A recent study reported that an aerosolized virus (COVID-19) can survive in the air for a few hours. It is highly possible that people get infected with the disease by breathing and contact with items contaminated by the aerosolized virus. However, the aerosolized virus transmission and trajectories in various meteorological environments remain unclear. This paper has investigated the movement of aerosolized viruses from a high concentration source across a dense urban area. The case study looks at the highly air polluted areas of London: University College Hospital (UCH) and King's Cross and St Pancras International Station (KCSPI). We explored the spread and decay of COVID-19 released from the hospital and railway stations with the prescribed meteorological conditions. The study has three key findings: the primary result is that the concentration of viruses decreases rapidly by a factor of 2–3 near the sources although the virus may travel from meters up to hundreds of meters from the source location for certain meteorological conditions. The secondary finding shows viruses released into the atmosphere from entry and exit points at KCSPI remain trapped within a small radial distance of < 50 m. This strengthens the case for the use of face coverings to reduce the infection rate. The final finding shows that there are different levels of risk at various door locations for UCH; depending on which door is used there can be a higher concentration of COVID-19. Although our results are based on London, since the fundamental knowledge processes are the same, our study can be further extended to other locations (especially the highly air polluted areas) in the world.

In this study, an alternative local Galerkin method (LGM), the o3o3 scheme, is proposed. o3o3 is a variant or generalization of the third-order spectral element method (SEM3). It uses third-order piecewise polynomials for the representation of a field and piecewise third-degree polynomials for fluxes. For the discretization, SEM3 uses the irregular Legendre–Gauss–Lobatto grid while o3o3 uses a regular collocation grid. o3o3 can be regarded as an inhomogeneous finite-difference scheme on a uniform grid, which means that the finite-difference equations are different for each group with three points. A particular version of o3o3 is set as an example of many possibilities to construct LGM schemes on piecewise polynomial spaces in which the basis functions used are continuous at corner points and function spaces having continuous derivatives are shortly discussed. We propose a standard o3o3 scheme and a spectral o3o3 scheme as alternatives to the standard method of using the quadrature approximation. These two particular schemes selected were chosen for ease of implementation rather than optimal performance. In one dimension, compared to standard SEM3, o3o3 has a larger CFL condition benefiting from the use of a regular collocation grid. While SEM3 uses the irregular Legendre–Gauss–Lobatto collocation grid, o3o3 uses a regular grid. This is considered an advantage for physical parameterizations. The shortest resolved wave is marginally smaller than that with SEM3. In two dimensions, o3o3 is implemented on a sparse grid where only a part of the points on the underlying regular grid are used for forecasting.

Adaptive meshes are pivotal in numerical modeling and simulation, offering a means to efficiently, precisely, and flexibly represent intricate physical phenomena, particularly when grappling with their intricacies and varying scales. However, the transition from two dimensions (2D) to three dimensions (3D) poses a substantial challenge, as the computational demands of dynamically adaptive mesh techniques increase exponentially. Addressing this challenge effectively, we turn to the cutting-edge realm of artificial intelligence and neural networks. In our study, we harness the innovative power of a long short-term memory (LSTM) neural network as an error estimator for adapting unstructured meshes in both 2D and 3D scenarios. This LSTM network predicts the evolution of the adaptive grid based on specified variables, presenting itself as an artificial intelligence-driven architecture to optimize the adaptive criterion for the target variable. This is achieved by establishing a direct correspondence between the Riemann metric and these variables. To demonstrate the practical applicability of our approach, we seamlessly integrate the LSTM error estimator into the 3D adaptive atmospheric model Fluidity-Atmosphere (Fluidity-Atmos), thereby enabling real-time mesh adaptation during numerical simulations. We assess the effectiveness of this method in terms of simulation precision and computational efficiency through a series of experiments in both 2D and 3D settings. Our results not only reveal that the mesh patterns generated by the LSTM error estimator within Fluidity-Atmos closely resemble those produced by traditional error estimators but also underscore its superior performance in enhancing simulation accuracy. Notably, as the number of nodes increases, the LSTM mesh generator substantially reduces CPU time requirements by up to 50% in 3D cases compared to the conventional mesh generator within Fluidity-Atmos, highlighting its remarkable computational efficiency.

Advection errors are common in basic terrain-following (TF) coordinates. Numerous methods, including the hybrid TF coordinate and smoothing vertical layers, have been proposed to reduce the advection errors. Advection errors are affected by the directions of velocity fields and the complexity of the terrain. In this study, an unstructured adaptive mesh together with the discontinuous Galerkin finite element method is employed to reduce advection errors over steep terrains. To test the capability of adaptive meshes, five two-dimensional (2D) idealized tests are conducted. Then, the results of adaptive meshes are compared with those of cut-cell and TF meshes. The results show that using adaptive meshes reduces the advection errors by one to two orders of magnitude compared to the cut-cell and TF meshes regardless of variations in velocity directions or terrain complexity. Furthermore, adaptive meshes can reduce the advection errors when the tracer moves tangentially along the terrain surface and allows the terrain to be represented without incurring in severe dispersion. Finally, the computational cost is analyzed. To achieve a given tagging criterion level, the adaptive mesh requires fewer nodes, smaller minimum mesh sizes, less runtime and lower proportion between the node numbers used for resolving the tracer and each wavelength than cut-cell and TF meshes, thus reducing the computational costs.