Skip to main content
Erschienen in: Journal of Applied and Industrial Mathematics 4/2020

01.11.2020

Application of Geodesic Grids for Modeling the Hydrodynamic Processes in Spherical Objects

verfasst von: I. M. Kulikov, E. I. Vorobyov, I. G. Chernykh, V. G. Elbakyan

Erschienen in: Journal of Applied and Industrial Mathematics | Ausgabe 4/2020

Einloggen

Aktivieren Sie unsere intelligente Suche um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

We propose a new numerical method that bases on the mathematical apparatus of geodesic grids. This approach allows us to simulate spherical objects without any singularities that occur in using spherical or cylindrical coordinates. Solution of hyperbolic equations is described in detail. The method is expanded to solve the equations of hydrodynamics and tested on the Sedov point explosion problem. The numerical method and the approach to grid construction make it possible to compute a rotation invariant solution in Cartesian coordinates. This in turn allows us to use this approach effectively for simulating various spherical astrophysical objects.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat K. Kadam, E. Vorobyov, Z. Regaly, A. Kospal, and P. Abraham, “Dynamical Gaseous Rings in Global Simulations of Protoplanetary Disk Formation,” Astrophys. J. 882 (2), Article No. 96 (2019). K. Kadam, E. Vorobyov, Z. Regaly, A. Kospal, and P. Abraham, “Dynamical Gaseous Rings in Global Simulations of Protoplanetary Disk Formation,” Astrophys. J. 882 (2), Article No. 96 (2019).
2.
Zurück zum Zitat E. Akiyama, E. Vorobyov, Liu H. Baobabu, et al. “A Tail Structure Associated with a Protoplanetary Disk Around SU Aurigae,” Astron. J. 157 (4), Article No. 165 (2019). E. Akiyama, E. Vorobyov, Liu H. Baobabu, et al. “A Tail Structure Associated with a Protoplanetary Disk Around SU Aurigae,” Astron. J. 157 (4), Article No. 165 (2019).
3.
Zurück zum Zitat D. M. Meyer, E. I. Vorobyov, and V. G. Elbakyan, “Burst Occurrence in Young Massive Stellar Objects,” Monthly Not. Royal Astron. Soc. 482 (4), 5459–5476 (2019).CrossRef D. M. Meyer, E. I. Vorobyov, and V. G. Elbakyan, “Burst Occurrence in Young Massive Stellar Objects,” Monthly Not. Royal Astron. Soc. 482 (4), 5459–5476 (2019).CrossRef
4.
Zurück zum Zitat Z. Regaly and E. Vorobyov, “The Circumstellar Disk Response to the Motion of the Host Star,” Astronomy and Astrophys. 601, Article No. A24 (2017). Z. Regaly and E. Vorobyov, “The Circumstellar Disk Response to the Motion of the Host Star,” Astronomy and Astrophys. 601, Article No. A24 (2017).
5.
Zurück zum Zitat I. Baraffe, V. G. Elbakyan, E. I. Vorobyov, and G. Chabrier, “Self-Consistent Evolution of Accreting Low-Mass Stars and Brown Dwarfs,” Astronomy and Astrophys. 597, Article No. A19 (2017). I. Baraffe, V. G. Elbakyan, E. I. Vorobyov, and G. Chabrier, “Self-Consistent Evolution of Accreting Low-Mass Stars and Brown Dwarfs,” Astronomy and Astrophys. 597, Article No. A19 (2017).
6.
Zurück zum Zitat V. Vshivkov, G. Lazareva, A. Snytnikov, I. Kulikov, and A. Tutukov, “Hydrodynamical Code for Numerical Simulation of the Gas Components of Colliding Galaxies,” Astrophys. J. Suppl. Ser. 194 (2), Article No. 47 (2011). V. Vshivkov, G. Lazareva, A. Snytnikov, I. Kulikov, and A. Tutukov, “Hydrodynamical Code for Numerical Simulation of the Gas Components of Colliding Galaxies,” Astrophys. J. Suppl. Ser. 194 (2), Article No. 47 (2011).
7.
Zurück zum Zitat I. Kulikov, G. Lazareva, A. Snytnikov, and V. Vshivkov, “Supercomputer Simulation of an Astrophysical Object Collapse by the Fluids-in-Cell Method,” in Lecture Notes in Computer Science, Vol. 5698 (Elsevier, Heidelberg, 2009), pp. 414–422. I. Kulikov, G. Lazareva, A. Snytnikov, and V. Vshivkov, “Supercomputer Simulation of an Astrophysical Object Collapse by the Fluids-in-Cell Method,” in Lecture Notes in Computer Science, Vol. 5698 (Elsevier, Heidelberg, 2009), pp. 414–422.
8.
Zurück zum Zitat I. Kulikov, “The Numerical Modeling of the Collapse of Molecular Cloud on Adaptive Nested Mesh,” J. Phys. Conf. Ser. 1103, Article No. 012011 (2018). I. Kulikov, “The Numerical Modeling of the Collapse of Molecular Cloud on Adaptive Nested Mesh,” J. Phys. Conf. Ser. 1103, Article No. 012011 (2018).
9.
Zurück zum Zitat N. Ardeljan, G. Bisnovatyi-Kogan, and S. Moiseenko, “An Implicit Lagrangian Code for the Treatment of Nonstationary Problems in Rotating Astrophysical Bodies,” Astron. Astrophys. 115, 573–594 (1996). N. Ardeljan, G. Bisnovatyi-Kogan, and S. Moiseenko, “An Implicit Lagrangian Code for the Treatment of Nonstationary Problems in Rotating Astrophysical Bodies,” Astron. Astrophys. 115, 573–594 (1996).
10.
Zurück zum Zitat V. Springel, “E Pur Si Muove: Galilean-Invariant Cosmological Hydrodynamical Simulations on a Moving Mesh,” Monthly Not. Royal Astron. Soc. 401, 791–851 (2010).CrossRef V. Springel, “E Pur Si Muove: Galilean-Invariant Cosmological Hydrodynamical Simulations on a Moving Mesh,” Monthly Not. Royal Astron. Soc. 401, 791–851 (2010).CrossRef
11.
12.
Zurück zum Zitat P. Mocz, M. Vogelsberger, D. Sijacki, R. Pakmor, and L. Hernquist, “A Discontinuous Galerkin Method for Solving the Fluid and Magnetohydrodynamic Equations in Astrophysical Simulations,” Monthly Not. Royal Astron. Soc. 437 (1), 397–414 (2014).CrossRef P. Mocz, M. Vogelsberger, D. Sijacki, R. Pakmor, and L. Hernquist, “A Discontinuous Galerkin Method for Solving the Fluid and Magnetohydrodynamic Equations in Astrophysical Simulations,” Monthly Not. Royal Astron. Soc. 437 (1), 397–414 (2014).CrossRef
13.
Zurück zum Zitat K. Schaal et al. “Astrophysical Hydrodynamics with a High-Order Discontinuous Galerkin Scheme and Adaptive Mesh Refinement,” Monthly Not. Royal Astron. Soc. 453 (4), 4278–4300 (2015). K. Schaal et al. “Astrophysical Hydrodynamics with a High-Order Discontinuous Galerkin Scheme and Adaptive Mesh Refinement,” Monthly Not. Royal Astron. Soc. 453 (4), 4278–4300 (2015).
14.
Zurück zum Zitat J. Murphy and A. Burrows, “BETHE-Hydro: An Arbitrary Lagrangian-Eulerian Multidimensional Hydrodynamics Code for Astrophysical Simulations,” Astrophys. J. Suppl. Ser. 179, 209–241 (2008).CrossRef J. Murphy and A. Burrows, “BETHE-Hydro: An Arbitrary Lagrangian-Eulerian Multidimensional Hydrodynamics Code for Astrophysical Simulations,” Astrophys. J. Suppl. Ser. 179, 209–241 (2008).CrossRef
15.
Zurück zum Zitat P. Hopkins, “A New Class of Accurate, Mesh-Free Hydrodynamic Simulation Methods,” Monthly Not. Royal Astron. Soc. 450 (1), 53–110 (2015).CrossRef P. Hopkins, “A New Class of Accurate, Mesh-Free Hydrodynamic Simulation Methods,” Monthly Not. Royal Astron. Soc. 450 (1), 53–110 (2015).CrossRef
16.
Zurück zum Zitat B. Glinsky, I. Kulikov, I. Chernykh, et al. “The Co-Design of Astrophysical Code for Massively Parallel Supercomputers,” in Lecture Notes in Computer Science, Vol. 10049 (Elsevier, Heidelberg, 2016), pp. 342–353. B. Glinsky, I. Kulikov, I. Chernykh, et al. “The Co-Design of Astrophysical Code for Massively Parallel Supercomputers,” in Lecture Notes in Computer Science, Vol. 10049 (Elsevier, Heidelberg, 2016), pp. 342–353.
17.
Zurück zum Zitat I. Kulikov, I. Chernykh, B. Glinskiy, D. Weins, and A. Shmelev, “Astrophysics Simulation on RSC Massively Parallel Architecture,” in Proceedings—2015 IEEE/ACM 15th International Symposium on Cluster, Cloud, and Grid Computing, CCGrid 2015 , pp. 1131–1134. I. Kulikov, I. Chernykh, B. Glinskiy, D. Weins, and A. Shmelev, “Astrophysics Simulation on RSC Massively Parallel Architecture,” in Proceedings—2015 IEEE/ACM 15th International Symposium on Cluster, Cloud, and Grid Computing, CCGrid 2015 , pp. 1131–1134.
18.
Zurück zum Zitat D. Balsara, V. Florinski, S. Garain, S. Subramanian, and K. Gurski, “Efficient, Divergence-Free, High-Order MHD on 3D Spherical Meshes with Optimal Geodesic Meshing,” Monthly Not. Royal Astron. Soc. 487 (1), 1283–1314 (2019).CrossRef D. Balsara, V. Florinski, S. Garain, S. Subramanian, and K. Gurski, “Efficient, Divergence-Free, High-Order MHD on 3D Spherical Meshes with Optimal Geodesic Meshing,” Monthly Not. Royal Astron. Soc. 487 (1), 1283–1314 (2019).CrossRef
19.
Zurück zum Zitat I. Kulikov, “GPUPEGAS: A New GPU-Accelerated Hydrodynamic Code for Numerical Simulations of Interacting Galaxies,” Astrophys. J. Suppl. Ser. 214, Article No. 12 (2014). I. Kulikov, “GPUPEGAS: A New GPU-Accelerated Hydrodynamic Code for Numerical Simulations of Interacting Galaxies,” Astrophys. J. Suppl. Ser. 214, Article No. 12 (2014).
20.
Zurück zum Zitat I. M. Kulikov, I. G. Chernykh, A. V. Snytnikov, B. M. Glinskiy, and A. V. Tutukov, “AstroPhi: A Code for Complex Simulation of Dynamics of Astrophysical Objects Using Hybrid Supercomputers,” Comput. Phys. Comm. 186, 71–80 (2015).CrossRef I. M. Kulikov, I. G. Chernykh, A. V. Snytnikov, B. M. Glinskiy, and A. V. Tutukov, “AstroPhi: A Code for Complex Simulation of Dynamics of Astrophysical Objects Using Hybrid Supercomputers,” Comput. Phys. Comm. 186, 71–80 (2015).CrossRef
21.
Zurück zum Zitat I. M. Kulikov, I. G. Chernykh, B. M. Glinskiy, and V. A. Protasov, “An Efficient Optimization of the Hill Method for the Second Generation of Intel Xeon Phi Processor,” Lobachevskii J. Math. 39 (4), 543–551 (2018).MathSciNetCrossRef I. M. Kulikov, I. G. Chernykh, B. M. Glinskiy, and V. A. Protasov, “An Efficient Optimization of the Hill Method for the Second Generation of Intel Xeon Phi Processor,” Lobachevskii J. Math. 39 (4), 543–551 (2018).MathSciNetCrossRef
22.
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
23.
Zurück zum Zitat D. Balsara and D. Spicer, “Maintaining Pressure Positivity in Magnetohydrodynamic Simulations,” J. Comput. Phys. 148, 133–148 (1999).MathSciNetCrossRef D. Balsara and D. Spicer, “Maintaining Pressure Positivity in Magnetohydrodynamic Simulations,” J. Comput. Phys. 148, 133–148 (1999).MathSciNetCrossRef
24.
Zurück zum Zitat V. Springel and L. Hernquist, “Cosmological Smoothed Particle Hydrodynamics Simulations: The Entropy Equation,” Monthly Not. Royal Astron. Soc. 333, 649–664 (2002).CrossRef V. Springel and L. Hernquist, “Cosmological Smoothed Particle Hydrodynamics Simulations: The Entropy Equation,” Monthly Not. Royal Astron. Soc. 333, 649–664 (2002).CrossRef
25.
Zurück zum Zitat S. Godunov and I. Kulikov, “Computation of Discontinuous Solutions of Fluid Dynamics Equations with Entropy Nondecrease Guarantee,” Comput. Math. Math. Phys. 54, 1012–1024 (2014).MathSciNetCrossRef S. Godunov and I. Kulikov, “Computation of Discontinuous Solutions of Fluid Dynamics Equations with Entropy Nondecrease Guarantee,” Comput. Math. Math. Phys. 54, 1012–1024 (2014).MathSciNetCrossRef
26.
Zurück zum Zitat I. Kulikov, I. Chernykh, and A. Tutukov, “A New Hydrodynamic Code with Explicit Vectorization Instructions Optimizations, 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, 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).
27.
Zurück zum Zitat 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).MathSciNetCrossRef 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).MathSciNetCrossRef
Metadaten
Titel
Application of Geodesic Grids for Modeling the Hydrodynamic Processes in Spherical Objects
verfasst von
I. M. Kulikov
E. I. Vorobyov
I. G. Chernykh
V. G. Elbakyan
Publikationsdatum
01.11.2020
Verlag
Pleiades Publishing
Erschienen in
Journal of Applied and Industrial Mathematics / Ausgabe 4/2020
Print ISSN: 1990-4789
Elektronische ISSN: 1990-4797
DOI
https://doi.org/10.1134/S1990478920040067

Weitere Artikel der Ausgabe 4/2020

Journal of Applied and Industrial Mathematics 4/2020 Zur Ausgabe

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.