A well-balanced finite volume scheme for the Euler equations with gravitation - The exact preservation of hydrostatic equilibrium with arbitrary entropy stratification
A well-balanced finite volume scheme for the Euler equations with gravitation - The exact preservation of hydrostatic equilibrium with arbitrary entropy stratification
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DOI：
10.1051/0004-6361/201527815
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发表时间：
2016-03
影响因子：
6.5
通讯作者：
R. Käppeli;Siddhartha Mishra
中科院分区：
文献类型：
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作者：
R. Käppeli;Siddhartha Mishra
上下文天体物理学中的许多问题都以接近流体静力平衡的流动为特征。然而，可压缩流体动力学的标准数值方案在近似这种静止状态时可能是有缺陷的，其中压力梯度几乎被重力平衡。目标。我们的目标是开发一个二阶的欧拉方程的平衡计划。该计划的目的是模仿一个离散版本的流体静力平衡。因此，它可以解决一个离散的流体静力平衡准确（机器精度）和传播扰动，在这个平衡的顶部，非常准确。方法.发展了局部二阶流体静力平衡保压重建方法。结合一个标准的中心引力源项离散和数值通量，解决静态接触不连续准确，实现了良好的平衡性能。结果所得到的平衡良好的计划是强大的，足够简单，可以很容易地实现在任何现有的计算机代码，解决时间显式或隐式的可压缩流体动力学方程。我们展示了几个天体物理学相关的应用程序的良好平衡的计划的性能：在恒星大气中的波传播，核心坍缩超新星的玩具模型，碳壳燃烧对流，和一个现实的原中子星星。
Context. Many problems in astrophysics feature flows which are close to hydrostatic equilibrium. However, standard numerical schemes for compressible hydrodynamics may be deficient in approximating this stationary state, where the pressure gradient is nearly balanced by gravitational forces. Aims. We aim to develop a second-order well-balanced scheme for the Euler equations. The scheme is designed to mimic a discrete version of the hydrostatic balance. It therefore can resolve a discrete hydrostatic equilibrium exactly (up to machine precision) and propagate perturbations, on top of this equilibrium, very accurately. Methods. A local second-order hydrostatic equilibrium preserving pressure reconstruction is developed. Combined with a standard central gravitational source term discretization and numerical fluxes that resolve stationary contact discontinuities exactly, the wellbalanced property is achieved. Results. The resulting well-balanced scheme is robust and simple enough to be very easily implemented within any existing computer code that solves time explicitly or implicitly the compressible hydrodynamics equations. We demonstrate the performance of the well-balanced scheme for several astrophysically relevant applications: wave propagation in stellar atmospheres, a toy model for core-collapse supernovae, convection in carbon shell burning, and a realistic proto-neutron star.