Godunov-Type Scheme for the Drift Flux Model with Variable Cross Section,” J. Petroleum Science and Engineering. 179, 796–813 (2019).CrossRef
37.
Zurück zum Zitat A. Alvarez Laguna, N. Ozak, A. Lani, H. Deconinck, and S. Poedts, “Fully-Implicit Finite Volume Method for the Ideal Two-Fluid Plasma Model,” Computer Physics Communications 231, 31–44 (2018).MathSciNetCrossRef A. Alvarez Laguna, N. Ozak, A. Lani, H. Deconinck, and S. Poedts, “Fully-Implicit Finite Volume Method for the Ideal Two-Fluid Plasma Model,” Computer Physics Communications 231, 31–44 (2018).MathSciNetCrossRef
38.
Zurück zum Zitat X. Xu and X.-L. Deng, “An Improved Weakly Compressible SPH Method for Simulating Free Surface Flows of Viscous and Viscoelastic Fluids,” Computer Physics Communications 201, 43–62 (2016).MathSciNetCrossRef X. Xu and X.-L. Deng, “An Improved Weakly Compressible SPH Method for Simulating Free Surface Flows of Viscous and Viscoelastic Fluids,” Computer Physics Communications 201, 43–62 (2016).MathSciNetCrossRef
39.
Zurück zum Zitat X. Xu and Yu. Peng, “Modeling and Simulation of Injection Molding Process of Polymer Melt by a Robust SPH Method,” Appl. Math. Model. 48, 384–409 (2017).MathSciNetCrossRef X. Xu and Yu. Peng, “Modeling and Simulation of Injection Molding Process of Polymer Melt by a Robust SPH Method,” Appl. Math. Model. 48, 384–409 (2017).MathSciNetCrossRef
40.
Zurück zum Zitat T.-R. Teschner, L. Konozsy, and K. Jenkins, “A Generalised and Low-Dissipative Multi-Directional Characteristics-Based Scheme with Inclusion of the Local Riemann Problem Investigating Incompressible Flows without Free-Surfaces,” Computer Physics Communications 239, 283–310 (2019).CrossRef T.-R. Teschner, L. Konozsy, and K. Jenkins, “A Generalised and Low-Dissipative Multi-Directional Characteristics-Based Scheme with Inclusion of the Local Riemann Problem Investigating Incompressible Flows without Free-Surfaces,” Computer Physics Communications 239, 283–310 (2019).CrossRef
41.
Zurück zum Zitat H. Nishikawa and K. Kitamura, “Very Simple, Carbuncle-Free, Boundary-Layer-Resolving, Rotated-Hybrid Riemann Solvers,” J. Comput. Phys. 227 (4), 2560–2581 (2008).MathSciNetCrossRef H. Nishikawa and K. Kitamura, “Very Simple, Carbuncle-Free, Boundary-Layer-Resolving, Rotated-Hybrid Riemann Solvers,” J. Comput. Phys. 227 (4), 2560–2581 (2008).MathSciNetCrossRef
42.
Zurück zum Zitat M. Dumbser and D. Balsara, “A New Efficient Formulation of the HLLEM Riemann Solver for General Conservative and Nonconservative Hyperbolic Systems,” J. Comput. Phys. 304, 275–319 (2016).MathSciNetCrossRef M. Dumbser and D. Balsara, “A New Efficient Formulation of the HLLEM Riemann Solver for General Conservative and Nonconservative Hyperbolic Systems,” J. Comput. Phys. 304, 275–319 (2016).MathSciNetCrossRef
43.
Zurück zum Zitat D. Balsara, J. Li, and O. Montecino, “An Efficient, Second Order Accurate, Universal Generalized Riemann Problem Solver Based on the HLLI Riemann Solver,” J. Comput. Phys. 375, 1238–1269 (2018).MathSciNetCrossRef D. Balsara, J. Li, and O. Montecino, “An Efficient, Second Order Accurate, Universal Generalized Riemann Problem Solver Based on the HLLI Riemann Solver,” J. Comput. Phys. 375, 1238–1269 (2018).MathSciNetCrossRef
Metadaten
Titel
On a Modification of the Rusanov Solver for the Equations of Special Relativistic Magnetic Hydrodynamics
verfasst von
I. M. Kulikov
Publikationsdatum
01.08.2020
Verlag
Pleiades Publishing
Erschienen in
Journal of Applied and Industrial Mathematics / Ausgabe 3/2020
Print ISSN: 1990-4789
Elektronische ISSN: 1990-4797
DOI
https://doi.org/10.1134/S1990478920030114

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