A Flux-Differencing Formula for Split-Form Summation By Parts Discretizations of Non-Conservative Systems: Applications to Subcell Limiting for magneto-hydrodynamics

In this paper, we show that diagonal-norm summation by parts (SBP) discretizations of general non-conservative systems of hyperbolic balance laws can be rewritten as a finite-volume-type formula, also known as flux-differencing formula, if the non-conservative terms can be written as the product of a local and a symmetric contribution. Furthermore, we show that the existence of a flux-differencing formula enables the use of recent subcell limiting strategies to improve the robustness of the high-order discretizations. To demonstrate the utility of the novel flux-differencing formula, we construct hybrid schemes that combine high-order SBP methods (the discontinuous Galerkin spectral element method and a high-order SBP finite difference method) with a compatible low-order finite volume (FV) scheme at the subcell level. We apply the hybrid schemes to solve challenging magnetohydrodynamics (MHD) problems featuring strong shocks

A flux-differencing formulation with Gauss nodes

In this work, we propose an extension of telescopic derivative operators for the DGSEM with Gauss nodes, and we prove that this formulation is equivalent to its usual matrix counterpart. Among other possible applications, this allows extending the stabilization methods already developed for Gauss-Lobatto nodes to Gauss nodes, also ensuring properties such as entropy stability while retaining their improved accuracy.Comment: Short not

Truncation Error-Based Anisotropic pp-Adaptation for Unsteady Flows for High-Order Discontinuous Galerkin Methods

In this work, we extend the $\tau$-estimation method to unsteady problems and use it to adapt the polynomial degree for high-order discontinuous Galerkin simulations of unsteady flows. The adaptation is local and anisotropic and allows capturing relevant unsteady flow features while enhancing the accuracy of time evolving functionals (e.g., lift, drag). To achieve an efficient and unsteady truncation error-based $p$-adaptation scheme, we first revisit the definition of the truncation error, studying the effect of the treatment of the mass matrix arising from the temporal term. Secondly, we extend the $\tau$-estimation strategy to unsteady problems. Finally, we present and compare two adaptation strategies for unsteady problems: the dynamic and static $p$-adaptation methods. In the first one (dynamic) the error is measured periodically during a simulation and the polynomial degree is adapted immediately after every estimation procedure. In the second one (static) the error is also measured periodically, but only one $p$-adaptation process is performed after several estimation stages, using a combination of the periodic error measures. The static $p$-adaptation strategy is suitable for time-periodic flows, while the dynamic one can be generalized to any flow evolution. We consider two test cases to evaluate the efficiency of the proposed $p$-adaptation strategies. The first one considers the compressible Euler equations to simulate the advection of a density pulse. The second one solves the compressible Navier-Stokes equations to simulate the flow around a cylinder at Re=100. The local and anisotropic adaptation enables significant reductions in the number of degrees of freedom with respect to uniform refinement, leading to speed-ups of up to $\times4.5$ for the Euler test case and $\times2.2$ for the Navier-Stokes test case

An Entropy Stable Nodal Discontinuous Galerkin Method for the resistive MHD Equations. Part II: Subcell Finite Volume Shock Capturing

The second paper of this series presents two robust entropy stable shock-capturing methods for discontinuous Galerkin spectral element(DGSEM)discretizations of the compressible magneto-hydrodynamics (MHD) equations. Specifically, we use the resistive GLM-MHD equations, which include a divergence cleaning mechanism that is based on a generalized Lagrange multiplier (GLM). For the continuous entropy analysis to hold, and due to the divergence-free constraint on the magnetic field, the GLM-MHD system requires the use of non-conservative terms, which need special treatment. Hennemann et al. ["A provably entropy stable subcell shock capturing approach for high order split form DG for the compressible Euler equations". JCP, 2020] recently presented an entropy stable shock-capturing strategy for DGSEM discretizations of the Euler equations that blends the DGSEM scheme with a subcell first-order finite volume (FV) method. Our first contribution is the extension of the method of Hennemann et al. to systems with non-conservative terms, such as the GLM-MHD equations. In our approach, the advective and non-conservative terms of the equations are discretized with a hybrid FV/DGSEM scheme, whereas the visco-resistive terms are discretized only with the high-order DGSEM method. We prove that the extended method is entropy stable on three-dimensional unstructured curvilinear meshes. Our second contribution is the derivation and analysis of a second entropy stable shock-capturing method that provides enhanced resolution by using a subcell reconstruction procedure that is carefully built to ensure entropy stability. We provide a numerical verification of the properties of the hybrid FV/DGSEM schemes on curvilinear meshes and show their robustness and accuracy with common benchmark cases, such as the Orszag-Tang vortex and the GEM (Geospace Environmental Modeling) reconnection challenge. Finally, we simulate a space physics application: the interaction of Jupiter's magnetic field with the plasma torus generated by the moon Io

Corneal endothelium assessment in specular microscopy images with Fuchs’ dystrophy via deep regression of signed distance maps

Specular microscopy assessment of the human corneal endothelium (CE) in Fuchs’ dystrophy is challenging due to the presence of dark image regions called guttae. This paper proposes a UNet-based segmentation approach that requires minimal post-processing and achieves reliable CE morphometric assessment and guttae identification across all degrees of Fuchs’ dystrophy. We cast the segmentation problem as a regression task of the cell and gutta signed distance maps instead of a pixel-level classification task as typically done with UNets. Compared to the conventional UNet classification approach, the distance-map regression approach converges faster in clinically relevant parameters. It also produces morphometric parameters that agree with the manually-segmented ground-truth data, namely the average cell density difference of -41.9 cells/mm2 (95% confidence interval (CI) [-306.2, 222.5]) and the average difference of mean cell area of 14.8 µm 2 (95% CI [-41.9, 71.5]). These results suggest a promising alternative for CE assessment.This work has been partly funded by Ministerio de Ciencia, Tecnología e Innovación, Colombia, Project 124489786239 (Contract 763-2021), Universidad Tecnológica de Bolívar (UTB) Project CI2021P02, and Agencia Estatal de Investigación del Gobierno de España (PID2020-114582RB-I00/ AEI / 10.13039/501100011033). J. Sierra thanks UTB for a post-graduate scholarship.Peer ReviewedPostprint (published version

Boost-based MPPT for the MTM PCDU of the Bepicolombo mission

BepiColombo is an ESA mission to Mercury to be launched in 2013. A better knowledge of the origin and evolution of the planet, of its structure and vestigial atmosphere, of its magnetosphere, and of the origin of its magnetic field are the main objectives for the program. The journey to Mercury will last for approximately 6 years, and will be based on the gravity of the Earth, Venus and Mercury, and on the use of Solar Electric Propulsion. For the last, the use of the MPPT concept is essential for the mission. A mission power demand of up to 14kW is foreseen in the cruise phase for the Mercury Transfer Module (MTM) PCDU, being the power subsystem based on a 100V bus. Under this scenario, the use of a classical step-down regulator for the implementation of the MPPT power cell would require to keep the worst case minimum solar array voltage over the bus for any mission operating condition. Then, the maximum solar array voltage would become as high as to overpass the insulating capability of the isolation layer between the solar array cells and the substrate, under the high temperature environment experienced by the spacecraft near Mercury. As a result, the development of a step-up MPPT Array Power Regulator (APR) becomes a critical issue for the mission feasibility. Moreover, due to the hard environment that the solar array will be exposed to, the segregation of the solar array power is a very desirable feature. Furthermore, apart from the two classical operating modes of the APR – conductance or MPPT, depending on the spacecraft user loads demand and the available solar array power – the APR will have to operate in S3R mode for solar array voltages over the bus, with a fully autonomous transition between the three operating modes. This paper covers all the aspects related with the design of the APR MPPT concept and its implementation: APR power cell topology, control scheme, control strategy, protections. The implications on the design of the MTM PCDU MEA will be also addressed. Finally, they will be presented the results of the test carried out over an 1/10 scaled-down engineering model of the BepiColombo PCU - including 3 APRs - in front of the real operating conditions foreseen for the MTM PCDU, including all the relevant issues related to the behaviour of the Electric Propulsion load like beam-out events and load transients

Treatment with tocilizumab or corticosteroids for COVID-19 patients with hyperinflammatory state: a multicentre cohort study (SAM-COVID-19)

Objectives: The objective of this study was to estimate the association between tocilizumab or corticosteroids and the risk of intubation or death in patients with coronavirus disease 19 (COVID-19) with a hyperinflammatory state according to clinical and laboratory parameters. Methods: A cohort study was performed in 60 Spanish hospitals including 778 patients with COVID-19 and clinical and laboratory data indicative of a hyperinflammatory state. Treatment was mainly with tocilizumab, an intermediate-high dose of corticosteroids (IHDC), a pulse dose of corticosteroids (PDC), combination therapy, or no treatment. Primary outcome was intubation or death; follow-up was 21 days. Propensity score-adjusted estimations using Cox regression (logistic regression if needed) were calculated. Propensity scores were used as confounders, matching variables and for the inverse probability of treatment weights (IPTWs). Results: In all, 88, 117, 78 and 151 patients treated with tocilizumab, IHDC, PDC, and combination therapy, respectively, were compared with 344 untreated patients. The primary endpoint occurred in 10 (11.4%), 27 (23.1%), 12 (15.4%), 40 (25.6%) and 69 (21.1%), respectively. The IPTW-based hazard ratios (odds ratio for combination therapy) for the primary endpoint were 0.32 (95%CI 0.22-0.47; p < 0.001) for tocilizumab, 0.82 (0.71-1.30; p 0.82) for IHDC, 0.61 (0.43-0.86; p 0.006) for PDC, and 1.17 (0.86-1.58; p 0.30) for combination therapy. Other applications of the propensity score provided similar results, but were not significant for PDC. Tocilizumab was also associated with lower hazard of death alone in IPTW analysis (0.07; 0.02-0.17; p < 0.001). Conclusions: Tocilizumab might be useful in COVID-19 patients with a hyperinflammatory state and should be prioritized for randomized trials in this situatio