Effects of discrete energy and helicity conservation in numerical simulations of helical turbulence

Helicity is the scalar product between velocity and vorticity and, just like energy, its integral is an in-viscid invariant of the three-dimensional incompressible Navier-Stokes equations. However, space-and time-discretization methods typically corrupt this property, leading to violation of the inviscid conservation principles. This work investigates the discrete helicity conservation properties of spectral and finite-differencing methods, in relation to the form employed for the convective term. Effects due to Runge-Kutta time-advancement schemes are also taken into consideration in the analysis. The theoretical results are proved against inviscid numerical simulations, while a scale-dependent analysis of energy, helicity and their non-linear transfers is performed to further characterize the discretization errors of the different forms in forced helical turbulence simulations

An effective criterion for periodicity of l-adic continued fractions

The theory of continued fractions has been generalized to l-adic numbers by several authors and presents many differences with respect to the real case. In the present paper we investigate the expansion of rationals and quadratic irrationals for the l-adic continued fractions introduced by Ruban. In this case, rational numbers may have a periodic non-terminating continued fraction expansion, moreover, for quadratic irrational numbers, no analogue of Lagrange's theorem holds. We give general explicit criteria to establish the periodicity of the expansion in both the rational and the quadratic case (for rationals, the qualitative result is due to Laohakosol).Comment: 25 pages. Improved version, Math. Comp. 201

Modeling growth, containment and decay of the COVID-19 epidemic in Italy

A careful inspection of the cumulative curve of confirmed COVID-19 infections in Italy and in other hard-hit countries reveals three distinct phases: i) an initial exponential growth (unconstrained phase), ii) an algebraic, power-law growth (containment phase), and iii) a relatively slow decay. We propose a parsimonious compartment model based on a time-dependent rate of depletion of the susceptible population that captures all such phases for a plausible range of model parameters. The results suggest an intimate interplay between the growth behavior, the timing and implementation of containment strategies, and the subsequent saturation of the outbreak.Peer ReviewedPostprint (published version

Moving beyond size: vorticity and energy loss are correlated with right ventricular dysfunction and exercise intolerance in repaired Tetralogy of Fallot

Background The global effect of chronic pulmonary regurgitation (PR) on right ventricular (RV) dilation and dysfunction in repaired Tetralogy of Fallot (rTOF) patients is well studied by cardiovascular magnetic resonance (CMR). However, the links between PR in the RV outflow tract (RVOT), RV dysfunction and exercise intolerance are not clarified by conventional measurements. Not all patients with RV dilation share the same intracardiac flow characteristics, now measurable by time resolved three-dimensional phase contrast imaging (4D flow). In our study, we quantified regional vorticity and energy loss in rTOF patients and correlated these parameters with RV dysfunction and exercise capacity. Methods rTOF patients with 4D flow datasets were retrospectively analyzed, including those with transannular/infundibular repair and conduit repair. Normal controls and RV dilation patients with atrial-level shunts (Qp:Qs¿>¿1.2:1) were included for comparison. 4D flow was post-processed using IT Flow (Cardioflow, Japan). Systolic/diastolic vorticity (¿, 1/s) and viscous energy loss (VEL, mW) in the RVOT and RV inflow were measured. To characterize the relative influence of diastolic vorticity in the two regions, an RV Diastolic Vorticity Quotient (¿RVOT-Diastole/¿RV Inflow-Diastole, RV-DVQ) was calculated. Additionally, RVOT Vorticity Quotient (¿RVOT-Diastole/¿RVOT-Systole, RVOT-VQ) and RVOT Energy Quotient (VELRVOT-Diastole/VELRVOT-Systole, RVOT-EQ) was calculated. In rTOF, measurements were correlated against conventional CMR and exercise stress test results. Results 58 rTOF patients, 28 RV dilation patients and 12 controls were included. RV-DVQ, RVOT-VQ, and RVOT-EQ were highest in rTOF patients with severe PR compared to rTOF patients with non-severe PR, RV dilation and controls (p¿<¿0.001). RV-DVQ positively correlated with RV end-diastolic volume (0.683, p¿<¿0.001), PR fraction (0.774, p¿<¿0.001) and negatively with RV ejection fraction (- 0.521, p¿=¿0.003). Both RVOT-VQ, RVOT-EQ negatively correlated with VO2-max (- 0.587, p¿=¿0.008 and - 0.617, p¿=¿0.005) and % predicted VO2-max (- 0.678, p¿=¿0.016 and - 0.690, p¿=¿0.001). Conclusions In rTOF patients, vorticity and energy loss dominate the RVOT compared to tricuspid inflow, correlating with RV dysfunction and exercise intolerance. These 4D flow-based measurements may be sensitive biomarkers to guide surgical management of rTOF patients.Peer ReviewedPostprint (published version

Effects of discrete energy and helicity conservation in numerical simulations of helical turbulence

Helicity is the scalar product between velocity and vorticity and, just like energy, its integral is an inviscid invariant of the three-dimensional incompressible Navier-Stokes equations. However, space- and time-discretization methods typically corrupt this prop- erty, leading to violation of the inviscid conservation principles. This work investigates the discrete helicity conservation properties of spectral and finite-differencing methods, in relation to the form employed for the convective term. Effects due to Runge-Kutta time- advancement schemes are also taken into consideration in the analysis. The theoretical results are proved against inviscid numerical simulations, while a scale-dependent analy- sis of energy, helicity and their non-linear transfers is performed to further characterize the discretization errors of the different forms in forced helical turbulence simulations.Postprint (published version

Cardiovascular magnetic resonance in right heart and pulmonary circulation disorders

Peer ReviewedPostprint (author's final draft

LEM characterization of synthetic jet actuators driven by piezoelectric element: a review

In the last decades, Synthetic jet actuators have gained much interest among the flow control techniques due to their short response time, high jet velocity and absence of traditional piping, which matches the requirements of reduced size and low weight. A synthetic jet is generated by the diaphragm oscillation (generally driven by a piezoelectric element) in a relatively small cavity, producing periodic cavity pressure variations associated with cavity volume changes. The pressured air exhausts through an orifice, converting diaphragm electrodynamic energy into jet kinetic energy. This review paper considers the development of various Lumped-Element Models (LEMs) as practical tools to design and manufacture the actuators. LEMs can quickly predict device performances such as the frequency response in terms of diaphragm displacement, cavity pressure and jet velocity, as well as the efficiency of energy conversion of input Joule power into useful kinetic power of air jet. The actuator performance is also analyzed by varying typical geometric parameters such as cavity height and orifice diameter and length, through a suited dimensionless form of the governing equations. A comprehensive and detailed physical modeling aimed to evaluate the device efficiency is introduced, shedding light on the different stages involved in the process. Overall, the influence of the coupling degree of the two oscillators, the diaphragm and the Helmholtz frequency, on the device performance is discussed throughout the paper.Peer ReviewedPostprint (published version

Reference ranges of left ventricular hemodynamic forces in healthy adults: a speckle-tracking echocardiographic study

Background: The normal limits of left ventricular (LV) hemodynamic forces (HDFs) are not exactly known. The aim of this study was to explore the full spectrum of HDF parameters in healthy subjects and determine their physiologic correlates. Methods: 269 healthy subjects were enrolled (mean age: 43 ± 14 years; 123 (45.7%) men). All participants underwent an echo-Doppler examination. Tri-plane tissue tracking from apical views was used to measure 2D global endocardial longitudinal strain (GLS), circumferential strain (GCS), and LV HDFs. HDFs were normalized with LV volume and divided by specific weight. Results: LV systolic longitudinal HDFs (%) were higher in men (20.8 ± 6.5 vs. 18.9 ± 5.6, p = 0.009; 22.0 ± 6.7 vs. 19.8 ± 5.6, p = 0.004, respectively). There was a significant correlation between GCS (increased) (r = -0.240, p < 0.001) and LV longitudinal HDFs (reduced) (r = -0.155, p = 0.01) with age. In a multivariable analysis age, BSA, pulse pressure, heart rate and GCS were the only independent variables associated with LV HDFs (ß coefficient = -0.232, p < 0.001; 0.149, p = 0.003; 0.186, p < 0.001; 0.396, p < 0.001; -0.328, p < 0.001; respectively). Conclusion: We report on the physiologic range of LV HDFs. Knowledge of reference values of HDFs may prompt their implementation into clinical routine and allow a more comprehensive assessment of the LV function.Postprint (published version

Numerical and experimental characterization of a double-orifice synthetic jet actuator

A complete investigation of a double- orifice synthetic jet actuator, focused on the device frequency response in terms of jet velocity, has been carried out. Numerical simulations have shown that, in many operation conditions, the flow within the actuator cavity can be considered as divided in two sub-volumes, each characterized by its own flow field. An analytical approach, based on the previous con- sideration, has allowed to obtain simple relationships for the three resonance frequencies and to provide further insights on the jets formation. The model has been validated through experimental tests carried out on two actuators manufactured in-house, having different geometrical and mechanical characteristics. Comparisons with the behavior of the twin single- orifice device have been discussed and useful consid- erations on the prediction of the actual formation of the synthetic jet are included .Postprint (published version

A conservative overlap method for multi-block parallelization of compact finite-volume schemes

A conservative approach for MPI-based parallelization of tridiagonal compact schemes is developed in the context of multi-block finite-volume methods. For each block, an enlarged linear system is solved by overlapping a certain number of neighbour cells from adjacent sub-domains. The values at block-to-block boundary faces are evaluated by a high-order centered approximation formula. Unlike previous methods, conservation is retained by properly re-computing the common interface value between two neighbouring blocks. Numerical tests show that parallelization artifacts decrease significantly as the number of overlapping cells is increased, at some expense of parallel efficiency. A reasonable trade-off between accuracy and performances is discussed in the paper with reference to both the spectral properties of the method and the results of fully turbulent numerical simulations.Peer ReviewedPostprint (published version