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We propose a more conservative, physically-intuitive criterion, namely, the boundary enstrophy flux ( $BEF$ ), to characterise leading-edge-type dynamic stall onset in incompressible flows. Our results are based on wall-resolved large-eddy simulations of pitching aerofoils, with fine spatial and temporal resolution around stall onset. We observe that $|BEF|$ reaches a maximum within the stall onset regime identified. By decomposing the contribution to $BEF$ from the flow field, we find that the dominant contribution arises from the laminar leading edge region, due to the combined effect of large clockwise vorticity and favourable pressure gradient. A relatively small contribution originates from the transitional/turbulent laminar separation bubble (LSB) region, due to LSB-induced counter-clockwise vorticity and adverse pressure gradient. This results in $BEF$ being nearly independent of the integration length as long as the region very close to the leading edge is included. This characteristic of $BEF$ yields a major advantage in that the effect of partial or complete inclusion of the noisy LSB region can be filtered out, without changing the $BEF$ peak location in time significantly. Next, we analytically relate $BEF$ to the net wall shear and show that its critical value ( $$=\max (|BEF|)$$ ) corresponds to the instant of maximum net shear prevailing at the wall. Finally, we have also compared $BEF$ with the leading edge suction parameter ( $LESP$ ) (Ramesh et al. , J. Fluid Mech. , vol. 751, 2014, pp. 500–538) and find that the former reaches its maximum value between $$0.3^{\circ }$$ and $$0.8^{\circ }$$ of rotation earlier. 

The paradigm of differentiable programming has significantly enhanced the scope of machine learning via the judicious use of gradient-based optimization. However, standard differentiable programming methods (such as autodiff) typically require that the machine learning models be differentiable, limiting their applicability. Our goal in this paper is to use a new, principled approach to extend gradient-based optimization to functions well modeled by splines, which encompass a large family of piecewise polynomial models. We derive the form of the (weak) Jacobian of such functions and show that it exhibits a block-sparse structure that can be computed implicitly and efficiently. Overall, we show that leveraging this redesigned Jacobian in the form of a differentiable" layer''in predictive models leads to improved performance in diverse applications such as image segmentation, 3D point cloud reconstruction, and finite element analysis. We also open-source the code at\url {https://github. com/idealab-isu/DSA}. 

We deploy a fully coupled thermo-fluidic finite element approach to simulating natural ventilation in a sustainably designed building with complex geometry. The 'interlock house' uses building design for climate control instead of mechanical means (such as air conditioning). Therefore, accurately modeling the natural ventilation flows is crucial to assess thermal comfort in such designs. A residual-based variational multiscale method (VMS) is employed, which is a Large Eddy Simulation (LES) type approach to turbulence modeling. Air diffusion performance index (ADPI) and predicted mean vote (PMV) are computed to investigate thermal comfort in both configurations. This work illustrates the ability of the framework to comprehensively model and predict natural ventilation under various operating scenarios. 

Efficiently and accurately simulating partial differential equations(PDEs) in and around arbitrarily defined geometries, especially with high levels of adaptivity, has significant implications for different application domains. A key bottleneck in the above process is the fast construction of a "good" adaptively-refined mesh. In this work, we present an efficient novel octree-based adaptive discretization approach capable of caring out arbitrarily shaped void regions from the parent domain: an essential requirement for fluid simulations around complex objects.