CUDA Implementation of a Navier-Stokes Solver on Multi-GPU Desktop Platforms for Incompressible Flows

Graphics processor units (GPU) that are traditionally designed for graphics rendering have emerged as massively-parallel co-processors to the central processing unit (CPU). Small-footprint desktop supercomputers with hundreds of cores that can deliver teraflops peak performance at the price of conventional workstations have been realized. A computational fluid dynamics (CFD) simulation capability with rapid computational turnaround time has the potential to transform engineering analysis and design optimization procedures. We describe the implementation of a Navier-Stokes solver for incompressible fluid flow using desktop platforms equipped with multi-GPUs. Specifically, NVIDIA’s Compute Unified Device Architecture (CUDA) programming model is used to implement the discretized form of the governing equations. The projection algorithm to solve the incompressible fluid flow equations is divided into distinct CUDA kernels, and a unique implementation that exploits the memory hierarchy of the CUDA programming model is suggested. Using a quad-GPU platform, we observe two orders of magnitude speedup relative to a serial CPU implementation. Our results demonstrate that multi-GPU desktops can serve as a cost-effective small-footprint parallel computing platform to accelerate CFD simulations substantially. I. Introductio

Generation of Vorticity Near Topography: Anticyclones in the Caribbean Sea

Mesoscale anticyclonic eddies dominate the sea-surface height variability in the Caribbean Sea. Although it is well established that these anticyclones are formed near the eastern boundary of the Caribbean Sea, which is demarcated by the Lesser Antilles, the source of their anticyclonic vorticity remains unclear. To gain insight into this source, we analyze the fluxes of vorticity into the Caribbean at its eastern boundary using a high-resolution numerical model. We find that the anticyclonic vorticity in the eastern Caribbean Sea predominantly originates from regions where intense ocean currents flow close to the Lesser Antilles. More specifically, St. Lucia and Grenada are hotspots for vorticity generation. The local generation rate scales with the amplitude of the volume transport through the passages between these islands. This finding is in contrast with the view that anticyclonic North Brazil Current (NBC) rings in the Atlantic Ocean are the main source of anticyclonic vorticity in the eastern Caribbean Sea. Our analyses reveal that the direct contribution of the vorticity of the NBC rings is of lesser importance than the local generation. However, the collision of upstream NBC rings with the Lesser Antilles increases the volume transport through the passages into the Caribbean Sea, so that their presence indirectly leads to enhanced local production of anticyclonic vorticity. This process is an example of the importance of vorticity generation near topography, which is ubiquitous in the oceans, and expected to be important whenever currents and steep topography meet

Ocean convergence and the dispersion of flotsam

Floating oil, plastics, and marine organisms are continually redistributed by ocean surface currents. Prediction of their resulting distribution on the surface is a fundamental, long-standing, and practically important problem. The dominant paradigm is dispersion within the dynamical context of a nondivergent flow: objects initially close together will on average spread apart but the area of surface patches of material does not change. Although this paradigm is likely valid at mesoscales, larger than 100 km in horizontal scale, recent theoretical studies of submesoscales (less than ∼10 km) predict strong surface convergences and downwelling associated with horizontal density fronts and cyclonic vortices. Here we show that such structures can dramatically concentrate floating material. More than half of an array of ∼200 surface drifters covering ∼20 × 20 km2 converged into a 60 × 60 m region within a week, a factor of more than 105 decrease in area, before slowly dispersing. As predicted, the convergence occurred at density fronts and with cyclonic vorticity. A zipperlike structure may play an important role. Cyclonic vorticity and vertical velocity reached 0.001 s−1 and 0.01 ms−1, respectively, which is much larger than usually inferred. This suggests a paradigm in which nearby objects form submesoscale clusters, and these clusters then spread apart. Together, these effects set both the overall extent and the finescale texture of a patch of floating material. Material concentrated at submesoscale convergences can create unique communities of organisms, amplify impacts of toxic material, and create opportunities to more efficiently recover such material

Ocean convergence and the dispersion of flotsam

Floating oil, plastics, and marine organisms are continually redistributed by ocean surface currents. Prediction of their resulting distribution on the surface is a fundamental, long-standing, and practically important problem. The dominant paradigm is dispersion within the dynamical context of a nondivergent flow: objects initially close together will on average spread apart but the area of surface patches of material does not change. Although this paradigm is likely valid at mesoscales, larger than 100 km in horizontal scale, recent theoretical studies of submesoscales (less than ∼10 km) predict strong surface convergences and downwelling associated with horizontal density fronts and cyclonic vortices. Here we show that such structures can dramatically concentrate floating material. More than half of an array of ∼200 surface drifters covering ∼20 × 20 km2 converged into a 60 × 60 m region within a week, a factor of more than 105 decrease in area, before slowly dispersing. As predicted, the convergence occurred at density fronts and with cyclonic vorticity. A zipperlike structure may play an important role. Cyclonic vorticity and vertical velocity reached 0.001 s−1 and 0.01 ms−1, respectively, which is much larger than usually inferred. This suggests a paradigm in which nearby objects form submesoscale clusters, and these clusters then spread apart. Together, these effects set both the overall extent and the finescale texture of a patch of floating material. Material concentrated at submesoscale convergences can create unique communities of organisms, amplify impacts of toxic material, and create opportunities to more efficiently recover such material

Vortex merger near a topographic slope in a homogeneous rotating fluid

This work is a contribution to the PHYSINDIEN research program. It was supported by CNRS-RFBR contract PRC 1069/16-55-150001.The effect of a bottom slope on the merger of two identical Rankine vortices is investigated in a two dimensional, quasi-geostrophic, incompressible fluid. When two cyclones initially lie parallel to the slope, and more than two vortex diameters away from the slope, the critical merger distance is unchanged. When the cyclones are closer to the slope, they can merge at larger distances, but they lose more mass into filaments, thus weakening the efficiency of merger. Several effects account for this: the topographic Rossby wave advects the cyclones, reduces their mutual distance and deforms them. This along shelf wave breaks into filaments and into secondary vortices which shear out the initial cyclones. The global motion of fluid towards the shallow domain and the erosion of the two cyclones are confirmed by the evolution of particles seeded both in the cyclone sand near the topographic slope. The addition of tracer to the flow indicates that diffusion is ballistic at early times. For two anticyclones, merger is also facilitated because one vortex is ejected offshore towards the other, via coupling with a topographic cyclone. Again two anticyclones can merge at large distance but they are eroded in the process. Finally, for taller topographies, the critical merger distance is again increased and the topographic influence can scatter or completely erode one of the two initial cyclones. Conclusions are drawn on possible improvements of the model configuration for an application to the ocean.PostprintPeer reviewe

Contribution of topographically-generated submesoscale turbulence to Southern Ocean overturning

The ocean’s global overturning circulation regulates the transport and storage of heat, carbon and nutrients. Upwelling across the Southern Ocean’s Antarctic Circumpolar Current and into the mixed layer, coupled to water mass modification by surface buoyancy forcing, has been highlighted as a key process in the closure of the overturning circulation. Here, using twelve high-resolution hydrographic sections in southern Drake Passage, collected with autonomous ocean gliders, we show that Circumpolar Deep Water originating from the North Atlantic, known as Lower Circumpolar Deep Water, intersects sloping topography in narrow and strong boundary currents. Observations of strong lateral buoyancy gradients, enhanced bottom turbulence, thick bottom mixed layers and modified water masses are consistent with growing evidence that topographically generated submesoscale flows over continental slopes enhance near-bottom mixing, and that cross-density upwelling occurs preferentially over sloping topography. Interactions between narrow frontal currents and topography occur elsewhere along the path of the Antarctic Circumpolar Current, which leads us to propose that such interactions contribute significantly to the closure of the overturning in the Southern Ocean

Cold filamentary intensification and oceanic surface convergence lines

International audienceThe reflectance images of the oceanic surface are full of surfactant lines created by surface velocity convergences, with typical line spacings of 0.1-10 km, i.e., in the submesoscale range. Here we propose a dynamical explanation by the process of filamentary intensification that shrinks the transverse scale of rectilinear surface temperature extrema at a super-exponential rate by the action of horizontal deformation flows associated with mesoscale eddies. This process is analogous to deformation-induced frontogenesis with sharpening temperature gradients accelerated by its ageostrophic secondary circulation. In the particular case of cold filaments, the shrinking rate, surface convergence, and downwelling are especially strong because of the configuration of ageostrophic acceleration. This behavior is demonstrated theoretically with idealized two-dimensional solutions and illustrated in a realistic regional circulation simulation near Peru

Mesoscale eddy generation through submesoscale instability at Gran Canaria (Canary Islands)

Trabajo presentado en el International Liège Colloquium on Ocean Dynamics, celebrado en Liège (Bélgica), del 23 al 27 de mayo de 2016Peer Reviewe

Mesoscale to submesoscale transition in the California current system. Part II: Frontal processes

International audienceThis is the second of three papers investigating the regime transition that occurs in numerical simulations for an idealized, equilibrium, subtropical, eastern boundary, upwelling current system similar to the California Current. The emergent upper-ocean submesoscale fronts are analyzed from phenomenological and dynamical perspectives, using a combination of composite averaging and separation of distinctive subregions of the flow. The initiating dynamical process for the transition is near-surface frontogenesis. The frontal behavior is similar to both observed meteorological surface fronts and solutions of the approximate dynamical model called surface dynamics (i.e., uniform interior potential vorticity q and diagnostic force balance) in the intensification of surface density gradients and secondary circulations in response to a mesoscale strain field. However, there are significant behavioral differences compared to the surface-dynamics model. Wind stress acts on fronts through nonlinear Ekman transport and creation and destruction of potential vorticity. The strain-induced frontogenesis is disrupted by vigorous submesoscale frontal instabilities that in turn lead to secondary frontogenesis events, submesoscale vortices, and excitation of even smaller-scale flows. Intermittent, submesoscale breakdown of geostrophic and gradient-wind force balance occurs during the intense frontogenesis and frontal-instability events