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In this article we develop an algorithm for the efficient simulation ofelectrolytes in the presence of physical boundaries. In previous work theDiscrete Ion Stochastic Continuum Overdamped Solvent (DISCOS) algorithm wasderived for triply periodic domains, and was validated through ion-ion paircorrelation functions and Debye-H{\"u}ckel-Onsager theory for conductivity,including the Wien effect for strong electric fields. In extending thisapproach to include an accurate treatment of physical boundaries we mustaddress several important issues. First, the modifications to the spreading andinterpolation operators necessary to incorporate interactions of the ions withthe boundary are described. Next we discuss the modifications to theelectrostatic solver to handle the influence of charges near either a fixedpotential or dielectric boundary. An additional short-ranged potential is alsointroduced to represent interaction of the ions with a solid wall. Finally, thedry diffusion term is modified to account for the reduced mobility of ions neara boundary, which introduces an additional stochastic drift correction. Severalvalidation tests are presented confirming the correct equilibrium distributionof ions in a channel. Additionally, the methodology is demonstrated usingelectro-osmosis and induced charge electro-osmosis, with comparison made totheory and other numerical methods. Notably, the DISCOS approach achievesgreater accuracy than a continuum electrostatic simulation method. We alsoexamine the effect of under-resolving hydrodynamic effects using a `drydiffusion' approach, and find that considerable computational speedup can beachieved with a negligible impact on accuracy.

Modeling Electrokinetic Flows with the Discrete Ion Stochastic Continuum Overdamped Solvent Algorithm