Scalable Multiphysics Solvers for Simulating Electrokinetic Flows in Porous Geometries
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Simulating electrokinetic flows in porous media is useful for providing physics-based scaling guidance for the design and analysis of microfluidic devices used in desalination and dialysis applications. This requires solving a highly stiff and coupled system of Navier-Stokes (NS) and Poisson-Nernst-Planck (PNP) equations on fully resolved space-time grids to capture interesting physics near complex domain boundaries. In this work, we present a massively scalable and parallelizable simulation framework for solving NSPNP equations, addressing key computational challenges through the following techniques. (i) a block iterative strategy to solve a decoupled and linearized version of NSPNP equations in order to mitigate strong coupling and non-linear solver requirements, (ii) an octree-based adaptive meshing framework suitable for complex geometries and MPI-based domain decomposition, (iii) variational multiscale formulations to ensure numerical stability, and (iv) a finite element framework integrated with PETSc to enable parallel handling of large linear systems We perform convergence and scaling studies on canonical cases, examining the solver’s wall-clock performance across increasing problem size and equation stiffness. Finally, the proposed framework is applied to model ion-concentration polarization in porous geometries, demonstrating matching trends in device metrics such as pressure drop and filtration efficiency.
