Abstract
The results of numerical modeling of white dwarf mergers on massive parallel supercomputers using a AVX-512 technique are presented. A hydrodynamic model of white dwarfs closed by a star equation of state and supplemented by a Poisson equation for the gravitational potential is constructed. This paper presents a modification based on a local linear reconstruction of the solution of the Rusanov scheme for the hydrodynamic equations. This reconstruction makes it possible to considerably decrease the numerical dissipation of the scheme for weak shock waves without any external piecewise polynomial reconstruction. The scheme is efficient for unstructured grids, when it is difficult to construct a piecewise polynomial solution, and also in parallel implementations of structured nested or adaptive grids, when the costs of interprocess interactions increase significantly. As input data, piecewise constant values of the physical variables in the left and right cells of a discontinuity are used. The smoothness of the solution is measured by the discrepancy between the maximum left and right eigenvalues. This discrepancy is used for a local piecewise polynomial reconstruction in the left and right cells. Then the solutions are integrated along the characteristics taking into account the piecewise linear representation of the physical variables. A performance of 234 gigaflops and 33-fold speedup are obtained on two Intel Skylake processors on the cluster NKS-1P of the Siberian Supercomputer Center ICM & MG SB RAS.
Similar content being viewed by others
REFERENCES
I. Iben and A. Tutukov, ‘‘On the evolution of close triple stars that produce type Ia supernovae,’’ Astrophys. J. 511, 324–334 (1999).
V. V. Rusanov, ‘‘The calculation of the interaction of non-stationary shock waves with barriers,’’ USSR Comput. Math. Math. Phys. 1, 304–320 (1962). https://doi.org/10.1016/0041-5553(62)90062-9
S. Chen, C. Yan, and X. Xiang, ‘‘Effective low-Mach number improvement for upwind schemes,’’ Comput. Math. Appl. 75, 3737–3755 (2018).
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).
M. Edwards, ‘‘The dominant wave-capturing flux: A finite-volume scheme without decomposition for systems of hyperbolic conservation laws,’’ J. Comput. Phys. 218, 275–294 (2006).
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).
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, 1207–1216 (2018).
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).
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).
M. H. Abbasi, S. Naderi Lordejani, N. Velmurugan, et al., ‘‘A Godunov-type scheme for the drift flux model with variable cross section,’’ J. Pet. Sci. Eng. 179, 796–813 (2019).
A. Alvarez Laguna, N. Ozak, A. Lani, H. Deconinck, and S. Poedts, ‘‘Fully-implicit finite volume method for the ideal two-fluid plasma model,’’ Comput. Phys. Commun. 231, 31–44 (2018).
X. Xu and X.-L. Deng, ‘‘An improved weakly compressible SPH method for simulating free surface flows of viscous and viscoelastic fluids,’’ Comput. Phys. Commun. 201, 43–62 (2016).
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).
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,’’ Comput. Phys. Commun. 239, 283–310 (2019).
H. Nishikawa and K. Kitamura, ‘‘Very simple, carbuncle-free, boundary-layer-resolving, rotated-hybrid Riemann solvers,’’ J. Comput. Phys. 227, 2560–2581 (2008).
M. Dumbser and D. Balsara, ‘‘A new efficient formulation of the HLLEM Riemann solver for general conservative and non-conservative hyperbolic systems,’’ J. Comput. Phys. 304, 275–319 (2016).
D. Balsara, J. Li, and G. Montecino, ‘‘An efficient, second order accurate, universal generalized Riemann problem solver based on the HLLI Riemann solver,’’ J. Comput. Phys. 375, 1238–1269 (2018).
F. X. Timmes and D. Arnett, ‘‘The accuracy, consistency, and speed of five equations of state for stellar hydrodynamics,’’ Astrophys. J. Suppl. Ser. 125, 277–294 (1999).
X. Deng, P. Boivin, and F. Xiao, ‘‘A new formulation for two-wave Riemann solver accurate at contact interfaces,’’ Phys. Fluids 31, 046102 (2019).
Funding
This work was supported by Russian Science Foundation (project no. 18-11-00044).
Author information
Authors and Affiliations
Corresponding authors
Additional information
(Submitted by Vl. V. Voevodin)
Rights and permissions
About this article
Cite this article
Kulikov, I.M., Chernykh, I.G., Sapetina, A.F. et al. A New Rusanov-Type Solver with a Local Linear Solution Reconstruction for Numerical Modeling of White Dwarf Mergers by Means Massive Parallel Supercomputers. Lobachevskii J Math 41, 1485–1491 (2020). https://doi.org/10.1134/S1995080220080090
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1995080220080090