Unstructured grid ocean models are advantageous for simulating the coastal ocean and river-estuary-plume systems.However, unstructured grid models tend to be diffusive and/or computationally expensive which limits their applicability to real life problems. In this paper, we describe a novel discontinuous Galerkin (DG) finite element discretization for the hydrostatic equations. The formulation is fully conservative and second-order accurate in space and time. Monotonicity of the advection scheme is ensured by using a strong stability preserving time integration method and slope limiters. Compared to previous DG models advantages include a more accurate mode splitting method, revised viscosity formulation, and new second-order time integration scheme. We demonstrate that the model is capable of simulating baroclinic flows in the eddying regime with a suite of test cases. Numerical dissipation is well-controlled, being comparable or lower than in existing state-of-the-art structured grid models.
IntroductionNumerical modeling of the coastal ocean is important for many environmental and industrial applications. Typical scenarios include modeling circulation at regional scales, coupled river-estuary-plume systems, river networks, lagoons, and harbors.Length scales range from some tens of meters in rivers and embayments to tens of kilometers in the coastal ocean; water depth ranges from less than a meter to kilometer scale at the shelf break. The time scales of the relevant processes range from minutes to hours, yet typical simulations span weeks or even decades. The dynamics are highly non-linear, characterized by local smallscale features such as fronts and density gradients, internal waves, and baroclinic eddies. These physical characteristics imply that coastal ocean modeling is intrinsically multi-scale, which imposes several technical challenges.Most coastal ocean models solve the hydrostatic Navier-Stokes equations under the Boussinesq approximation -a valid approximation for mesoscale and sub-mesoscale (1 km) processes. Small-scale processes (< 100 m) are, however, inherently three-dimensional where non-hydrostatic effects can be important, especially in areas with pronounced density structure and stratification (Marshall et al., 1997b;Mahadevan, 2006). Non-hydrostatic modeling requires very high horizontal mesh resolu-1 arXiv:1711.08552v2 [physics.ao-ph]
Deep learning is a promising tool to determine the physical model that describes our universe. To handle the considerable computational cost of this problem, we present CosmoFlow: a highly scalable deep learning application built on top of the TensorFlow framework. CosmoFlow uses efficient implementations of 3D convolution and pooling primitives, together with improvements in threading for many element-wise operations, to improve training performance on Intel ® Xeon Phi™ processors. We also utilize the Cray PE Machine Learning Plugin for efficient scaling to multiple nodes.We demonstrate fully synchronous data-parallel training on 8192 nodes of Cori with 77% parallel efficiency, achieving 3.5 Pflop/s sustained performance. To our knowledge, this is the first large-scale science application of the TensorFlow framework at supercomputer scale with fully-synchronous training. These enhancements enable us to process large 3D dark matter distribution and predict the cosmological parameters ΩM , σ8 and ns with unprecedented accuracy.
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