Performance tests and analyses are critical to effective high-performance computing software development and are central components in the design and implementation of computational algorithms for achieving faster simulations on existing and future computing architectures for large-scale application problems. In this article, we explore performance and space-time trade-offs for important compute-intensive kernels of large-scale numerical solvers for partial differential equations (PDEs) that govern a wide range of physical applications. We consider a sequence of PDE-motivated bake-off problems designed to establish best practices for efficient high-order simulations across a variety of codes and platforms. We measure peak performance (degrees of freedom per second) on a fixed number of nodes and identify effective code optimization strategies for each architecture. In addition to peak performance, we identify the minimum time to solution at 80% parallel efficiency. The performance analysis is based on spectral and p-type finite elements but is equally applicable to a broad spectrum of numerical PDE discretizations, including finite difference, finite volume, and h-type finite elements.

A main route for SARS-CoV-2 (severe acute respiratory syndrome coronavirus) transmission involves airborne droplets and aerosols generated when a person talks, coughs, or sneezes. The residence time and spatial extent of these virus-laden aerosols are mainly controlled by their size and the ability of the background flow to disperse them. Therefore, a better understanding of the role played by the flow driven by respiratory events is key in estimating the ability of pathogen-laden particles to spread the infection. Here, we numerically investigate the hydrodynamics produced by a violent expiratory event resembling a mild cough. Coughs can be split into an initial jet stage during which air is expelled through mouth and a dissipative phase over which turbulence intensity decays as the puff penetrates the environment. Time-varying exhaled velocity and buoyancy due to temperature differences between the cough and the ambient air affect the overall flow dynamics. The direct numerical simulation (DNS) of an idealized isolated cough is used to characterize the jet/puff dynamics using the trajectory of the leading turbulent vortex ring and extract its topology by fitting an ellipsoid to the exhaled fluid contour. The three-dimensional structure of the simulated cough shows that the assumption of a spheroidal puff front fails to capture the observed ellipsoidal shape. Numerical results suggest that, although analytical models provide reasonable estimates of the distance traveled by the puff, trajectory predictions exhibit larger deviations from the DNS. The fully resolved hydrodynamics presented here can be used to inform new analytical models, leading to improved prediction of cough-induced pathogen-laden aerosol dispersion.

Airborne particles are a major route for transmission of COVID-19 and many other infectious diseases. When a person talks, sings, coughs, or sneezes, nasal and throat secretions are spewed into the air. After a short initial fragmentation stage, the expelled material is mostly composed of spherical particles of different sizes. While the dynamics of the largest droplets are dominated by gravitational effects, the smaller aerosol particles, mostly transported by means of hydrodynamic drag, form clouds that can remain afloat for long times. In subsaturated air environments, the dependence of pathogen-laden particle dispersion on their size is complicated due to evaporation of the aqueous fraction. Particle dynamics can significantly change when ambient conditions favor rapid evaporation rates that result in a transition from buoyancy-to-drag dominated dispersion regimes. To investigate the effect of particle size and evaporation on pathogen-laden cloud evolution, a direct numerical simulation of a mild cough was coupled with an evaporative Lagrangian particle advection model. The results suggest that while the dispersion of cough particles in the tails of the size distribution are unlikely to be disrupted by evaporative effects, preferential aerosol diameters (30–40 μ m) may exhibit significant increases in the residence time and horizontal range under typical ambient conditions. Using estimations of the viral concentration in the spewed fluid and the number of ejected particles in a typical respiratory event, we obtained a map of viral load per volume of air at the end of the cough and the number of virus copies per inhalation in the emitter vicinity.

The Bulle effect is a phenomenon in which a disproportionately higher amount of near‐bed sediment load at a fluvial diversion moves into the diverted channel, even for cases in which the proportion of water (with respect to the main flow) entering the diversion channel is relatively small. This phenomenon has wide‐ranging implications for both engineered and natural systems: from efficient design of channels to redirect water and sediment for reclaiming sinking deltas, designing navigational channels that do not need frequent dredging, to morphological evolution of river bifurcations. The first ever, and one of the most extensive set of experiments conducted to explore this phenomenon, were conducted by Bulle in . In the current study the experiments conducted by Bulle have been simulated using an open‐source, free‐surface finite‐element‐based hydrodynamic solver. The main objectives were to explore to what extent the complex phenomenon of the Bulle effect at the scale of a laboratory experiment can be simulated accurately using Reynolds‐averaged Navier–Stokes (RANS)‐based hydrodynamic solver, and to understand the details of the hydrodynamics that Bulle could not analyze through his experiments. The hydrodynamics captured by the simulations were found to match the observations made by Bulle through his experiments, and the distributions of sediment at the diversion predicted by the numerical simulations were found to match the general trend observed in the laboratory experiments. The results from the numerical simulations were also compared with existing one‐dimensional models for sediment distribution at bifurcations, and the three‐dimensional numerical model was found to perform appreciably better. This is expected due to the complex flow features at the diversion, which can only be captured satisfactorily using a three‐dimensional hydrodynamic model. Copyright © 2017 John Wiley & Sons, Ltd.

We present scalable implementations of spectral-element-based Schwarz overlapping (overset) methods for the incompressible Navier-Stokes (NS) equations. Our SEM-based overset grid method is implemented at the level of the NS equations, which are advanced independently within separate subdomains using interdomain velocity and pressure boundarydata exchanges at each timestep or sub-timestep. Central to this implementation is a general, robust, and scalable interpolation routine, gslib-findpts, that rapidly determines the computational coordinates (processor p, element number e, and local coordinates (r, s, t) ∈Ω := [−1, 1] 3 ) for any arbitrary point x * = (x * , y * , z * ) ∈ Ω ⊂ lR 3 . The communication kernels in gslib execute with at most log P complexity for P MPI ranks, have scaled to P > 10 6 , and obviate the need for development of any additional MPI-based code for the Schwarz implementation. The original interpolation routine has been extended to account for multiple overlapping domains. The new implementation discriminates the possessing subdomain by distance to the domain boundary, such that the interface boundary data is taken from the inner-most interior points. We present application of this approach to several heat transfer and fluid dynamic problems, discuss the computation/communication complexity and accuracy of the approach, and present performance measurements for P > 12, 000.