Statistical analysis and simulation of random shocks in stochastic Burgers equation
Statistical analysis and simulation of random shocks in stochastic Burgers equation
复制标题
随机Burgers方程中随机冲击的统计分析与模拟
DOI：
10.1098/rspa.2014.0080
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
G. Karniadakis
中科院分区：
文献类型：
--
作者：
Heyrim Cho;D. Venturi;G. Karniadakis
研究了随机Burgers方程在随机时空扰动和随机初始条件下随机冲击波的统计性质。利用响应-激发概率密度函数（PDF）方法和不可逆统计力学的Mori-Zwanzig（MZ）公式，推导出解场的一点和两点PDF的精确降阶方程.特别是，我们计算的统计特性的随机冲击波的无粘极限使用自适应（冲击捕获）间断Galerkin方法在物理和概率空间。我们认为随机流所产生的高维随机初始条件和随机添加剂强迫项，产生多个相互作用的冲击波崩溃成集群和沉降到一个相似的状态。我们还解决了如何随机冲击波在空间和时间表现在概率空间的问题。所提出的新的数学框架可以应用于不同的守恒律，可能导致新的见解高维随机动力系统和更有效的计算算法。
We study the statistical properties of random shock waves in stochastic Burgers equation subject to random space–time perturbations and random initial conditions. By using the response–excitation probability density function (PDF) method and the Mori–Zwanzig (MZ) formulation of irreversible statistical mechanics, we derive exact reduced-order equations for the one-point and two-point PDFs of the solution field. In particular, we compute the statistical properties of random shock waves in the inviscid limit by using an adaptive (shock-capturing) discontinuous Galerkin method in both physical and probability spaces. We consider stochastic flows generated by high-dimensional random initial conditions and random additive forcing terms, yielding multiple interacting shock waves collapsing into clusters and settling down to a similarity state. We also address the question of how random shock waves in space and time manifest themselves in probability space. The proposed new mathematical framework can be applied to different conservation laws, potentially leading to new insights into high-dimensional stochastic dynamical systems and more efficient computational algorithms.
影响因子：
3.1
作者：
Al-Mohy, Awad H.;Higham, Nicholas J.
通讯作者：
Higham, Nicholas J.
伦格伦·莫尼·诺维科夫层次：湍流的动力学方程
影响因子：
1.4
作者：
Rudolf Friedrich;Anton Daitche;Oliver Kamps;Johannes Lülff;Michel Voßkuhle;Michael Wilczek
通讯作者：
Michael Wilczek