A New Rusanov-Type Solver with a Local Linear Solution Reconstruction for Numerical Modeling of White Dwarf Mergers by M
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A New Rusanov-Type Solver with a Local Linear Solution Reconstruction for Numerical Modeling of White Dwarf Mergers by Means Massive Parallel Supercomputers I. M. Kulikov1* , I. G. Chernykh1** , A. F. Sapetina1*** , S. V. Lomakin1**** , and A. V. Tutukov2***** (Submitted by Vl. V. Voevodin) 1
Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 630090 Russia 2 Institute of Astronomy Russian Academy of Sciences, Moscow, 119017 Russia Received February 29, 2020; revised April 16, 2020; accepted April 20, 2020
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. DOI: 10.1134/S1995080220080090 Keywords and phrases: computational astrophysics, hydrodynamics solver, high performance computing.
1. INTRODUCTION The Supernovae are major sources of “life” elements—from carbon to iron. Type Ia supernovae are very bright and, therefore, they are used as “standard candles” to determine distances to galaxies and the expansion rate of the Universe. Mathematical simulation of explosions of supernovas is a major tool in studying their dynamics and formation. The formation of complex flows in supernova explosions imposes rigid requirements on the spatial resolution of the simulation. A major scenario [1] of supernova explosion is based on the merging of two degenerate white dwarfs with subsequent collapse of the new star when it reaches the Chandrasekhar mass, ignition of the carbon burning process, and type Ia supernova explosion. *
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