In this study, we propose a non-linear continuous stochastic velocity process for simulations of monatomic gas flows. The model equation is derived from a FokkerPlanck approximation of the Boltzmann equation. By introducing a cubic non-linear drift term, the model leads to the correct Prandtl number of 2/3 for monatomic gas, which is crucial to study heat transport phenomena. Moreover, a highly accurate scheme to evolve the computational particles in velocity-and physical space is devised. An important property of this integration scheme is that it ensures energy conservation and honours the tortuosity of particle trajectories. Especially in situations with small to moderate Knudsen numbers, this allows to proceed with much larger time steps than with direct simulation Monte Carlo (DSMC), i.e. the mean collision time not necessarily has to be resolved, and thus leads to more efficient simulations. Another computational advantage is that no direct collisions have to be calculated in the proposed algorithm. For validation, different micro-channel flow test cases in the near continuum and transitional regimes were considered. Detailed comparisons with DSMC for Knudsen numbers between 0.07 and 2 reveal that the new solution algorithm based on the Fokker-Planck approximation for the collision operator can accurately predict molecular stresses and heat flux and thus also gas velocity and temperature profiles. Moreover, for the Knudsen Paradox, it is shown that good agreement with DSMC is achieved up to a Knudsen number of about 5.

Relevant pandemic-spread scenario simulations provide guiding principles for containment and mitigation policy developments. Here we devise a simple model to predict the effectiveness of different mitigation strategies. The model consists of a set of simple differential equations considering the population size, reported and unreported infections, reported and unreported recoveries and the number of Covid-19-inflicted deaths. For simplification, we assume that Covid-19 survivors are immune (e.g. mutations are not considered) and that the virus can only be passed on by persons with undetected infections. While the latter assumption is a simplification (it is neglected that e.g. hospital staff may be infected by detected patients with symptoms), it was introduced here to keep the model as simple as possible. Moreover, the current version of the model does not account for age-dependent differences in the death rates, but considers higher mortality rates due to temporary shortage of intensive care units. Some of the model parameters have been fitted to the reported cases outside of China 1 from January 22 to March 12 of the 2020 Covid-19 pandemic. The other parameters were chosen in a plausible range to the best of our knowledge. We compared infection rates, the total number of people getting infected and the number of deaths in six different scenarios. Social distancing or increased testing can contain or drastically reduce the infections and the predicted number of deaths when compared to a situation without mitigation. We find that mass-testing alone and subsequent isolation of detected cases can be an effective mitigation strategy, alone and in combination with social distancing. However, unless one assumes that the virus can be globally defeated by reducing the number of infected persons to zero, testing must be upheld, albeit at reduced intensity, to prevent subsequent waves of infection. The model suggests that testing strategies can be equally effective as social distancing, though at much lower economical costs. We discuss how our mathematical model may help to devise an optimal mix of mitigation strategies against the Covid-19 pandemic. The website corona-lab.ch provides an interactive simulation tool based on the presented model. Lay SummaryThe Covid-19 pandemic is a serious threat that can be mitigated by different strategies. Social isolation is currently practiced in most countries in Europe, at least until alternative mitigation strategies can be implemented or therapies and vaccines become available. We have formulated a simple mathematical model to estimate how well social isolation or improved identification of Covid-19 infected people can slow down virus spread and reduce the death toll.

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A realistic outflow boundary condition model for pulsatile flow in a compliant vessel is studied by taking into account physiological effects: compliance, resistance, and wave reflection of the downstream vasculature. The new model extends the computational domain with an elastic tube terminated in a rigid contraction. The contraction ratio, the length, and elasticity of the terminal tube can be adjusted to represent effects of the truncated vasculature. Using the wave intensity analysis method, we apply the model to the test cases of a straight vessel and the aorta and find good agreement with the physiological characteristics of blood flow and pressure. The model is suitable for cardiac transient (non-periodic) events and easily employed using so-called black box software.

A Fokker–Planck based kinetic model is presented here, which also accounts for internal energy modes characteristic for diatomic gas molecules. The model is based on a Fokker–Planck approximation of the Boltzmann equation for monatomic molecules, whereas phenomenological principles were employed for the derivation. It is shown that the model honors the equipartition theorem in equilibrium and fulfills the Landau–Teller relaxation equations for internal degrees of freedom. The objective behind this approximate kinetic model is accuracy at reasonably low computational cost. This can be achieved due to the fact that the resulting stochastic differential equations are continuous in time; therefore, no collisions between the simulated particles have to be calculated. Besides, because of the devised energy conserving time integration scheme, it is not required to resolve the collisional scales, i.e., the mean collision time and the mean free path of molecules. This, of course, gives rise to much more efficient simulations with respect to other particle methods, especially the conventional direct simulation Monte Carlo (DSMC), for small and moderate Knudsen numbers. To examine the new approach, first the computational cost of the model was compared with respect to DSMC, where significant speed up could be obtained for small Knudsen numbers. Second, the structure of a high Mach shock (in nitrogen) was studied, and the good performance of the model for such out of equilibrium conditions could be demonstrated. At last, a hypersonic flow of nitrogen over a wedge was studied, where good agreement with respect to DSMC (with level to level transition model) for vibrational and translational temperatures is shown.

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In February 2021, in response to emergence of more transmissible SARS-CoV-2 virus variants, the Canton Grisons launched a unique RNA mass testing program targeting the labour force in local businesses. Employees were offered weekly tests free of charge and on a voluntary basis. If tested positive, they were required to self-isolate for ten days and their contacts were subjected to daily testing at work. Thereby, the quarantine of contact persons could be waved.Here, we evaluate the effects of the testing program on the tested cohorts. We examined 121,364 test results from 27,514 participants during February–March 2021. By distinguishing different cohorts of employees, we observe a noticeable decrease in the test positivity rate and a statistically significant reduction in the associated incidence rate over the considered period. The reduction in the latter ranges between 18 and 50%. The variability is partly explained by different exposures to exogenous infection sources (e.g., contacts with visiting tourists or cross-border commuters). Our analysis provides the first empirical evidence that applying repetitive mass testing to a real population over an extended period of time can prevent spread of COVID-19 pandemic. However, to overcome logistic, uptake, and adherence challenges it is important that the program is carefully designed and that disease incursion from the population outside of the program is considered and controlled.