High order pressure-based semi-implicit IMEX schemes for the 3D Navier-Stokes equations at all Mach numbers


Walter Boscheri, Lorenzo Pareschi (4/8/2020 preprint arXiv:2008.01789)

This article aims at developing a high order pressure-based solver for the solution of the 3D compressible Navier-Stokes system at all Mach numbers. We propose a cell-centered discretization of the governing equations that splits the fluxes into a fast and a slow scale part, that are treated implicitly and explicitly, respectively. A novel semi-implicit discretization is proposed for the kinetic energy as well as the enthalpy fluxes in the energy equation, hence avoiding any need of iterative solvers. The implicit discretization yields an elliptic equation on the pressure that can be solved for both ideal gas and general equation of state (EOS).

Hyperbolic models for the spread of epidemics on networks: kinetic description and numerical methods

Giulia Bertaglia, Lorenzo Pareschi (8/7/2020, preprint arXiv:2007.04019)

We consider the development of hyperbolic transport models for the propagation in space of an epidemic phenomenon described by a classical compartmental dynamics. The model is based on a kinetic description at discrete velocities of the spatial movement and interactions of a population of susceptible, infected and recovered individuals. Thanks to this, the unphysical feature of instantaneous diffusive effects, which is typical of parabolic models, is removed. In particular, we formally show how such reaction-diffusion models are recovered in an appropriate diffusive limit.

Uncertainty quantification of viscoelastic parameters in arterial hemodynamics with the a-FSI blood flow model




Giulia Bertaglia, Valerio Caleffi, Lorenzo Pareschi, Alessandro Valiani (3/7/2020 preprint arXiv:2007.01907)

This work aims at identifying and quantifying uncertainties related to elastic and viscoelastic parameters, which characterize the arterial wall behavior, in one-dimensional modeling of the human arterial hemodynamics. The chosen uncertain parameters are modeled as random Gaussian-distributed variables, making stochastic the system of governing equations. The proposed methodology is initially discussed for a model equation, presenting a thorough convergence study which confirms the spectral accuracy of the stochastic collocation method and the second-order of accuracy of the IMEX finite volume scheme chosen to solve the mathematical model.

Relaxing lockdown measures in epidemic outbreaks using selective socio-economic containment with uncertainty

Giacomo Albi, Lorenzo Pareschi, Mattia Zanella (13/5/2020 medRxiv preprint doi: 10.1101/2020.05.12.20099721)

After an initial phase characterized by the introduction of timely and drastic containment measures aimed at stopping the epidemic contagion from SARS-CoV2, many governments are preparing to relax such measures in the face of a severe economic crisis caused by lockdowns. Assessing the impact of such openings in relation to the risk of a resumption of the spread of the disease is an extremely difficult problem due to the many unknowns concerning the actual number of people infected, the actual reproduction number and infection fatality rate of the disease. In this work, starting from a compartmental model with a social structure, we derive models with multiple feedback controls depending on the social activities that allow to assess the impact of a selective relaxation of the containment measures in the presence of uncertain data.