A Finite-Volume Method for Fluctuating Dynamical Density Functional Theory
A Finite-Volume Method for Fluctuating Dynamical Density Functional Theory
复制标题
脉动动力密度泛函理论的有限体积方法
DOI：
10.1016/j.jcp.2020.109796
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
S. Kalliadasis
中科院分区：
文献类型：
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作者：
A. Russo;Sergio P. Perez;M. Durán;P. Yatsyshin;J. Carrillo;S. Kalliadasis
介绍了一种求解随机梯度流方程的有限体积数值格式。在涨落流体力学和动态密度泛函理论的框架内，这些方程是至关重要的。我们提出的方案涉及一般的自由能泛函，例如，包括外场或相互作用势。这使我们能够模拟一系列物理现象，其中热涨落起着至关重要的作用，例如成核和其他能量-势垒跨越转变。基于确定性项和随机项的混合空间离散化以及不同的隐式和显式时间积分器，导出了密度的正性保持算法。我们通过大量的应用表明，我们的方案不仅能够准确地再现物理系统的统计性质(结构因子和关联)，而且还允许我们模拟平均场方法无法捕捉到的能量垒穿越动力学。
We introduce a finite-volume numerical scheme for solving stochastic gradient flow equations. Such equations are of crucial importance within the framework of fluctuating hydrodynamics and dynamic density functional theory. Our proposed scheme deals with general free-energy functionals, including, for instance, external fields or interaction potentials. This allows us to simulate a range of physical phenomena where thermal fluctuations play a crucial role, such as nucleation and other energy-barrier crossing transitions. A positivity-preserving algorithm for the density is derived based on a hybrid space discretization of the deterministic and the stochastic terms and different implicit and explicit time integrators. We show through numerous applications that not only our scheme is able to accurately reproduce the statistical properties (structure factor and correlations) of physical systems, but also allows us to simulate energy barrier crossing dynamics, which cannot be captured by mean-field approaches.