We investigate the temporal accuracy of two generalized-schemes for the incompressible Navier-Stokes equations. In a widely-adopted approach, the pressure is collocated at the time step t n + 1 while the remainder of the Navier-Stokes equations is discretized following the generalized-scheme. That scheme has been claimed to be second-order accurate in time. We developed a suite of numerical code using inf-sup stable higher-order non-uniform rational B-spline (NURBS) elements for spatial discretization. In doing so, we are able to achieve high spatial accuracy and to investigate asymptotic temporal convergence behavior. Numerical evidence suggests that only first-order accuracy is achieved, at least for the pressure, in this aforesaid temporal discretization approach. On the other hand, evaluating the pressure at the intermediate time step t n+ f recovers second-order accuracy, and the numerical implementation is simplified. We recommend this second approach as the generalized-scheme of choice when integrating the incompressible Navier-Stokes equations.

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The timing and sequence of safe campus reopening has remained the most controversial topic in higher education since the outbreak of the COVID-19 pandemic. By the end of March 2020, almost all colleges and universities in the United States had transitioned to an all online education and many institutions have not yet fully reopened to date. For a residential campus like Stanford University, the major challenge of reopening is to estimate the number of incoming infectious students at the first day of class. Here we learn the number of incoming infectious students using Bayesian inference and perform a series of retrospective and projective simulations to quantify the risk of campus reopening. We create a physics-based probabilistic model to infer the local reproduction dynamics for each state and adopt a network SEIR model to simulate the return of all undergraduates, broken down by their year of enrollment and state of origin. From these returning student populations, we predict the outbreak dynamics throughout the spring, summer, fall, and winter quarters using the inferred reproduction dynamics of Santa Clara County. We compare three different scenarios: the true outbreak dynamics under the wild-type SARS-CoV-2, and the hypothetical outbreak dynamics under the new COVID-19 variants B.1.1.7 and B.1.351 with 56% and 50% increased transmissibility. Our study reveals that even small changes in transmissibility can have an enormous impact on the overall case numbers. With no additional countermeasures, during the most affected quarter, the fall of 2020, there would have been 203 cases under base-line reproduction, compared to 4727 and 4256 cases for the B.1.1.7 and B.1.351 variants. Our results suggest that population mixing presents an increased risk for local outbreaks, especially with new and more infectious variants emerging across the globe. Tight outbreak control through mandatory quarantine and test-trace-isolate strategies will be critical in successfully managing these local outbreak dynamics.

The timing and sequence of safe campus reopening has remained the most controversial topic in higher education since the outbreak of the COVID-19 pandemic. By the end of March 2020, almost all colleges and universities in the United States had transitioned to an all online education and many institutions have not yet fully reopened to date. For a residential campus like Stanford University, the major challenge of reopening is to estimate the number of incoming infectious students at the first day of class. Here we learn the number of incoming infectious students using Bayesian inference and perform a series of retrospective and projective simulations to quantify the risk of campus reopening. We create a physics-based probabilistic model to infer the local reproduction dynamics for each state and adopt a network SEIR model to simulate the return of all undergraduates, broken down by their year of enrollment and state of origin. From these returning student populations, we predict the outbreak dynamics throughout the spring, summer, fall, and winter quarters using the inferred reproduction dynamics of Santa Clara County. We compare three different scenarios: the true outbreak dynamics under the wild-type SARS-CoV-2, and the hypothetical outbreak dynamics under the new COVID-19 variants B.1.1.7 and B.1.351 with 56% and 50% increased transmissibility. Our study reveals that even small changes in transmissibility can have an enormous impact on the overall case numbers. With no additional countermeasures, during the most affected quarter, the fall of 2020, there would have been 203 cases under baseline reproduction, compared to 4727 and 4256 cases for the B.1.1.7 and B.1.351 variants. Our results suggest that population mixing presents an increased risk for local outbreaks, especially with new and more infectious variants emerging across the globe. Tight outbreak control through mandatory quarantine and test-trace-isolate strategies will be critical in successfully managing these local outbreak dynamics.

No abstract