Highly accurate simulation of electrokinetic transport processes in nanopores

子项目B3致力于在外加电势下对瞬变纳米孔中的离子传输过程进行详细的建模和高精度的模拟。因此，这与电可调制纳米孔的指导性实验有直接联系。B3的科学重点是开发自适应和混合方法，特别适合在这些运输过程中弥合通常非常不同的空间和时间尺度，并在数字上充分实施运输机制之间通常很强的耦合。中心目标是为离子传输开发高数值和物理保真度的数值方法，以产生物理上准确的解。这一点具有很高的相关性，因为经典的数值保真度测量(精度、稳定性、一致性)不足以解决系统物理如何由特定的数值方法表示的问题。在实践中，这是一个隐秘而微妙的问题，因为这样的故障很少会因为不稳定而导致模拟完全中止，即它可能会被忽视，从而导致物理上不正确但收敛的结果。该项目将有助于推进数值方法领域，并解决日益增长的对复杂系统中离子传输过程的物理精确解决方案的需求，例如在施加电势的瞬变纳米孔中。特别是，我们将设计一种混合原子-连续介质(HAC)方法，以分别耦合分子动力学(MD)和连续介质求解器。这使得能够对使用MD的孔壁附近的离子传输过程进行详细的计算分析。这种方法对于检查瞬变孔隙系统特别有用，在那里纯MD在计算上是令人望而却步的。至于连续体求解器，我们将致力于使用改进的闭包来实现最新的模型公式，以考虑离子在电解质中的有限大小和溶剂化等影响。此外，中心目标是开发一种高保真的数值方法，该方法通过隐式联立求解方法来解释运输过程之间的显著耦合。

Subproject B3 is dedicated to the detailed modelling and highly accurate simulation of ion transport processes in transient nanopores under an applied potential. Thus, there is a direct link to the guiding experiment Electrically Modulatable Nanopores. The scientific focus of B3 is on the development of adaptive and hybrid approaches, which are particularly suitable to bridge the typically very different spatial and temporal scales in these transport processes and to numerically adequately implement the usually strong coupling between transport mechanisms. The central aim is to develop numerical methods of high numerical and physical fidelity for ion transport to produce physically accurate solutions. This is of high relevance, since classical measures of numerical fidelity (accuracy, stability, consistency) are not sufficient to address how well the system physics is represented by a particular numerical method. In practice, this is a surreptitious and subtle problem, since such a failure rarely causes outright abort of simulations due to instabilities, i.e., it can potentially go unnoticed leading to physically incorrect but converged results. This project will contribute to advancing the field of numerical methods and address the growing need for physically accurate solutions of ion transport processes in complex systems such as in transient nanopores under an applied potential. In particular, we will devise a hybrid atomistic-continuum (HAC) approach so as to couple molecular dynamics (MD) and continuum solvers, respectively. This enables a detailed computational analysis of ion transport processes close to the pore walls, where MD is used. Such an approach is particularly useful to examine transient pore systems where pure MD would be computationally prohibitive. As for the continuum solver, we will aim to implement most recent model formulations using improved closures to take into account effects like the finite size and solvation of ions in electrolytes. Moreover, a central objective is to develop a numerical method of high fidelity which accounts for the significant coupling between transport processes by means of an implicit simultaneous solution approach.