Integral-Consistent Numerical Technique for Self-gravitating Medium Model

机译：自重介质模型的整体一致数值技术

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The supercompression of matter caused by gravitational coupling or self-gravitational forces leads to density growth by several orders in magnitude. Keeping in mind the importance of self-gravitation in astrophysical processes like supernovae star evolution we consider it reasonable to develop a numerical technique based on the consistent approximation to the terms describing gravitational energy transfer into the kinetic energy of a matter in the star along its life cycle. The so-called completely conservative gas-dynamics difference schemes including the gravitation effects are the proper numerical technique able to simulate correctly the problems concerning gravitational coupling effects. The accounting for gravitational forces in the construction of completely conservative difference schemes is a significant complication. In the paper, we propose an integrally-consistent difference scheme that utilizes the method of support difference operators thus providing a possibility to conform the balance between kinetic and gravitational energy increments or losses. According to this method, we use the result of the total gravitational energy varying and construct the symmetrized strain rate tensor as the base operator. The result of varying the gravitational energy of the system is a discrete convolution of the Newton gravitational tensor in the difference media under study, which exhaustively answers all the gravitational processes unfolding against the background of the hydro-dynamic motion of matter. The symmetrized strain tensor governs the kinematic motion in a considered system. The conjugate operator related to the convolution of these tensors automatically gives the approximation to the gravitational forces acting in the interior of the balance volume of the difference model built via the support operator approach.

机译：由引力耦合或自引力引起的物质超压缩导致密度增长几个数量级。考虑到自引力在诸如超新星演化等天体过程中的重要性，我们认为有必要发展一种数值技术，该方法基于描述引力能量转换成物质沿其生命的动能的术语的一致近似周期。所谓的包括重力效应的完全保守的气体动力学差异方案是能够正确模拟与重力耦合效应有关的问题的适当数值技术。在构造完全保守的差分方案时考虑重力是一个很大的复杂性。在本文中，我们提出了一种整体一致的差分方案，该方案利用了支持差分算子的方法，从而提供了一种可能性，可以使动能和引力的能量增量或损失之间达到平衡。根据此方法，我们使用总重力能量变化的结果，并构造对称应变率张量作为基本算符。改变系统引力的结果是牛顿引力张量在所研究的差分介质中的离散卷积，它穷尽地回答了在物质的水动力运动背景下展开的所有引力过程。对称应变张量控制着所考虑系统中的运动。与这些张量的卷积相关的共轭算子会自动估算通过支持算子方法建立的差分模型的平衡体积内部所作用的重力。

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《Finite difference methods: theory and applications》|2018年|461-467|共7页
会议地点 Lozenetz(BG)
作者
Yu. S. Sharova; Yu. A. Poveshchenko; V. A. Gasilov; N. S. Smirnova; V. O. Podryga;
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作者单位

Keldysh Institute of Applied Mathematics of RAS, Moscow, Russia;

Keldysh Institute of Applied Mathematics of RAS, Moscow, Russia,National Research Nuclear University MEPhI, Moscow, Russia;

Keldysh Institute of Applied Mathematics of RAS, Moscow, Russia,National Research Nuclear University MEPhI, Moscow, Russia;

Laboratoire d'Annecy-le-Vieux de Physique Theorique, Annecy, France;

Keldysh Institute of Applied Mathematics of RAS, Moscow, Russia,Moscow Automobile and Road Construction State Technical University, Moscow, Russia;

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原文格式 PDF
正文语种 eng
中图分类
关键词
Self-gravitation; Mathematical modeling;

机译：自重；数学建模;

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Integral-Consistent Numerical Technique for Self-gravitating Medium Model

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