Domain Decomposition Methods for Multiscale Modeling

Multiscale simulation of fluids: coupling molecular and continuum

“…The term multiplied by ξ is proportional to the momentum difference between the molecular and continuum systems, a proportional control in the language of control theory. In the review of Bian and Praprotnik 9 the work of O’Connell and Thompson 31 is described as ‘relaxation dynamics’, and in Delgado-Buscalioni 49 as a Langevin equation. However, it is important to note the derivation in the thesis of O’Connell 151 is rigorously derived from the principle of least action, with no stochastic terms, and is mathematically and physically identical to the form given in the work of Nie et al 58 as shown later in this section.…”

“…the first line, eqn (23), simply states the time evolution of the molecular volume must be subtracted and replaced by the time evolution of its overlapping CFD counterpart. The CV momentum equation, eqn (9), is then used to obtain eqn (24) in terms of surface fluxes. The final equality gives eqn (25), to compare to the Nie et al 58 constraint force.…”

“…Despite an initial flurry of interest, work on the theoretical framework, especially the constraint forces, largely stopped with the work of Flekkøy et al 56 and has since focused on development of molecular insertion. 9 In comparison, the solid mechanics community has seen extensive research into the theoretical underpinning of atomistic-continuum coupling, traced back to the first papers in the 1970s. 120 This has led to a wide range of different solid coupling methodologies such as the quasicontinuum, CLS method, the FEAt, the fully non-local QC (QC-FNL) method and the CADD method, all summarised and compared in.Curtin and Miller 120 Solid mechanics typically uses the finite element form of the continuum equations, which has a clear mathematical link to the continuum equations of motion.…”

“…Therefore, this does not aim to be a thorough review of the literature for every single simulation method, there have been a wide range of reviews. [6][7][8][9][10][11][12] We also do not aim to discuss aspects, such as the creation of coarse-grained models from bottom-up approaches (e.g. iterative Boltzmann inversion methods, free energy methods, etc.…”

“…The theoretical contributions are shown in red, [31][32][33][34][35][36][37][38][39][40][41][42][43][44]51,[56][57][58]60,62 the applications are shown in black, 7,[45][46][47][48]50,[52][53][54][55]59,61 and the review articles are shown in blue. 6,[8][9][10][11][12]49,63 This journal is © the Owner Societies 2024 a preferred model. With this in mind, we focus in this perspective on trying to present a unified framework which can link together various models applied throughout the literature.…”