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DOI：
10.2307/j.ctv209xn61.33
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Zhiwen Zhang
中科院分区：
文献类型：
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作者：
Zhongjian Wang;J. Xin;Zhiwen Zhang
在本文中，我们研究的问题，计算的有效扩散率的粒子运动在混沌和随机流。此外，我们还数值研究了混沌平流中的剩余扩散现象。残余扩散是指由于流线的混沌混合而导致的在零分子扩散极限中的非零有效（均质化）扩散。在这种极限下，传统的数值方法通常会失败，因为对流扩散方程的解会产生尖锐的梯度。而不是在欧拉公式中求解福克-普朗克方程，我们计算的拉格朗日公式，这是由随机微分方程（SDES）建模的粒子的运动。我们提出了一个新的数值积分器的基础上随机分裂方法来解决相应的SDES中的确定性子问题是保辛的，而随机子问题可以被视为一个扰动。我们提供了严格的误差分析，新的数值积分器使用向后误差分析技术，并表明我们的方法优于标准的基于欧拉的积分。数值结果表明，所提出的方法的精度和效率的几个典型的混沌和随机流问题的物理利益。AMS科目分类：76 R99、35 B27、65 T40、65 M70
In this paper we study the problem of computing the effective diffusivity for a particle moving in chaotic and stochastic flows. In addition we numerically investigate the residual diffusion phenomenon in chaotic advection. The residual diffusion refers to the non-zero effective (homogenized) diffusion in the limit of zero molecular diffusion as a result of chaotic mixing of the streamlines. In this limit traditional numerical methods typically fail since the solutions of the advection-diffusion equation develop sharp gradients. Instead of solving the Fokker-Planck equation in the Eulerian formulation, we compute the motion of particles in the Lagrangian formulation, which is modelled by stochastic differential equations (SDEs). We propose a new numerical integrator based on a stochastic splitting method to solve the corresponding SDEs in which the deterministic subproblem is symplectic preserving while the random subproblem can be viewed as a perturbation. We provide rigorous error analysis for the new numerical integrator using the backward error analysis technique and show that our method outperforms standard Euler-based integrators. Numerical results are presented to demonstrate the accuracy and efficiency of the proposed method for several typical chaotic and stochastic flow problems of physical interests. AMS subject classification: 76R99, 35B27, 65T40, 65M70
DOI：
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发表时间：
2005
期刊：
Sugaku Expositions, Amer. Math. Soc. Vol.18
影响因子：
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作者：
S. Kanagawa;S. Ogawa
通讯作者：
S. Ogawa