Background. Adequate ventilation is imperative for controlling respiratory transmission, particularly in the context of the COVID-19 pandemic. The commercial portable air cleaners have emerged as practical solutions to reduce contaminated aerosols in dental treatment rooms. This study employs computational fluid dynamics (CFD) to assess their impact on airflow dynamics. Methods. Dental treatment room models were constructed using SolidWorks software, encompassing two distinct air conditioner grille orientations (straightening and 45-degree downward directions) and five different positions for the portable air cleaner (two located at the rear left/right of the dental unit and three at the foot end of the dental unitcenter, left, and right corners). The study examined alterations in airflow direction and residual aerosol concentrations using ANSYS Fluent software. Results. The incorporation of portable air cleaners in dental treatment rooms significantly reduced aerosol levels across all model configurations. Notably, the placement of the portable air cleaner emerged as a critical factor influencing airflow patterns. In models with straightening and 45-degree downward air conditioner grille orientations, optimal positioning was near the operating field and at the foot end of the dental chair, respectively. Conclusion. This investigation highlights the pivotal role of strategic portable air cleaner placement in dental treatment rooms for effective aerosol removal. Placing the air cleaner near the operating field or at the foot end of the dental chair not only improved airflow patterns but also enhanced aerosol removal efficiency, ultimately promoting superior air quality within dental treatment environments.

We present an interface-splitting algorithm (ITS) for solving diagonally dominant tridiagonal systems in parallel. The construction of the ITS algorithm profits from bidirectional links in modern networks, and it only needs one synchronization step to solve the system. The algorithm trades some necessary accuracy for better parallel performance. The accuracy and the performance of the ITS algorithm are evaluated on four different parallel machines of up to 2048 processors. The proposed algorithm scales very well, and it is significantly faster than the algorithm used in ScaLAPACK. The applicability of the algorithm is demonstrated in the three-dimensional simulations of turbulent channel flow at Reynolds number 41,430.

This paper presents the finite-surface method for solving the Navier-Stokes equations (NSE). This method defines the velocities as a surface-averaged value on the surfaces of the pressure cells. Consequently, the mass conservation on the pressure cells becomes an exact equation. The only things left to approximate is the momentum equation and the pressure at the new time step. At certain conditions, the exact mass conservation enables the explicit n-th order accurate NSE solver to be used with the pressure treatment that is two or four order less accurate without losing the apparent convergence rate. This feature was not possible with finite volume of finite difference methods. The convergence rate for laminar flows are presented. In addition to these result which was already presented elsewhere, this work presents a resolution criteria needed to achieve a DNS-like solution. The turbulent channel flow with friction Reynolds number 590 is used in this study. Previously, it was found that a fourth-order scheme is effectively 10X faster than the second-order scheme, at the comparable accuracy. The newly developed sixth-order FSM is 4X faster than the fourth-order scheme and thus it is a very interesting numerical method for solving turbulent flow. This speedup is possible due to the reduction of the number of grid points.

A very-high-order Multi-Moment (MM) framework is developed for the Eulerian convection--diffusion equation in which multiple moments are advanced as independent degrees of freedom rather than reconstructed from a single primary representation. Pointwise and integral moments distributed over complementary geometric entities provide additional subcell information, extending the resolving capability attainable on a fixed grid. A systematic construction is presented up to twenty-fourth order, together with a coupled Fourier analysis that characterizes inter-moment coupling, dispersion, phase velocity, and amplitude behavior. Frontogenesis tests show that the proposed schemes achieve the target accuracy with fewer degrees of freedom than explicit finite-difference methods of equivalent order and provide an average 1.49X speedup across the tested error range. Their resolving efficiency is also competitive with compact finite-difference and discontinuous Galerkin schemes. For nonlinear problems, fourth-order flux correction generally preserves the accuracy advantage of the eighth- and tenth-order MM schemes, while sixth-order correction becomes necessary for the tenth-order scheme only at an error tolerance of 10-5. These results establish independently evolved multi-moment discretization as an efficient strategy for high-order, high-resolution transport simulation. To facilitate reproducibility, the open-source MM2D solver implementation for the Frontogenesis benchmark is made publicly available.