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We present a 3D finite element solver for the nonlinear Poisson-Nernst-Planck (PNP) equations for electrodiffusion, coupled to the Stokes system of fluid dynamics. The model serves as a building block for the simulation of macromolecule dynamics inside nanopore sensors.We add to existing numerical approaches by deploying goal-oriented adaptive mesh refinement. To reduce the computation overhead of mesh adaptivity, our error estimator uses the much cheaper PoissonBoltzmann equation as a simplified model, which is justified on heuristic grounds but shown to work well in practice. To address the nonlinearity in the full PNP-Stokes system, three different linearization schemes are proposed and investigated, with two segregated iterative approaches both outperforming a naive application of Newton's method. Numerical experiments are reported on a real-world nanopore sensor geometry.We also investigate two different models for the interaction of target molecules with the nanopore sensor through the PNP-Stokes equations. In one model, the molecule is of finite size and is explicitly built into the geometry; while in the other, the molecule is located at a single point and only modeled implicitly -after solution of the system -which is computationally favorable. We compare the resulting force profiles of the electric and velocity fields acting on the molecule, and conclude that the point-size model fails to capture important physical effects such as the dependence of charge selectivity of the sensor on the molecule radius.

Two-dimensional shallow-water schemes on Cartesian grids are amendable for graphics processing units and thus a convenient choice for fast flood simulations. A comparison of recent schemes and validation of important use cases is essential for developers and practitioners working with flood simulation tools. In this paper, we discuss three state-of-the-art shallow-water schemes: a first-order upwind scheme, a second-order upwind scheme, and a second-order central-upwind scheme. We analyze the advantages and disadvantages of each scheme on historical Danube river floods at three regions in Austria. We study the Lobau region as a floodplain with several small channels, the Wachau region with the meandering Danube in a steep valley, and the Marchfeld region located at the river confluence of March and Danube. The validation case studies show that the second-order schemes provide better estimates of the water levels than the first-order scheme. Still, the first order scheme is useful because it offers fast simulations and reasonable results at higher resolutions. The best trade-off between accuracy and computational effort for simulating river floods is provided by the second-order upwind scheme. individual papers. This paper is part of the Journal of Hydraulic Engineering, © ASCE, ISSN 0733-9429. © ASCE 05019005-1 J. Hydraul. Eng. J. Hydraul. Eng., 2020, 146(1): 05019005 Downloaded from ascelibrary.org by 44.224.250.200 on 07/04/20. Copyright ASCE. For personal use only; all rights reserved. © ASCE 05019005-2 J. Hydraul. Eng. J. Hydraul. Eng., 2020, 146(1): 05019005 Downloaded from ascelibrary.org by 44.224.250.200 on 07/04/20. Copyright ASCE. For personal use only; all rights reserved. © ASCE 05019005-3 J. Hydraul. Eng. J. Hydraul. Eng., 2020, 146(1): 05019005 Downloaded from ascelibrary.org by 44.224.250.200 on 07/04/20. Copyright ASCE. For personal use only; all rights reserved. © ASCE 05019005-5 J. Hydraul. Eng. J. Hydraul. Eng., 2020, 146(1): 05019005 Downloaded from ascelibrary.org by 44.224.250.200 on 07/04/20. Copyright ASCE. For personal use only; all rights reserved. © ASCE 05019005-7 J. Hydraul. Eng. J. Hydraul. Eng., 2020, 146(1): 05019005 Downloaded from ascelibrary.org by 44.224.250.200 on 07/04/20. Copyright ASCE. For personal use only; all rights reserved. © ASCE 05019005-8 J. Hydraul. Eng. J. Hydraul. Eng., 2020, 146(1): 05019005 Downloaded from ascelibrary.org by 44.224.250.200 on 07/04/20. Copyright ASCE. For personal use only; all rights reserved. © ASCE 05019005-9 J. Hydraul. Eng. © ASCE 05019005-10 J. Hydraul. Eng. J. Hydraul. Eng., 2020, 146(1): 05019005 Downloaded from ascelibrary.org by 44.224.250.200 on 07/04/20. Copyright ASCE. For personal use only; all rights reserved. © ASCE 05019005-14 J. Hydraul. Eng. J. Hydraul. Eng., 2020, 146(1): 05019005 Downloaded from ascelibrary.org by 44.224.250.200 on 07/04/20. Copyright ASCE. For personal use only; all rights reserved. © ASCE 05019005-16 J. Hydraul. Eng.

In this paper, we present a real‐time technique to visualize large‐scale adaptive height fields with C ‐continuous surface reconstruction. Grid‐based shallow water simulation is an indispensable tool for interactive flood management applications. Height fields defined on adaptive grids are often the only viable option to store and process the massive simulation data. Their visualization requires the reconstruction of a continuous surface from the spatially discrete simulation data. For regular grids, fast linear and cubic interpolation are commonly used for surface reconstruction. For adaptive grids, however, there exists no higher‐order interpolation technique fast enough for interactive applications. Our proposed technique bridges the gap between fast linear and expensive higher‐order interpolation for adaptive surface reconstruction. During reconstruction, no matter if regular or adaptive, discretization and interpolation artifacts can occur, which domain experts consider misleading and unaesthetic. We take into account boundary conditions to eliminate these artifacts, which include water climbing uphill, diving towards walls, and leaking through thin objects. We apply realistic water shading with visual cues for depth perception and add waves and foam synthesized from the simulation data to emphasize flow directions. The versatility and performance of our technique are demonstrated in various real‐world scenarios. A survey conducted with domain experts of different backgrounds and concerned citizens proves the usefulness and effectiveness of our technique.