Eigensolution analysis of spectral/hp continuous Galerkin approximations to advection-diffusion problems: insights into spectral vanishing viscosity

AbstractThis study addresses linear dispersion–diffusion analysis for the spectral/hp continuous Galerkin (CG) formulation in one dimension. First, numerical dispersion and diffusion curves are obtained for the advection–diffusion problem and the role of multiple eigencurves peculiar to spectral/hp methods is discussed. From the eigencurves' behaviour, we observe that CG might feature potentially undesirable non-smooth dispersion/diffusion characteristics for under-resolved simulations of problems strongly dominated by either convection or diffusion. Subsequently, the linear advection equation augmented with spectral vanishing viscosity (SVV) is analysed. Dispersion and diffusion characteristics of CG with SVV-based stabilization are verified to display similar non-smooth features in flow regions where convection is much stronger than dissipation or vice-versa, owing to a dependency of the standard SVV operator on a local Péclet number. First a modification is proposed to the traditional SVV scaling that enforces a globally constant Péclet number so as to avoid the previous issues. In addition, a new SVV kernel function is suggested and shown to provide a more regular behaviour for the eigencurves along with a consistent increase in resolution power for higher-order discretizations, as measured by the extent of the wavenumber range where numerical errors are negligible. The dissipation characteristics of CG with the SVV modifications suggested are then verified to be broadly equivalent to those obtained through upwinding in the discontinuous Galerkin (DG) scheme. Nevertheless, for the kernel function proposed, the full upwind DG scheme is found to have a slightly higher resolution power for the same dissipation levels. These results show that improved CG-SVV characteristics can be pursued via different kernel functions with the aid of optimization algorithms

Linear dispersion-diffusion analysis and its application to under-resolved turbulence simulations using discontinuous Galerkin spectral/hp methods

We investigate the potential of linear dispersion–diffusion analysis in providing direct guidelines for turbulence simulations through the under-resolved DNS (sometimes called implicit LES) approach via spectral/hp methods. The discontinuous Galerkin (DG) formulation is assessed in particular as a representative of these methods. We revisit the eigensolutions technique as applied to linear advection and suggest a new perspective to the role of multiple numerical modes, peculiar to spectral/hp methods. From this new perspective, “secondary” eigenmodes are seen to replicate the propagation behaviour of a “primary” mode, so that DG's propagation characteristics can be obtained directly from the dispersion–diffusion curves of the primary mode. Numerical dissipation is then appraised from these primary eigencurves and its effect over poorly-resolved scales is quantified. Within this scenario, a simple criterion is proposed to estimate DG's effective resolution in terms of the largest wavenumber it can accurately resolve in a given hp approximation space, also allowing us to present points per wavelength estimates typically used in spectral and finite difference methods. Although strictly valid for linear advection, the devised criterion is tested against (1D) Burgers turbulence and found to predict with good accuracy the beginning of the dissipation range on the energy spectra of under-resolved simulations. The analysis of these test cases through the proposed methodology clarifies why and how the DG formulation can be used for under-resolved turbulence simulations without explicit subgrid-scale modelling. In particular, when dealing with communication limited hardware which forces one to consider the performance for a fixed number of degrees of freedom, the use of higher polynomial orders along with moderately coarser meshes is shown to be the best way to translate available degrees of freedom into resolution power

Gradient jump penalty stabilisation of spectral/hp element discretisation for under-resolved turbulence simulations

One of the strengths of the discontinuous Galerkin (DG) method has been its balance between accuracy and robustness, which stems from DG’s intrinsic (upwind) dissipation being biased towards high frequencies/wavenumbers. This is particularly useful in high Reynolds-number flow simulations where limitations on mesh resolution typically lead to potentially unstable under-resolved scales. In continuous Galerkin (CG) discretisations, similar properties are achievable through the addition of artificial diffusion, such as spectral vanishing viscosity (SVV). The latter, although recognised as very useful in CG-based high-fidelity turbulence simulations, has been observed to be sub-optimal when compared to DG at intermediate polynomials orders (P ≈ 3). In this paper we explore an alternative stabilisation approach by the introduction of a continuous interior penalty on the gradient discontinuity at elemental boundaries, which we refer to as a gradient jump penalisation (GJP). Analogous to DG methods, this introduces a penalisation at the elemental interfaces as opposed to the interior element stabilisation of SVV. Detailed eigenanalysis of the GJP approach shows its potential as equivalent (sometimes superior) to DG dissipation and hence superior to previous SVV approaches. Through eigenanalysis, a judicious choice of GJP’s P-dependent scaling parameter is made and found to be consistent with previous apriori error analysis. The favourable properties of the GJP stabilisation approach are also supported by turbulent flow simulations of the incompressible Navier-Stokes equation, as we achieve high-quality flow solutions at P = 3 using GJP, whereas SVV performs marginally worse at P = 5 with twice as many degrees of freedom in total

Deformation of the Fermi surface in the extended Hubbard model

The deformation of the Fermi surface induced by Coulomb interactions is investigated in the t-t'-Hubbard model. The interplay of the local U and extended V interactions is analyzed. It is found that exchange interactions V enhance small anisotropies producing deformations of the Fermi surface which break the point group symmetry of the square lattice at the Van Hove filling. This Pomeranchuck instability competes with ferromagnetism and is suppressed at a critical value of U(V). The interaction V renormalizes the t' parameter to smaller values what favours nesting. It also induces changes on the topology of the Fermi surface which can go from hole to electron-like what may explain recent ARPES experiments.Comment: 5 pages, 4 ps figure

Industry-relevant implicit large-eddy simulation of a high-performance road car via spectral/HP element methods

This is the author accepted manuscript. The final version is available from the Society for Industrial and Applied Mathematics via the DOI in this recordWe present a successful deployment of high-fidelity Large-Eddy Simulation (LES) technologies based on spectral/hp element methods to industrial flow problems, which are characterized by high Reynolds numbers and complex geometries. In particular, we describe the numerical methods, software development and steps that were required to perform the implicit LES of a real automotive car, namely the Elemental Rp1 model. To the best of the authors’ knowledge, this simulation represents the first high-order accurate transient LES of an entire real car geometry. Moreover, this constitutes a key milestone towards considerably expanding the computational design envelope currently allowed in industry, where steady-state modelling remains the standard. To this end, a number of novel developments had to be made in order to overcome obstacles in mesh generation and solver technology to achieve this simulation, which we detail in this paper. The main objective is to present to the industrial and applied mathematics community, a viable pathway to translate academic developments into industrial tools, that can substantially advance the analysis and design capabilities of high-end engineering stakeholders. The novel developments and results were achieved using the academic-driven open-source framework Nektar++.Engineering and Physical Sciences Research Council (EPSRC)European Union Horizon 2020Imperial College High Performance Computing ServiceNational University of SingaporeAirbu

Hypercalcemia in a patient with disseminated paracoccidioidomycosis: a case report

<p>Abstract</p> <p>Introduction</p> <p>Hypercalcemia is well described in various granulomatous disorders, such as sarcoidosis, tuberculosis, berylliosis, leprosy and fungal infections. However, the association of <it>Paracoccidioides brasiliensis </it>and hypercalcemia is rare: to the best of our knowledge, only two cases have previously been reported, and neither had a clear documentation of the etiology of the hypercalcemia.</p> <p>Case presentation</p> <p>We report the case of a 22-year-old man in whom disseminated infection with paracoccidioidomycosis was associated with hypercalcemia. The patient had a high normal serum level of 1,25-dihydroxyvitamin D and a suppressed parathyroid hormone value, an indication that the hypercalcemia was not mediated by parathyroid hormone and might be associated with 1,25-dihydroxyvitamin D.</p> <p>Conclusion</p> <p>The episode resolved readily with administration of corticosteroids, an outcome suggesting that this is an effective treatment of hypercalcemia of this origin. On follow-up, while receiving antifungal therapy for <it>P. brasiliensis </it>the patient's calcium values remained normal.</p

Bioelectrochemical conversion of CO2 to value added product formate using engineered Methylobacterium extorquens

The conversion of carbon dioxide to formate is a fundamental step for building C1 chemical platforms. Methylobacterium extorquens AM1 was reported to show remarkable activity converting carbon dioxide into formate. Formate dehydrogenase 1 from M. extorquens AM1 (MeFDH1) was verified as the key responsible enzyme for the conversion of carbon dioxide to formate in this study. Using a 2% methanol concentration for induction, microbial harboring the recombinant MeFDH1 expressing plasmid produced the highest concentration of formate (26.6 mM within 21 hours) in electrochemical reactor. 60 ??M of sodium tungstate in the culture medium was optimal for the expression of recombinant MeFDH1 and production of formate (25.7 mM within 21 hours). The recombinant MeFDH1 expressing cells showed maximum formate productivity of 2.53 mM/g-wet cell/hr, which was 2.5 times greater than that of wild type. Thus, M. extorquens AM1 was successfully engineered by expressing MeFDH1 as recombinant enzyme to elevate the production of formate from CO2 after elucidating key responsible enzyme for the conversion of CO2 to formate

A Comparative Study on Three Analytical Methods for the Determination of the Neurotoxin BMAA in Cyanobacteria

The cyanobacterial neurotoxin β-N-methylamino-L-alanine (BMAA) has been considered a serious health threat because of its putative role in multiple neurodegenerative diseases. First reports on BMAA concentrations in cyanobacteria were alarming: nearly all cyanobacteria were assumed to contain high BMAA concentrations, implying ubiquitous exposure. Recent studies however question this presence of high BMAA concentrations in cyanobacteria. To assess the real risk of BMAA to human health, this discrepancy must be resolved. We therefore tested whether the differences found could be caused by the analytical methods used in different studies. Eight cyanobacterial samples and two control samples were analyzed by three commonly used methods: HPLC-FLD analysis and LC-MS/MS analysis of both derivatized and underivatized samples. In line with published results, HPLC-FLD detected relatively high BMAA concentrations in some cyanobacterial samples, while both LC-MS/MS methods only detected BMAA in the positive control (cycad seed sarcotesta). Because we could eliminate the use of different samples and treatments as causal factors, we demonstrate that the observed differences were caused by the analytical methods. We conclude that HPLC-FLD overestimated BMAA concentrations in some cyanobacterial samples due to its low selectivity and propose that BMAA might be present in (some) cyanobacteria, but in the low µg/g or ng/g range instead of the high µg/g range as sometimes reported before. We therefore recommend to use only selective and sensitive analytical methods like LC-MS/MS for BMAA analysis. Although possibly present in low concentrations in cyanobacteria, BMAA can still form a health risk. Recent evidence on BMAA accumulation in aquatic food chains suggests human exposure through consumption of fish and shellfish which expectedly exceeds exposure through cyanobacteria

Avaliação das técnicas de massagem e ordenha no tratamento do ingurgitamento mamário por termografia

OBJETIVO: evaluar los métodos de masaje y bombeo en el tratamiento de la congestión mamaria posparto a través de la termografía. MÉTODO: el estudio se realizó en el Banco de Leche Humana de un hospital en Curitiba, Brasil. Se seleccionaron al azar 16 mujeres en periodo de lactancia con congestión con clasificación lobar, ampular y glandular, moderada e intensa. Se compararon los patrones diferenciales de temperatura, antes y después del tratamiento por medio de masaje y bombeo. RESULTADOS: se encontró un degradado negativo de 0,3°C de temperatura entre el pre y post-tratamiento en el grupo experimental. Las mamas con intensa congestión eran 0,7°C más caliente en comparación a aquellos con congestión moderada. CONCLUSIÓN: el masaje y el bombeo electromecánico fueron superiores a los métodos manuales cuando se evaluaron por termografía. REBEC: U1111-1136-9027.OBJETIVO: avaliar técnicas de massagem e ordenha no tratamento do ingurgitamento mamário puerperal, por meio da termografia. MÉTODO: a pesquisa foi realizada no Banco de Leite Humano de um hospital de Curitiba, Brasil. Selecionaram-se, aleatoriamente, 16 lactantes com ingurgitamento com classificação lobar, ampolar e glandular moderado e intenso. Compararam-se os padrões diferenciais de temperatura, antes e após o tratamento realizado, por meio de massagem e ordenha. RESULTADOS: constatou-se um gradiente negativo de 0,3ºC de temperatura entre o pré e o pós-tratamento no grupo experimental. Mamas com ingurgitamento intenso foram 0,7ºC mais quentes quando comparadas com ingurgitamento moderado. CONCLUSÃO: a massagem e ordenha eletromecânicas são superiores às manuais, quando avaliadas por termografia. REBEC: U1111-1136-9027.OBJECTIVE: to evaluate techniques of massage and pumping in the treatment of postpartum breast engorgement through thermography. METHOD: the study was conducted in the Human Milk Bank of a hospital in Curitiba, Brazil. We randomly selected 16 lactating women with engorgement with the classification lobar, ampullary and glandular, moderate and intense. We compared the differential patterns of temperature, before and after the treatment by means of massage and pumping. RESULTS: we found a negative gradient of 0.3°C of temperature between the pre- and post-treatment in the experimental group. Breasts with intense engorgement were 0.7°C warmer when compared with moderate engorgement. CONCLUSION: massage and electromechanical pumping were superior to manual methods when evaluated by thermography. REBEC: U1111-1136-9027