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Computational modeling of charged species transport has enabled the analysis,design, and optimization of a diverse array of electrochemical andelectrokinetic devices. These systems are represented by thePoisson-Nernst-Planck (PNP) equations coupled with the Navier-Stokes (NS)equation. Direct numerical simulation (DNS) to accurately capture thespatio-temporal variation of ion concentration and current flux remainschallenging due to the (a) small critical dimension of the diffuse charge layer(DCL), (b) stiff coupling due to fast charge relaxation times, large advectiveeffects, and steep gradients close to boundaries, and (c) complex geometriesexhibited by electrochemical devices. In the current study, we address thesechallenges by presenting a direct numerical simulation framework thatincorporates (a) a variational multiscale (VMS) treatment, (b) ablock-iterative strategy in conjunction with semi-implicit (for NS) andimplicit (for PNP) time integrators, and (c) octree based adaptive meshrefinement. The VMS formulation provides numerical stabilization critical forcapturing the electro-convective flows often observed in engineered devices.The block-iterative strategy decouples the difficulty of non-linear couplingbetween the NS and PNP equations and allows the use of tailored numericalschemes separately for NS and PNP equations. The carefully designedsecond-order, hybrid implicit methods circumvent the harsh timesteprequirements of explicit time steppers, thus enabling simulations over longertime horizons. Finally, the octree-based meshing allows efficient and targetedspatial resolution of the DCL. These features are incorporated into a massivelyparallel computational framework, enabling the simulation of realisticengineering electrochemical devices. The numerical framework is illustratedusing several challenging canonical examples.

Direct numerical simulation of electrokinetic transport phenomena in fluids: variational multi-scale stabilization and octree-based mesh refinement