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首页> 外文期刊>Journal of Computational Physics >Second order symmetry-preserving conservative Lagrangian scheme for compressible Euler equations in two-dimensional cylindrical coordinates
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Second order symmetry-preserving conservative Lagrangian scheme for compressible Euler equations in two-dimensional cylindrical coordinates

机译：二维圆柱坐标系中可压缩欧拉方程的二阶保对称保守拉格朗日方案

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摘要

In applications such as astrophysics and inertial confinement fusion, there are many three-dimensional cylindrical-symmetric multi-material problems which are usually simulated by Lagrangian schemes in the two-dimensional cylindrical coordinates. For this type of simulation, a critical issue for the schemes is to keep spherical symmetry in the cylindrical coordinate system if the original physical problem has this symmetry. In the past decades, several Lagrangian schemes with such symmetry property have been developed, but all of them are only first order accurate. In this paper, we develop a second order cell-centered Lagrangian scheme for solving compressible Euler equations in cylindrical coordinates, based on the control volume discretizations, which is designed to have uniformly second order accuracy and capability to preserve one-dimensional spherical symmetry in a two-dimensional cylindrical geometry when computed on an equal-angle-zoned initial grid. The scheme maintains several good properties such as conservation for mass, momentum and total energy, and the geometric conservation law. Several two-dimensional numerical examples in cylindrical coordinates are presented to demonstrate the good performance of the scheme in terms of accuracy, symmetry, non-oscillation and robustness. The advantage of higher order accuracy is demonstrated in these examples.
机译：在诸如天体物理学和惯性约束聚变的应用中，存在许多三维圆柱对称多材料问题，这些问题通常是通过拉格朗日方案在二维圆柱坐标中模拟的。对于这种类型的仿真，方案的关键问题是，如果原始物理问题具有对称性，则在圆柱坐标系中保持球对称性。在过去的几十年中，已经开发出了几种具有这种对称性的拉格朗日方案，但是所有这些方案都是一阶精确的。在本文中，我们基于控制体积离散化，开发了一种用于解决圆柱坐标中可压缩Euler方程的二阶以细胞为中心的拉格朗日方案，该方案设计为具有均匀的二阶精度和保持一维球对称性的能力。在等角区域的初始网格上计算时的二维圆柱几何。该方案保留了几个良好的属性，例如质量，动量和总能量守恒，以及几何守恒律。给出了圆柱坐标系中的几个二维数值示例，以证明该方案在准确性，对称性，非振动性和鲁棒性方面的良好性能。这些示例演示了更高阶精度的优势。

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