The structure of hypersonic shock waves using Navier-Stokes equations modified to include mass diffusion

Howard Brenner has recently proposed modifications to the Navier-Stokes equations that relate to a diffusion of fluid volume that would be significant for flows with high density gradients. In a previous paper (Greenshields & Reese, 2007), we found these modifications gave good predictions of the viscous structure of shock waves in argon in the range Mach 1.0-12.0 (while conventional Navier-Stokes equations are known to fail above about Mach 2). However, some areas of concern with this model were a somewhat arbitrary choice of modelling coefficient, and potentially unphysical and unstable solutions. In this paper, we therefore present slightly different modifications to include molecule mass diffusion fully in the Navier-Stokes equations. These modifications are shown to be stable and produce physical solutions to the shock problem of a quality broadly similar to those from the family of extended hydrodynamic models that includes the Burnett equations. The modifications primarily add a diffusion term to the mass conservation equation, so are at least as simple to solve as the Navier-Stokes equations; there are none of the numerical implementation problems of conventional extended hydrodynamics models, particularly in respect of boundary conditions. We recommend further investigation and testing on a number of different benchmark non-equilibrium flow cases.Comment: written for the 2nd European Conference on AeroSpace Sciences (EUCASS), Belgium, 200

The structure of shock waves as a test of Brenner's modifications to the Navier-Stokes equations

Brenner has recently proposed modifications to the Navier-Stokes equations that are based on theoretical arguments but supported only by experiments having a fairly limited range. These modifications relate to a diffusion of fluid volume that would be significant for flows with high density gradients. So the viscous structure of shock waves in gases should provide an excellent test case for this new model. In this paper we detail the shock structure problem and propose exponents for the gas viscosity-temperature relation based on empirical viscosity data that is independent of shock experiments. We then simulate shocks in the range Mach 1.0-12.0 using the Navier-Stokes equations, both with and without Brenner's modifications. Initial simulations showed Brenner's modifications display unphysical behaviour when the coefficient of volume diffusion exceeds the kinematic viscosity. Our subsequent analyses attribute this behaviour to both an instability to temporal disturbances and a spurious phase velocity-frequency relationship. On equating the volume diffusivity to the kinematic viscosity, however, we find the results with Brenner's modifications are significantly better than those of the standard Navier-Stokes equations, and broadly similar to those from the family of extended hydrodynamic models that includes the Burnett equations. Brenner's modifications add only two terms to the Navier-Stokes equations, and the numerical implementation is much simpler than conventional extended hydrodynamic models, particularly in respect of boundary conditions. We recommend further investigation and testing on a number of different benchmark non-equilibrium flow cases

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS

Implementation of semi-discrete, non-staggered central schemes in a colocated, polyhedral, finite volume framework, for high-speed viscous flow

Prevalence of Clinical and Subclinical Myocarditis in Competitive Athletes With Recent SARS-CoV-2 Infection: Results From the Big Ten COVID-19 Cardiac Registry

Importance: Myocarditis is a leading cause of sudden death in competitive athletes. Myocardial inflammation is known to occur with SARS-CoV-2. Different screening approaches for detection of myocarditis have been reported. The Big Ten Conference requires comprehensive cardiac testing including cardiac magnetic resonance (CMR) imaging for all athletes with COVID-19, allowing comparison of screening approaches. Objective: To determine the prevalence of myocarditis in athletes with COVID-19 and compare screening strategies for safe return to play. Design, Setting, and Participants: Big Ten COVID-19 Cardiac Registry principal investigators were surveyed for aggregate observational data from March 1, 2020, through December 15, 2020, on athletes with COVID-19. For athletes with myocarditis, presence of cardiac symptoms and details of cardiac testing were recorded. Myocarditis was categorized as clinical or subclinical based on the presence of cardiac symptoms and CMR findings. Subclinical myocarditis classified as probable or possible myocarditis based on other testing abnormalities. Myocarditis prevalence across universities was determined. The utility of different screening strategies was evaluated. Exposures: SARS-CoV-2 by polymerase chain reaction testing. Main Outcome and Measure: Myocarditis via cardiovascular diagnostic testing. Results: Representing 13 universities, cardiovascular testing was performed in 1597 athletes (964 men [60.4%]). Thirty-seven (including 27 men) were diagnosed with COVID-19 myocarditis (overall 2.3%; range per program, 0%-7.6%); 9 had clinical myocarditis and 28 had subclinical myocarditis. If cardiac testing was based on cardiac symptoms alone, only 5 athletes would have been detected (detected prevalence, 0.31%). Cardiac magnetic resonance imaging for all athletes yielded a 7.4-fold increase in detection of myocarditis (clinical and subclinical). Follow-up CMR imaging performed in 27 (73.0%) demonstrated resolution of T2 elevation in all (100%) and late gadolinium enhancement in 11 (40.7%). Conclusions and Relevance: In this cohort study of 1597 US competitive athletes with CMR screening after COVID-19 infection, 37 athletes (2.3%) were diagnosed with clinical and subclinical myocarditis. Variability was observed in prevalence across universities, and testing protocols were closely tied to the detection of myocarditis. Variable ascertainment and unknown implications of CMR findings underscore the need for standardized timing and interpretation of cardiac testing. These unique CMR imaging data provide a more complete understanding of the prevalence of clinical and subclinical myocarditis in college athletes after COVID-19 infection. The role of CMR in routine screening for athletes safe return to play should be explored further