Search Results (408)

Langmuir turbulence is a key and common process in the ocean surface boundary layer, playing a major role in vertical mixing, heat flux, and material transport. However, because direct simulation of Langmuir turbulence demands considerable computational resources, parameterizations within established schemes like the K-profile parameterization (KPP) offer a practical alternative for representing its effects in ocean and climate models. However, Langmuir turbulence parameterizations based on KPP may overestimate vertical mixing when convection is significant. To address this, we introduce a dynamic weighting factor, based on characteristic velocity scales, to balance the contributions of convective and Langmuir turbulence. The improved scheme shows a significant enhancement in performance, especially under strong convective conditions. We compare and evaluate the new parameterization schemes against other widely used schemes in three typical scenarios. Additionally, we validate it using large-eddy simulation results and field observation data. Our enhanced mixing scheme is highly competitive and performs robustly under a variety of conditions. Full article

This study investigates unsteady magnetohydrodynamic free convection flow past a rotating vertical plate embedded in a Darcy–Forchheimer porous medium. The formulation incorporates Hall current, thermal radiation, viscous dissipation, Joule heating, and an Arrhenius-type chemical reaction with activation energy to represent thermo-reactive transport in an electrically conducting fluid. The coupled nonlinear equations governing momentum, thermal energy, and species concentration are transformed into dimensionless form and solved numerically using the Crank–Nicolson scheme. Grid independence and validation tests confirm the accuracy and stability of the numerical procedure. The results show that electromagnetic forces, rotation, porous resistance, and thermo-reactive effects significantly influence wall shear stress, heat transfer, and mass transport. In particular, the interaction between magnetic field strength and Hall current alters near-wall transport behavior, highlighting the role of electromagnetic coupling in rotating porous systems. The study provides physical insight relevant to the design and analysis of transport processes in high-temperature energy systems, rotating reactors, and porous thermal management devices. Full article

Detonation phenomena in reactive flow systems continue to pose significant challenges for accurate simulation, particularly in 3D validation against experiments and achieving community standardization for schemes. Among the primary difficulties is the selection of suitable convective schemes, which are essential for capturing the complex dynamics of wave propagation and reaction fronts. This study provides a comprehensive historical review of the development and implementation of convective schemes in OpenFOAM, covering the period from 2013 to the present. In addition to documenting the evolution of these methods, we present a detailed technical description of various convective approximation techniques used in detonation simulations within OpenFOAM. This includes an exploration of their underlying principles, advantages, and limitations. Our analysis synthesizes key findings from recent studies and offers practical guidance to researchers when choosing schemes for specific detonation scenarios. It is found that currently, within OpenFOAM, the dominant schemes for convection are the HLLC and KN. Full article

In battery systems, external mechanical compression is commonly applied to pouch/prismatic cells to improve their electrical performance and mechanical integrity. However, cell clamping can hinder system heat rejection by introducing an additional thermal insulation layer. A novel battery clamping scheme was designed with reduced contact area to explore the system thermal behaviour under different cooling regimes. Experimental data obtained from battery characterisation and performance tests is analysed with a thermal-coupled equivalent circuit model to quantify changes in cell impedance and system thermal properties. By reducing the clamping area by 70%, the temperature rise of the cell was decreased by 0.5 °C in comparison to the reference condition of a cell with no clamping during a 1C discharge under natural convection. Under immersion cooling using BOT2100 dielectric liquid, the thermal benefit was amplified, resulting in temperature reductions of 0.9 °C at 1C and 4 °C at 3C. The principal conclusion of this work is that reshaping the clamping plate has the potential to reduce ohmic heating by lowering battery internal resistance, which outweighs the additional thermal resistance introduced by partial surface coverage. This novel experimental approach demonstrates the potential to improve battery thermal management through geometry-optimised cell clamping, particularly for high-power applications, and further directs the community towards cell clamping solution designed to optimise both thermal and mechanical cell performance. Full article

Anaerobic digesters operating under neotropical conditions face significant technological constraints. High humidity, intense solar radiation, and pronounced diurnal temperature variations increase conductive, convective, and radiative heat losses. These factors reduce internal thermal stability and directly affect methane production rates and overall energy efficiency. As a result, thermal instability becomes a recurrent operational bottleneck in biogas plants without active temperature control. This review examines the thermal and dynamic behavior of anaerobic reactors from a process-engineering perspective. It integrates energy balances, heat-transfer mechanisms, and computational fluid dynamics (CFD) modeling. The combined effects of temperature gradients, hydrodynamic mixing patterns, and structural material properties are analyzed to determine their influence on thermal homogeneity, microbial stability, and methane yield consistency under mesophilic conditions. Technological strategies to mitigate thermal losses are evaluated. These include passive insulation using low-conductivity materials, geometry optimization supported by numerical modeling, and thermal recirculation schemes, as these factors govern temperature distribution and process resilience. Current limitations are also discussed, particularly the frequent decoupling between ADM1-based kinetic models and transient heat-transfer analysis. This separation restricts predictive capability under real-scale diurnal temperature oscillations. The development and validation of coupled hydrodynamic–thermal–biokinetic models under fluctuating neotropical boundary conditions are proposed as critical steps. Such integrated approaches can enhance operational stability, ensure consistent methane production, and improve energy self-sufficiency in organic waste valorization systems. Full article

This study introduces a modified computational scheme for handling linear and nonlinear fractal time-dependent partial differential equations. The method is constructed using three different stages that provide third-order accuracy in the fractal time variable. The stability of the approach is examined using scalar fractal models and Fourier analysis, while convergence is established for coupled convection–diffusion systems. The numerical algorithm is applied to analyze the mixed convective flow of a Carreau–Yasuda non-Newtonian fluid over stationary and oscillating plates under the influence of viscous dissipation and magnetic field effects. For spatial discretization, the incompressible continuity equation is handled by a first-order difference scheme, whereas higher-order compact schemes are implemented for the momentum, thermal, and concentration equations. The numerical findings show that increasing the Weissenberg number and magnetic field inclination reduces the velocity distribution. An accuracy assessment against existing numerical techniques demonstrates that the present method yields smaller computational errors, particularly when central difference schemes are used in space. In addition, a surrogate machine learning model is developed to predict the skin friction coefficient and local Nusselt number using Reynolds, Weissenberg, Prandtl, and Eckert numbers as input features. The predictive capability of the model is validated through Parity plots, bar charts for sensitivity analysis, scatter visualization, and Taylor Diagrams, confirming strong agreement with the numerical results. Full article

This study evaluates the performance of eleven Planetary Boundary Layer (PBL) schemes within the Weather Research and Forecasting (WRF) model over the Central Amazon Basin, focusing on contrasting wet and dry season conditions observed during the GoAmazon2014/5 campaign. High-resolution (1 km) simulations were conducted for representative periods in each season and validated against in situ observations. Model performance was assessed using multiple statistical metrics with the explicit separation of daytime convective and nighttime stable PBL regimes. Results reveal substantial variability among PBL schemes, strongly modulated by the season and diurnal cycle. Overall performance was higher during the wet period, whereas dry period simulations exhibited larger uncertainties, particularly under nocturnal conditions. The Shin–Hong (SH) PBL scheme had the best skill on average to reproduce the observed PBL height (PBLH) during the wet period, while the University of Washington (UW) PBL scheme was the best during the dry period. The Mellor–Yamada–Janjic (MYJ) PBL scheme had the best skill for daytime PBLH in both periods. Spatial analysis demonstrated how PBL schemes impact the PBLH distribution over the Central Amazon Basin, revealing a river-influenced pattern. These findings highlight the strong sensitivity of the Amazon PBL depth to PBL schemes and underscore the importance of appropriate PBL parameterizations and the vertical resolution for tropical applications. Full article

In this article, we explore the possibility of using reinforcement learning to create convective flow approximation schemes that maintain accuracy and stability at high Courant-Friedrichs-Lewy (CFL) numbers in the finite-volume discretization of advection equations. Unlike most existing data-driven discretization methods, which primarily concentrate on spatial grid refinement, this work emphasizes increasing the allowable time step without compromising solution accuracy. This approach reduces the total number of time integration steps, thereby enabling faster computation. A neural network is used as a surrogate model for reconstructing the convective flow, which takes as input local information about the flow, scalars, and geometry and predicts scalar values at node points. Reinforcement learning is used for training and is formulated as a policy optimization problem, where the long-term reward is defined as the difference between the numerical and reference solutions over the entire simulation period. Both the genetic algorithm and the Deep Deterministic Policy Gradient (DDPG) method are investigated. The effectiveness of the approach is evaluated using a one-dimensional nonlinear advection problem with a constant velocity field. Despite the simplicity of the test case, the results demonstrate that the trained convective flux approximation scheme achieves accuracy comparable to or better than the classical second-order linear upwind (LUD) scheme, while operating at CFL numbers 2–50 times higher than the optimal CFL for LUD, thereby reducing the simulation time by the same factor. This allows for a wider range of stability and accuracy in the finite-volume method and the use of larger time steps without compromising the quality of the solution. The study is intentionally limited to a single spatial dimension and serves as a basic analysis of the method’s applicability. The results demonstrate that reinforcement learning can successfully find more convective flow approximation schemes that improve efficiency at high CFL numbers than conventional explicit second-order schemes, establishing a framework that is subsequently extended in our follow-up work to improve training methods and three-dimensional complex transport problems. The proposed method improves the spatial discretization of convective fluxes, which is independent of the choice of time integration scheme. Therefore, the neural reconstruction can in principle be used in both explicit and implicit finite-volume solvers. Full article

Hailstorms frequently develop in Yun-Gui Plateau, Western China, which bring about significant economic damage. Due to the high terrain, these storms are typically shallow, rapidly evolving, and challenging to forecast. An X-band phased-array radar (XPAR) network is set up at Weining in Yun-Gui Plateau to study these storms. To explore these XPAR data for numerical prediction of hailstorms in this region, we implement the Weather Research and Forecast (WRF) model and Hydrometeor and Latent Heat Nudging (HLHN) method to assimilate the data and conduct prediction experiments. The XPAR data was evaluated along with the operational Severe Weather Automatic Nowcast (SWAN) system radar mosaic data. Furthermore, a humidity adjustment scheme is used to overcome inconsistency of the humidity field and related prediction errors. The model results show that in comparison to the SWAN data, assimilating XPAR data in 1-min intervals significantly reduces the model error, and improves the representation of rapid hail cloud evolution. Additionally, adjusting the model humidity based on vertically integrated liquid (VIL) derived from the radar data can effectively correct model analyses of humidity and temperatures, suppressing spurious convection, thus improving the hailstorm forecast. Overall, we recommend joint assimilation of the high spatiotemporal resolution XPAR data along with SWAN radar data with the improved WRF-HLHN for hailstorm prediction over the study region, and the algorithm can be promptly adapted to forecasting hailstorms in other regions. Full article

This study introduces an efficient and accurate two-stage explicit computational scheme for solving partial differential equations (PDEs) containing first-order time derivatives. The suggested method is a modification of the classical Runge–Kutta scheme that introduces a new first-stage formulation. This minimizes numerical error with moderate step sizes while preserving the stability region of the classical method. Spatial discretization is performed using a sixth-order compact finite-difference scheme to obtain high-resolution solutions. The analysis of stability and convergence is strictly determined for both scalar and system forms of convection–diffusion-type equations. To illustrate the suitability of the method, a dimensionless mathematical model of the unsteady, incompressible, laminar flow of a Prandtl-type non-Newtonian nanofluid over a Riga plate is considered, accounting for viscous dissipation, thermophoresis, Brownian motion, and a magnetic field. Here, the Prandtl ternary nanofluid is defined as a non-Newtonian nanofluid that follows the Prandtl rheological model, and it exhibits three critical transport phenomena: heat conduction, viscous dissipation, and nanoparticle diffusion. Representative values of the Prandtl number $P_r=3$ and Reynolds number $R_e=5$ are used to perform the simulation, and other parameters, including but not limited to the Hartmann number $H_a$, Williamson number $W_e$, thermophoresis $N_t$ and Brownian motion $N_b$, are varied to evaluate the flow behavior. Moreover, an artificial neural network (ANN)-developed surrogate model is used to calculate the skin friction coefficient and the local Sherwood number, using five input parameters: the Reynolds number, Prandtl number, Schmidt number, Brownian motion parameter, and thermophoresis parameter. The governing partial differential equations yield high-fidelity numerical data used to train the surrogate model. The data is split into 80% for training, 10% for validation, and 10% for testing. The ANN is tested using regression analysis and error histograms, which demonstrate high accuracy and generalization capacity. Numerical simulation combined with AI-based prediction is a cost-efficient method for real-time estimation of complex non-Newtonian nanofluid systems. Full article

The Earth system model ICON (ICOsahedral Nonhydrostatic general circulation) is a flexible framework that can be configured and tuned for various applications such as weather forecasting, simulations of aerosols and trace gases, and climate modelling. The numerical weather prediction component ICON is used in limited area mode (ICON-LAM) in Romania to obtain realistic weather simulations that support operational forecasting activities. The sensitivity of ICON-LAM is preliminarily evaluated for the geographical area of Romania. Numerical simulations using two parameterization schemes for radiation processes, two convection settings and different values for the laminar resistance of heat transfer from the surface to the air are evaluated against a control run employed for operational forecasts at the National Meteorological Administration. The validation is performed focusing on the precipitation field and surface continuous parameters. All configurations were integrated for a short period in summer when forecasted precipitation was strongly overestimated. Further on, selected configurations were evaluated for winter cases. The experiment with the shallow convection only, the ecRad radiation parameterization, and the laminar heat value 10 emerged as the best fit for Romania. This configuration (considered optimal) was evaluated alongside the operational control run for August 2022. Overall results indicate the selected optimal configuration generally outperforms the control run both with regard to precipitation and in forecasting surface parameters. This experiment has been adapted and implemented in operational workflow. Full article

In this paper, the nonlinear time-fractional convection-diffusion equations are solved by the Legendre spectral method. The Caputo time-fractional derivative is discretized by the $L2$–$1_{\sigma }$ scheme. A priori estimates of the fully discrete scheme are derived, and the existence and uniqueness of the numerical solution are analyzed. It is rigorously proved that the fully discrete scheme is unconditionally stable, and the convergence order of the numerical scheme is $O(N^{1-m}+{\tau }^2)$. Finally, numerical results are presented to verify the theoretical analysis. Full article

We consider two steady-state heat conduction systems called, S and $S_{\alpha }$, in a multidimensional bounded domain D for the Poisson equation with source energy g. In one system, we impose mixed boundary conditions (temperature b on the boundary ${\mathsf{\Gamma }}_1$, heat flux q on ${\mathsf{\Gamma }}_2$ and an adiabatic condition on ${\mathsf{\Gamma }}_3$). In the other system, the condition on ${\mathsf{\Gamma }}_1$ is replaced by a convective heat flux condition with coefficient $\alpha$. For each of these systems, we consider three associated optimization problems $\left(P_i\right)$ and $\left(P_{i\alpha }\right)$, $i=1,2,3$, where the variable is the source energy g, the heat flux q and the environmental temperature b, respectively. In the particular case where D is a rectangle, the explicit continuous optimization variables and the corresponding state of the systems are known. In the present work, by using a finite difference scheme, we obtain the discrete systems $\left(S^h\right)$ and $\left(S_{\alpha }^h\right)$ and discrete optimization problems $\left(P_i^h\right)$ and $\left(P_{i\alpha }^h\right)$, $i=1,2,3$, where h is the space step in the discretization. Explicit discrete solutions are found, and convergence and estimation errors results are proved when h goes to zero and when $\alpha$ goes to infinity. Moreover, some numerical simulations are provided in order to test theoretical results. Finally, we note that the use of a three-point finite-difference approximation for the Neumann or Robin boundary condition at the boundary improves the global order of convergence from $O\left(h\right)$ to $O\left(h^2\right)$. Full article

To address the challenge of rapidly selecting optimal numerical model products for weather forecasting in critical applications such as aviation route planning, this study proposes an enhanced object-based methodology comprising individual object scoring matching and a regional overall forecast selection scheme, building upon previous research. The method focuses on radar reflectivity forecasts within critical areas along air routes. Individual thunderstorm cells are evaluated using weighted scores for multiple parameters, including the Threat Score (TS), center-of-mass position, maximum radar reflectivity intensity, and shape forecasting accuracy. The regional overall score is then calculated by applying different weights to each convective cell within the area. After examining case studies of various convection types and bulk tests from June to September of 2024 and 2025, the results demonstrate that this method effectively selects the optimal convective forecasts from among the numerical models initiated at different times. The methodology shows promising applications in aviation weather forecasting. Different optimal selection schemes yield varying results: for large-scale convective weather, various test schemes generally align with TS score selection; for small-scale convective weather, schemes emphasizing radar reflectivity intensity show better performance; for scattered convection, schemes prioritizing center-of-mass position forecasting demonstrate superior results. These findings provide valuable insights for precision weather forecasting in both aviation and the agricultural–ecological sectors, in which accurate convective weather prediction is crucial for operational safety and resource management. Full article

The Burgers–Huxley equation is a nonlinear partial differential equation that incorporates convective, diffusive and reactive effects and arises in various reaction–diffusion and fluid flow models. In this paper, a numerical method based on the method of lines is proposed for its solution. The spatial derivatives are approximated using a third-order finite difference scheme, which converts the governing partial differential equation into a system of ordinary differential equations. The resulting semi-discrete system is solved in time using the classical fourth-order Runge–Kutta method. The stability and convergence properties of the proposed scheme are analyzed to establish its numerical reliability. Several numerical experiments are presented to illustrate the accuracy and efficiency of the method. The computed results confirm that the proposed approach provides accurate and stable solutions for the Burgers–Huxley equation. Full article