Lattice Boltzmann Model for The Volume-Averaged Navier-Stokes Equations

A numerical method, based on the discrete lattice Boltzmann equation, is presented for solving the volume-averaged Navier-Stokes equations. With a modified equilibrium distribution and an additional forcing term, the volume-averaged Navier-Stokes equations can be recovered from the lattice Boltzmann equation in the limit of small Mach number by the Chapman-Enskog analysis and Taylor expansion. Due to its advantages such as explicit solver and inherent parallelism, the method appears to be more competitive with traditional numerical techniques. Numerical simulations show that the proposed model can accurately reproduce both the linear and nonlinear drag effects of porosity in the fluid flow through porous media.Comment: 9 pages, 2 figure

Towards dual consistency of the dual weighted residual method based on a Newton-GMG framework for steady Euler equations

The dual consistency, which is an important issue in developing dual-weighted residual error estimation towards the goal-oriented mesh adaptivity, is studied in this paper both theoretically and numerically. Based on the Newton-GMG solver, dual consistency had been discussed in detail to solve the steady Euler equations. Theoretically, based on the Petrov-Galerkin method, the primal and dual problems, as well as the dual consistency, are deeply studied. It is found that dual consistency is important both for error estimation and stable convergence rate for the quantity of interest. Numerically, through the boundary modification technique, dual consistency can be guaranteed for the problem with general configuration. The advantage of taking care of dual consistency on the Newton-GMG framework can be observed clearly from numerical experiments, in which an order of magnitude savings of mesh grids can be expected for calculating the quantity of interest, compared with the dual-inconsistent implementation. Besides, the convergence behavior from the dual-consistent algorithm is stable, which guarantees the precisions would be better with the refinement in this framework.Comment: In this work, we validated the dual consistency under the Newton-GMG framework. Based on the previous work, we further constructed the h-adaptivity method for the steady Euler equations in the AFVM4CFD packag

Towards the efficient calculation of quantity of interest from steady Euler equations II: a CNNs-based automatic implementation

In \cite{wang2023towards}, a dual-consistent dual-weighted residual-based $h$-adaptive method has been proposed based on a Newton-GMG framework, towards the accurate calculation of a given quantity of interest from Euler equations. The performance of such a numerical method is satisfactory, i.e., the stable convergence of the quantity of interest can be observed in all numerical experiments. In this paper, we will focus on the efficiency issue to further develop this method, since efficiency is vital for numerical methods in practical applications such as the optimal design of the vehicle shape. Three approaches are studied for addressing the efficiency issue, i.e., i). using convolutional neural networks as a solver for dual equations, ii). designing an automatic adjustment strategy for the tolerance in the $h$-adaptive process to conduct the local refinement and/or coarsening of mesh grids, and iii). introducing OpenMP, a shared memory parallelization technique, to accelerate the module such as the solution reconstruction in the method. The feasibility of each approach and numerical issues are discussed in depth, and significant acceleration from those approaches in simulations can be observed clearly from a number of numerical experiments. In convolutional neural networks, it is worth mentioning that the dual consistency plays an important role to guarantee the efficiency of the whole method and that unstructured meshes are employed in all simulations.Comment: In this papers, we use the CNNs architecture to solve the dual equations proble

Water use efficiency of China\u27s terrestrial ecosystems and responses to drought

Water use efficiency (WUE) measures the trade-off between carbon gain and water loss of terrestrial ecosystems, and better understanding its dynamics and controlling factors is essential for predicting ecosystem responses to climate change. We assessed the magnitude, spatial patterns, and trends of WUE of China’s terrestrial ecosystems and its responses to drought using a process-based ecosystem model. During the period from 2000 to 2011, the national average annual WUE (net primary productivity (NPP)/evapotranspiration (ET)) of China was 0.79 g C kg−1 H2O. Annual WUE decreased in the southern regions because of the decrease in NPP and the increase in ET and increased in most northern regions mainly because of the increase in NPP. Droughts usually increased annual WUE in Northeast China and central Inner Mongolia but decreased annual WUE in central China. “Turning-points” were observed for southern China where moderate and extreme droughts reduced annual WUE and severe drought slightly increased annual WUE. The cumulative lagged effect of drought on monthly WUE varied by region. Our findings have implications for ecosystem management and climate policy making. WUE is expected to continue to change under future climate change particularly as drought is projected to increase in both frequency and severity

Refinements of Aczél-Type Inequality and Their Applications

We present some new sharpened versions of Aczél-type inequality. Moreover, as applications, some refinements of integral type of Aczél-type inequality are given

The 2010 spring drought reduced primary productivity in southwestern China

Many parts of the world experience frequent and severe droughts. Summer drought can significantly reduce primary productivity and carbon sequestration capacity. The impacts of spring droughts, however, have received much less attention. A severe and sustained spring drought occurred in southwestern China in 2010. Here we examine the influence of this spring drought on the primary productivity of terrestrial ecosystems using data on climate, vegetation greenness and productivity. We first assess the spatial extent, duration and severity of the drought using precipitation data and the Palmer drought severity index. We then examine the impacts of the drought on terrestrial ecosystems using satellite data for the period 2000–2010. Our results show that the spring drought substantially reduced the enhanced vegetation index (EVI) and gross primary productivity (GPP) during spring 2010 (March–May). Both EVI and GPP also substantially declined in the summer and did not fully recover from the drought stress until August. The drought reduced regional annual GPP and net primary productivity (NPP) in 2010 by 65 and 46 Tg C yr−1, respectively. Both annual GPP and NPP in 2010 were the lowest over the period 2000–2010. The negative effects of the drought on annual primary productivity were partly offset by the remarkably high productivity in August and September caused by the exceptionally wet conditions in late summer and early fall and the farming practices adopted to mitigate drought effects. Our results show that, like summer droughts, spring droughts can also have significant impacts on vegetation productivity and terrestrial carbon cycling

Quantifying the effects of harvesting on carbon fluxes and stocks in northern temperate forests

Harvest disturbance has substantial impacts on forest carbon (C) fluxes and stocks. The quantification of these effects is essential for the better understanding of forest C dynamics and informing forest management in the context of global change. We used a process-based forest ecosystem model, PnET-CN, to evaluate how, and by what mechanisms, clear-cuts alter ecosystem C fluxes, aboveground C stocks (AGC), and leaf area index (LAI) in northern temperate forests. We compared C fluxes and stocks predicted by the model and observed at two chronosequences of eddy covariance flux sites for deciduous broadleaf forests (DBF) and evergreen needleleaf forests (ENF) in the Upper Midwest region of northern Wisconsin and Michigan, USA. The average normalized root mean square error (NRMSE) and the Willmott index of agreement (d) for carbon fluxes, LAI, and AGC in the two chronosequences were 20% and 0.90, respectively. Simulated gross primary productivity (GPP) increased with stand age, reaching a maximum (1200–1500 g C m−2 yr−1) at 11–30 years of age, and leveled off thereafter (900–1000 g C m−2 yr−1). Simulated ecosystem respiration (ER) for both plant functional types (PFTs) was initially as high as 700–1000 g C m−2 yr−1 in the first or second year after harvesting, decreased with age (400–800 g C m−2 yr−1) before canopy closure at 10–25 years of age, and increased to 800–900 g C m−2 yr−1 with stand development after canopy recovery. Simulated net ecosystem productivity (NEP) for both PFTs was initially negative, with net C losses of 400–700 g C m−2 yr−1 for 6–17 years after clear-cuts, reaching peak values of 400–600 g C m−2 yr−1 at 14–29 years of age, and eventually stabilizing in mature forests (\u3e 60 years old), with a weak C sink (100–200 g C m−2 yr−1). The decline of NEP with age was caused by the relative flattening of GPP and gradual increase of ER. ENF recovered more slowly from a net C source to a net sink, and lost more C than DBF. This suggests that in general ENF may be slower to recover to full C assimilation capacity after stand-replacing harvests, arising from the slower development of photosynthesis with stand age. Our model results indicated that increased harvesting intensity would delay the recovery of NEP after clear-cuts, but this had little effect on C dynamics during late succession. Future modeling studies of disturbance effects will benefit from the incorporation of forest population dynamics (e.g., regeneration and mortality) and relationships between age-related model parameters and state variables (e.g., LAI) into the model

Metro Passenger Flow Forecast with a Novel Markov-Grey Model

Accurate forecasts of passenger flow entering and leaving metro stations is an important work for Metro operation management, such as for the automatic adjustment of train operation diagrams or station passenger crowd regulation planning measures. In this study, Grey theory is introduced to develop a time series GM (1, 1) model for total passenger forecasting. Two modification factors determined by two minimum mean square error principles are proposed to decrease the discreteness of input data and thus improve the forecast accuracy. Moreover, the Markov chain approach is further used to optimize the residual error series. Passenger flow data entering and leaving the Xiaozhai station of Xi'an Metro Line 2 from September 1-30, 2015, were utilized to verify the effectiveness of the proposed method; the forecast results show that this novel Markov-Grey model performs well in terms of forecast accuracy with smaller SMSE and MAPE values. To this effect, the proposed method is especially well-suited to smooth passenger flow forecasting compared to other forecast techniques