流体中电动输运现象的直接数值模拟：变分多尺度稳定化与八叉树网格细化
Direct numerical simulation of electrokinetic transport phenomena in fluids: variational multi-scale stabilization and octree-based mesh refinement
AI总结：
针对电动输运直接数值模拟中的多尺度与刚性挑战，提出融合变分多尺度稳定化、块迭代隐式时间积分及八叉树自适应网格细化的并行框架，可高效精确模拟电化学装置中的离子输运与电对流。
摘要：
带电物质输运的计算建模已使得对多种电化学和电动装置的分析、设计与优化成为可能。这些系统由泊松-能斯特-普朗克（PNP）方程与纳维-斯托克斯（NS）方程耦合表示。直接数值模拟（DNS）以精确捕捉离子浓度和电流通量的时空变化仍具挑战性，原因在于：（a）扩散电荷层（DCL）的临界尺寸较小，（b）由于快速电荷弛豫时间、大的对流效应以及边界附近的陡峭梯度导致的刚性耦合，以及（c）电化学装置所呈现的复杂几何形状。在本研究中，我们通过提出一个直接数值模拟框架来应对这些挑战，该框架包含：（a）变分多尺度（VMS）处理，（b）结合半隐式（用于NS）和隐式（用于PNP）时间积分器的块迭代策略，以及（c）基于八叉树的自适应网格细化。VMS公式提供了数值稳定化，对于捕捉工程装置中常见的电对流流动至关重要。块迭代策略解耦了NS与PNP方程之间非线性耦合的困难，并允许分别针对NS和PNP方程使用定制的数值方案。精心设计的二阶混合隐式方法规避了显式时间步进器严苛的时间步长要求，从而能够在更长的时间范围内进行模拟。最后，基于八叉树的网格划分允许对DCL进行高效且有针对性的空间分辨。这些特性被整合到一个大规模并行计算框架中，使得能够模拟真实的工程电化学装置。该数值框架通过几个具有挑战性的典型算例进行了说明。
英文摘要：
Computational modeling of charged species transport has enabled the analysis, design, and optimization of a diverse array of electrochemical and electrokinetic devices. These systems are represented by the Poisson-Nernst-Planck (PNP) equations coupled with the Navier-Stokes (NS) equation. Direct numerical simulation (DNS) to accurately capture the spatio-temporal variation of ion concentration and current flux remains challenging due to the (a) small critical dimension of the diffuse charge layer (DCL), (b) stiff coupling due to fast charge relaxation times, large advective effects, and steep gradients close to boundaries, and (c) complex geometries exhibited by electrochemical devices. In the current study, we address these challenges by presenting a direct numerical simulation framework that incorporates (a) a variational multiscale (VMS) treatment, (b) a block-iterative strategy in conjunction with semi-implicit (for NS) and implicit (for PNP) time integrators, and (c) octree based adaptive mesh refinement. The VMS formulation provides numerical stabilization critical for capturing the electro-convective flows often observed in engineered devices. The block-iterative strategy decouples the difficulty of non-linear coupling between the NS and PNP equations and allows the use of tailored numerical schemes separately for NS and PNP equations. The carefully designed second-order, hybrid implicit methods circumvent the harsh timestep requirements of explicit time steppers, thus enabling simulations over longer time horizons. Finally, the octree-based meshing allows efficient and targeted spatial resolution of the DCL. These features are incorporated into a massively parallel computational framework, enabling the simulation of realistic engineering electrochemical devices. The numerical framework is illustrated using several challenging canonical examples.
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