Asymptotic behaviour at the wall in compressible turbulent channels

The asymptotic behaviour of Reynolds stresses close to walls is well established in incompressible flows owing to the constraint imposed by the solenoidal nature of the velocity field. For compressible flows, thus, one may expect a different asymptotic behaviour, which has indeed been noted in the literature. However, the transition from incompressible to compressible scaling, as well as the limiting behaviour for the latter, is largely unknown. Thus, we investigate the effects of compressibility on the near-wall, asymptotic behaviour of turbulent fluxes using a large direct numerical simulation (DNS) database of turbulent channel flow at higher than usual wall-normal resolutions. We vary the Mach number at a constant friction Reynolds number to directly assess compressibility effects. We observe that the near-wall asymptotic behaviour for compressible turbulent flow is different from the corresponding incompressible flow even if the mean density variations are taken into account and semi-local scalings are used. For Mach numbers near the incompressible regimes, the near-wall asymptotic behaviour follows the well-known theoretical behaviour. When the Mach number is increased, turbulent fluxes containing wall-normal components show a decrease in the slope owing to increased dilatation effects. We observe that $R_{vv}$ approaches its high-Mach-number asymptote at a lower Mach number than that required for the other fluxes. We also introduce a transition distance from the wall at which turbulent fluxes exhibit a change in scaling exponents. Implications for wall models are briefly presented.

Super-resolution of low-fidelity flow solutions via generative adversarial networks

While computational fluid dynamics (CFD) can solve a wide variety of fluid flow problems, accurate CFD simulations require significant computational resources and time. We propose a general method for super-resolution of low-fidelity flow simulations using deep learning. The approach is based on a conditional generative adversarial network (GAN) with inexpensive, low-fidelity solutions as inputs and high-fidelity simulations as outputs. The details, including the flexible structure, unique loss functions, and handling strategies, are thoroughly discussed, and the methodology is demonstrated using numerical simulations of incompressible flows. The distinction between low- and high-fidelity solutions is made in terms of discretization and physical modeling errors. Numerical experiments demonstrate that the approach is capable of accurately forecasting high-fidelity simulations.

The role of urban development in the formation of a “heat island”

Для оценки роли городской застройки в формировании “острова тепла” и исследования его влияния на распространение загрязняющих веществ разработана микромасштабная математическая модель городской среды. В качестве модельной задачи рассматривалось локальное влияние городской застройки микрорайона г. Красноярска. Установлено, что наибольший вклад в формирование “острова тепла” вносят наружные стены зданий и их верхние конструкции - крыши. При учете теплообмена наблюдаются рост средней скорости воздушного потока внутри квартала и уменьшение низкоскоростных областей более чем на 0.5 м/с. Также выявлено, что при учете теплообмена наблюдается заброс загрязняющих веществ, поступающих от дороги, на б´ольшую высоту, чем без него. Разработанная математическая модель позволяет комплексно подойти к исследованию гидродинамики и прогнозированию экологической обстановки урбанизированных территорий Introduction. The configuration of modern micro districts leads to the formation of zones with low velocity, in which the accumulation of pollutants occurs. On the other hand, during the construction of cities, the surface of the Earth is covered with materials that actively absorb solar radiation, which leads to the formation of an urban heat island. Our work is devoted to the study of the local influence of urban development on the spread of pollutants, which takes into account the above mentioned factors. Mathematical model. For solving our problems we developed the microscale mathematical model based on the Reynolds-averaged Navier-Stokes equations for incompressible flows with variable density. For the correct calculation of the temperature on the surface of buildings, we used a model of conjugate heat transfer with a one-dimensional equation of thermal conductivity. As a model problem, we considered the Krasnoyarsk area with dense development and the presence of a highrise building for two seasons: winter and summer. The source of emission of pollutants was traffic. Results. The results of the calculations show a significant decrease in velocity around buildings. On the contrary, solar radiation leads to the intensification of free convective motion, especially in the surface area. That can double the near-surface velocity compared to the solution that does not account for the heat transfer. Conclusions. The developed mathematical model allows a comprehensive approach to solving hydrodynamic problems of prediction the ecological situation of cities

A Cartesian Method with Second-Order Pressure Resolution for Incompressible Flows with Large Density Ratios

An Eulerian method to numerically solve incompressible bifluid problems with high density ratio is presented. This method can be considered as an improvement of the Ghost Fluid method, with the specificity of a sharp second-order numerical scheme for the spatial resolution of the discontinuous elliptic problem for the pressure. The Navier–Stokes equations are integrated in time with a fractional step method based on the Chorin scheme and discretized in space on a Cartesian mesh. The bifluid interface is implicitly represented using a level-set function. The advantage of this method is its simplicity to implement in a standard monofluid Navier–Stokes solver while being more accurate and conservative than other simple classical bifluid methods. The numerical tests highlight the improvements obtained with this sharp method compared to the reference standard first-order methods.