Top

Journal of Applied and Industrial Mathematics

Published in:

01-11-2020

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

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

Published in: Journal of Applied and Industrial Mathematics | Issue 4/2020

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

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.

previous article On Invariant Surfaces in Gene Network Models

next article Numerical Methods for Constructing Suboptimal Packings of Nonconvex Domains with Curved Boundary

Dont have a licence yet? Then find out more about our products and how to get one now:

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!

inform now

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!

inform now

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).

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).

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

Z. Regaly and E. Vorobyov, “The Circumstellar Disk Response to the Motion of the Host Star,” Astronomy and Astrophys. 601, Article No. A24 (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).

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).

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, “The Numerical Modeling of the Collapse of Molecular Cloud on Adaptive Nested Mesh,” J. Phys. Conf. Ser. 1103, Article No. 012011 (2018).

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.

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.

S. Lloyd, “Least Squares Quantization in PCM,” IEEE Trans. Inform. Theory 28 (2), 129–137 (1982).MathSciNetCrossRef

12.

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.

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.

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.

P. Hopkins, “A New Class of Accurate, Mesh-Free Hydrodynamic Simulation Methods,” Monthly Not. Royal Astron. Soc. 450 (1), 53–110 (2015).CrossRef

16.

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.

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.

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.

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.

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.

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.

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.

D. Balsara and D. Spicer, “Maintaining Pressure Positivity in Magnetohydrodynamic Simulations,” J. Comput. Phys. 148, 133–148 (1999).MathSciNetCrossRef

24.

V. Springel and L. Hernquist, “Cosmological Smoothed Particle Hydrodynamics Simulations: The Entropy Equation,” Monthly Not. Royal Astron. Soc. 333, 649–664 (2002).CrossRef

25.

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.

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.

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

Title: Application of Geodesic Grids for Modeling the Hydrodynamic Processes in Spherical Objects
Authors: I. M. Kulikov
E. I. Vorobyov
I. G. Chernykh
V. G. Elbakyan
Publication date: 01-11-2020
Publisher: Pleiades Publishing
Published in: Journal of Applied and Industrial Mathematics / Issue 4/2020
Print ISSN: 1990-4789
Electronic ISSN: 1990-4797
DOI: https://doi.org/10.1134/S1990478920040067

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Other articles of this Issue 4/2020

A Maximum Dicut in a Digraph Induced by a Minimal Dominating Set

A Mathematical Model of Aseptic Inflammation Dynamics

Analytical Solutions to the Differential Equation of Transverse Vibrations of a Piecewise Homogeneous Beam in the Frequency Domain for the Boundary Conditions of Various Types

On Phase Correction in Tomographic Research

Estimating Nonlinearity Characteristics for Iterative Transformations of a Vector Space

On Integration of a Matrix Riccati Equation

Premium Partners