Rayleigh-Taylor instability is a classical hydrodynamic instability of great interest in various disciplines of science and engineering, including astrophyics, atmospheric sciences and climate, geophysics, and fusion energy. Analytical methods cannot be applied to explain the long-time behavior of Rayleigh-Taylor instability, and therefore numerical simulation of the full problem is required. However, in order to capture the growth of amplitude of perturbations accurately, both the spatial and temporal discretization need to be extremely fine for traditional numerical methods, and the long-time simulation may become prohibitively expensive. In this paper, we propose efficient reduced order model techniques to accelerate the simulation of Rayleigh-Taylor instability in compressible gas dynamics. We introduce a general framework for decomposing the solution manifold to construct the temporal domain partition and temporally-local reduced order model construction with varying Atwood number. We propose two practical approaches in this framework, namely decomposition by using physical time and penetration distance respectively. Numerical results are presented to examine the performance of the proposed approaches.
翻译:Rayleigh-Taylor不稳定是一个古老的流体动力不稳定现象,对各种科学和工程学科,包括富营养学、大气科学和气候、地球物理学和聚合能源,具有极大的兴趣。分析方法无法用来解释Rayleigh-Taylor不稳定的长期行为,因此需要对问题进行数字模拟。然而,为了准确反映扰动的振幅增长,对于传统的数字方法来说,空间和时间离散需要极其精细,而长期模拟可能变得过于昂贵。在本文件中,我们提出高效的减少订单模型技术,以加速模拟可压缩气体动态中的Rayleigh-Taylor不稳定现象。我们引入一个总框架,将各种解决方案分解成多种,以建造时地段分布和时间-局部缩减的订单模型,使用不同的Atwood编号。我们在此框架内提出了两种切实可行的办法,即分别使用物理时间和穿透距离进行分解。我们提出了数字结果,以审查拟议方法的绩效。