共移曲线坐标中的人工黏度:朝向几何上一致的微分隐式平流方案

Harald Höller, Antti Koskela, Ernst Dorfi, Werner Benger
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引用次数: 2

摘要

我们提出了一种修正的人工粘度张量,适用于一般运动的曲线网格。给出了研究恒星非线性脉动的辐射流体动力学方程的强守恒形式。然而,我们提出的修正是一般的数学性质。我们分析地研究了一个微分几何一致的人工粘度,并将我们的方法与以前的实现进行了可视化的比较,将其应用于一个简单的自相似速度场,该速度场在恒星中有直接应用,因为脉动的基本模式是径向的。本文首先对人工黏度作了一般性的介绍,并对其在数值计算中的应用进行了探讨。然后我们展示了当超越普通的静态欧拉或拉格朗日共同移动矩形网格时,如何设计人工粘度张量。我们推导并陈述了修正方程,其中包括调节人工粘度张量的各向同性(压力)部分的测量项。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

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Artificial viscosity in comoving curvilinear coordinates: towards a differential geometrically consistent implicit advection scheme

We propose a modification for the tensor of artificial viscosity employable for generally comoving, curvilinear grids. We present a strong conservation form for the equations of radiation hydrodynamics for studying nonlinear pulsations of stars. However, the modification we propose is of general mathematical nature. We study a differential geometrically consistent artificial viscosity analytically and visualize a comparison of our approach to previous implementations by applying it to a simple self-similar velocity field which has a direct application in stars as the fundamental mode of pulsation is radial. We first give a general introduction to artificial viscosity and motivate its application in numerical computations. We then show how a tensor of artificial viscosity has to be designed when going beyond common static Eulerian or Lagrangian comoving rectangular grids. We derive and state the modified equations which include metrical terms that adjust the isotropic (pressure) part of the tensor of artificial viscosity.

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期刊介绍: Computational Astrophysics and Cosmology (CompAC) is now closed and no longer accepting submissions. However, we would like to assure you that Springer will maintain an archive of all articles published in CompAC, ensuring their accessibility through SpringerLink's comprehensive search functionality.
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