Advection Terms Research Articles

Comparative study on predicting turbulent kinetic energy budget using high-order upwind scheme and non-dissipative central scheme

The accurate computation of different turbulent statistics poses different requirements on numerical methods. In this paper, we investigate the capabilities of two representative numerical schemes in predicting mean velocities, Reynolds stress and budget of turbulent kinetic energy (TKE) in low Mach number flows. With concerns on numerical order of accuracy, dissipation and dispersion properties, a high-order upwind scheme with relatively good dispersion and dissipation and a second-order non-dissipative central scheme with perfect dissipation but poor dispersion are adopted for this comparative study. By carrying out a series of numerical simulations including Taylor-Green vortex, turbulent channel flow at Reτ=180\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Re_{\ au }=180$$\\end{document} and turbulent flow over periodic hill at Reb=10595\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Re_{b}=10595$$\\end{document}, it can be obtained that although the high-order upwind scheme lacks perfection of dissipation in high wave number range, it still demonstrates superior predictive capability compared with the second-order non-dissipative central scheme, especially with relatively coarse grids. Finally, by taking the high-order upwind scheme as a suitable selection for turbulence simulation, the turbulent flow over a 30P30N multi-element airfoil is investigated as an application study. After briefly comparing the simulated profiles and spectrum with reference experimental results as validation, the budget of TKE is analyzed to locate the dominant flow structures and regions. It is found that the production and dissipation terms behave in a “monopole” pattern in the locations with strong shears and wakes. Whereas the advection and diffusion terms show an “inward” pattern and an “outward” pattern, which indicate the spatial transport of TKE between the center of the shear layer and nearby locations.

A fully-coupled algorithm with implicit surface tension treatment for interfacial flows with large density ratios

The stability of most surface-tension-driven interfacial flow simulations is governed by the capillary time-step constraint. This concerns particularly small-scale flows and, more generally, highly-resolved liquid-gas simulations with moderate inertia. To date, the majority of interfacial-flow simulations are performed using an explicit surface-tension treatment, which restrains the performance of such simulations. Recently, an implicit treatment of surface tension able to breach the capillary time-step constraint using the volume-of-fluid (VOF) method was proposed, based on a fully-coupled pressure-based finite-volume algorithm. To this end, the interface-advection equation is incorporated implicitly into the linear flow solver, resulting in a tight coupling between all implicit solution variables (colour function, pressure, velocity). However, this algorithm is limited to uniform density and viscosity fields. Here, we present a fully-coupled algorithm for interfacial flows with implicit surface tension applicable to interfacial flows with large density and viscosity ratios. This is achieved by solving the continuity and momentum equations in conservative form, whereby the density is treated implicitly with respect to the colour function, and the advection term of the interface-advection equation is discretised using the THINC/QQ algebraic VOF scheme, yielding a consistent discretisation of the advective terms. This new algorithm is tested by considering representative surface-tension-dominated interfacial flows, including the Laplace equilibrium of a stationary droplet and the three-dimensional Rayleigh-Plateau instability of a liquid filament. The presented results demonstrate that interfacial flows with large density and viscosity ratios can be simulated and energy conservation is ensured, even with a time step larger than the capillary time-step constraint, provided that other time-step restrictions are satisfied.

An Improved Scheme for the Finite Difference Approximation of the Advective Term in the Heat or Solute Transport Equations

AbstractTransport equations are widely used to describe the evolution of scalar quantities subject to advection, dispersion and, possibly, reactions. Numerical methods are required to solve these equations in applications, adopting either the advective or conservative formulations. Conservative formulations are usually preferred in practice because they conserve mass. Advective formulations do not, but have received more mathematical attention and are required for Lagrangian solution methods. To obtain an advective formulation that conserves mass, we subtract the discretized fluid flow equation, multiplied by concentration, from the conservative form of the transport equation. The resulting scheme not only conserves mass, but is also elegant in that it can be interpreted as averaging the advective term at cell interfaces, instead of approximating it at cell centers as in traditional centered schemes. The two schemes are identical when fluid velocity is constant, and both have second-order convergence, but the truncation errors are slightly different. We argue that the error terms appearing in the proposed scheme actually imply an improved representation of subgrid spreading/contraction and acceleration/deceleration caused by variable velocity. We compare the proposed and traditional schemes on several problems with variable velocity caused by recharge, discharge or evaporation, including two newly developed analytical solutions. The proposed method yields results that are slightly, but consistently, better than the traditional scheme, while always conserving mass (i.e., mass at the end equals mass at the beginning plus inputs minus outputs), which the traditional centered finite differences scheme does not. We conclude that this scheme should be preferred in finite difference solutions of transport.

A novel direct interpolation boundary element method formulation for solving diffusive–advective problems

The capability of dealing with the advective transport term constitutes a challenging issue for the performance of the majority of the numerical techniques, which significantly lose their precision with the increasing in the relative magnitude of this term. Recently, a new boundary element technique called direct interpolation (DIBEM) has emerged, mainly characterized by the approximation of the entire kernel of the remaining domain integrals. The DIBEM model has been successfully applied to several scalar field problems and recently applied to certain diffusive–advective problems with superior accuracy compared to dual reciprocity formulation (DRBEM). Using DIBEM, a broader range of precise responses for flows with higher Peclet numbers can be reached beyond a lower computational cost due to the simplicity of its matrix operations. These advantages are due DIBEM concept that employs a simple interpolation procedure to approximate the kernel of the advective domain integral. However, it was noticed that in some physical scenarios with spatial variation in the velocity field, the accuracy of DIBEM did not have the same quality observed in other applications. Therefore, this work presents a new DIBEM model so that the integral equations include the explicit calculation of spatial derivatives and simultaneously solve the variation of the divergent velocity field if this is not zero. Conversely, reactive and source terms were also included to expand numerical comparisons. Thus, in the proposed examples, the results of two DIBEM models, the standard (DIBEM-S) and the new, so-called alternative model (DIBEM-A), are compared with DRBEM and also with available analytical solutions.

Resolution dependence of southern Atlantic Ocean stratocumulus decks

AbstractOceanic stratocumulus decks of clouds are among the largest contributors to the Earth's radiation budget, covering around a fifth of the planet's surface and reflecting a large part of the incoming solar radiation. Unfortunately, these clouds are not well represented in modern climate models, resulting in one of the leading causes of uncertainty in climate change projections. This contribution analyses this issue from a novel perspective and sheds light on the mechanisms behind the misrepresentation and resolution dependence of these large clouds. The analysis is based on realistic week‐long simulations performed over a km oceanic domain. Four horizontal resolutions, between 4.4 and 0.55 km, are employed, resulting in a timely investigation, especially in light of the high resolutions employed by present and near‐future climate projections. Results show that the liquid cloud water, the main contributor to the simulated grid‐scale clouds, decreases with a power‐law decay as the resolution increases, whereas the water vapour, responsible for subgrid‐scale clouds, is much less affected by the grid spacing. The leading cause is identified as an imbalance between the rates of change of the advection and turbulence parametrisation terms. In order to verify this observation and provide a possible mitigation to the issue, a second set of simulations is performed where the turbulence parametrisation is tuned. The strategy proves to be successful, confirming the hypotheses and resulting not only in a resolution‐independent radiation budget but also cloud coverage.

An advection–diffusion equation with a generalized advection term: Well-posedness analysis and examples

We consider a Cauchy–Dirichlet problem for a semilinear advection–diffusion equation with a generalized advection term. Specific examples include an incision–diffusion landscape evolution model and a viscous Hamilton–Jacobi equation with an absorbing gradient term. We establish existence and uniqueness of a weak solution and its continuous dependence on initial data and a source term.

Role of Dry Dynamics in the Maritime Continent Barrier Effect in the Madden Julian Oscillation

Abstract Eastward-moving moist deep convection and atmospheric circulation signals associated with the tropical Madden Julian Oscillation (MJO) sometimes break down as they cross the Maritime Continent region, but other times the signal propagates across the region maintaining amplitude or regaining it over the West Pacific Basin. This paper assesses the hypothesis that upper tropospheric zonal diffluence of the background wind over the Maritime Continent causes much of this Maritime Continent barrier effect and its variation over time, through two mechanisms. 1. By slowing down the MJO as stronger than average background upper tropospheric zonal wind over the Indian Ocean advects the MJO circulation signal westward, slowing its eastward advance, and 2. through zonal advection of background wind by subseasonal zonal wind across a region of zonal diffluence of the background wind, which advects background wind of the opposite sign to the MJO wind. Advection of the opposite-signed background wind counteracts the MJO wind and reduces its associated upper tropospheric mass divergence, weakening the mechanisms of the upper tropospheric Kelvin wave component of the MJO circulation. Composites of MJO-associated zonal wind and outgoing longwave radiation signals diminish as they cross the Maritime Continent region when the region’s background zonal winds are diffluent, and composites of data reconstructing the relevant advection terms reveal the direct action of the advection mechanisms.

How do morphological characteristics affect tidal asymmetry in the Radial Sand Ridges?

While it is widely recognized that the Radial Sand Ridges (RSR) in the South Yellow Sea are predominantly shaped by tidal forces, there remains a limited understanding of how this distinctive morphological configuration—characterized by an interlaced channel-ridge system—can subsequently influence local tidal dynamics. This study examines the effects of morphological features on tidal asymmetry, taking into account seabed slope, relative depths between ridges and channels, and channel convergence. Three principal indices—namely tidal-duration-asymmetry (TDA), peak-current-asymmetry (PCA), and slack-water-asymmetry (SWA)—are employed to quantify various dimensions of tidal asymmetry. The findings indicate that SWA serves as the most morphology-sensitive indicator, whereas TDA exhibits minimal sensitivity to morphological changes. Furthermore, seabed steepness emerges as a critical factor influencing tidal asymmetry within the RSR; steeper slopes enhance intrinsic energy conversion processes, thereby inducing tidal asymmetries. Additional analysis reveals that streamwise advection accounts for an average of 88 % of total advection scale while controlling for spatial heterogeneity. Specifically, the average integral sum of advection terms along submerged sand ridges is 2.53 times greater than that along the deepest section of the tidal channel line—a significant contributor to spatial variability in SWA. With a positive seabed slope, the apex of the RSR acts as a source for overtides which interact with incoming astronomical tides, consequently generating tidal asymmetries. Moreover, this study illustrates varying dependencies of tidal asymmetry on bottom stress across channels and ridges, contributing to spatial variability in arc direction among RSRs. Ultimately, this research elucidates complex interactions between tidal flow and morphological characteristics within RSRs and provides insights into tide evolution in analogous ebb-shoal systems.

Flow Field Characteristics at the Spanwise Edge of a Vegetative Canopy Model

This study investigates the complex flow field across a spanwise vegetative model canopy edge focusing on turbulent transport processes. Utilizing stereoscopic particle image velocimetry, the three velocity components were measured in wall-parallel planes at various elevations within canopy across the spanwise canopy edge. Conventional ensemble averaged results were contrasted with those obtained by conditionally averaged flow properties across instantaneous internal interfaces in the flow to understand their contribution to the ensemble average. The conditional average captured the strong gradients in mean velocities, Reynolds stresses, vorticity, swirling strength, and turbulent kinetic energy production across the dynamically changing instantaneous interface. In contrast, the conventional ensemble average smeared out the strong gradients. Small magnitudes of advective terms in the turbulent kinetic energy transport equation suggested weak secondary transverse flows in the present model canopy. The turbulent flow structure across the spanwise canopy edge was further investigated using Quadrant-Hole analysis for both averaging approaches. Conventional ensemble averaged results indicated a shift from sweep to ejection dominance when moving from canopy into the open patch, while the conditional average showed only sweep dominated transport. In contrast to a homogeneous canopy layout, below canopy height at the canopy edge, sweeps and ejections lose their dominance in vertical turbulent transport. The present results show that the dynamics of internal interfaces govern the ensemble averaged results and a possible implementation into existing models is proposed. The present results are expected to increase understanding of spanwise turbulent transport and aid in developing strategies to mitigate desertification.

Analytical solutions for the advective–diffusive ice column in the presence of strain heating

Abstract. A thorough understanding of ice thermodynamics is essential for an accurate description of glaciers, ice sheets and ice shelves. Yet there exists a significant gap in our theoretical knowledge of the time-dependent behaviour of ice temperatures due to the inevitable compromise between mathematical tractability and the accurate description of physical phenomena. In order to bridge this shortfall, we have analytically solved the 1D time-dependent advective–diffusive heat problem including additional terms due to strain heating and depth-integrated horizontal advection. Newton's law of cooling is applied as a Robin-type top boundary condition to consider potential non-equilibrium temperature states across the ice–air interface. The solution is expressed in terms of confluent hypergeometric functions following a separation of variables approach. Non-dimensionalization reduces the parameter space to four numbers that fully determine the shape of the solution at equilibrium: surface insulation, effective geothermal heat flow, the Péclet number and the Brinkman number. The initial temperature distribution exponentially converges to the stationary solution. Transient decay timescales are only dependent on the Péclet number and the surface insulation, so higher advection rates and lower insulating values imply shorter equilibration timescales, respectively. In contrast, equilibrium temperature profiles are mostly independent of the surface insulation parameter. We have extended our study to a broader range of vertical velocities by using a general power-law dependence on depth, unlike prior studies limited to linear and quadratic velocity profiles. Lastly, we present a suite of benchmark experiments to test numerical solvers. Four experiments of gradually increasing complexity capture the main physical processes for heat propagation. Analytical solutions are then compared to their numerical counterparts upon discretization over unevenly spaced coordinate systems. We find that a symmetric scheme for the advective term and a three-point asymmetric scheme for the basal boundary condition best match our analytical solutions. A further convergence study shows that n≥15 vertical points are sufficient to accurately reproduce the temperature profile. The solutions presented herein are general and fully applicable to any problem with an equivalent set of boundary conditions and any given initial temperature distribution.

An Eulerian formulation for the computational modeling of phase-contrast MRI.

Computational simulation of phase-contrast MRI (PC-MRI) is an attractive way to physically interpret properties and errors in MRI-reconstructed flow velocity fields. Recent studies have developed PC-MRI simulators that solve the Bloch equation, with the magnetization transport being modeled using a Lagrangian approach. Because this method expresses the magnetization as spatial distribution of particles, influences of particle densities and their spatial uniformities on numerical accuracy are well known. This study developed an alternative method for PC-MRI modeling using an Eulerian approach in which the magnetization is expressed as a spatially smooth continuous function. The magnetization motion was described using the Bloch equation with an advection term and computed on a fixed grid using a finite difference method, and k-space sampling was implemented using the spoiled gradient echo sequence. PC-MRI scans of a fully developed flow in straight and stenosed cylinders were acquired to provide numerical examples. Reconstructed flow in a straight cylinder showed excellent agreement with input velocity profiles and mean errors were less than 0.5% of the maximum velocity. Numerical cases of flow in a stenosed cylinder successfully demonstrated the velocity profiles, with displacement artifacts being dependent on scan parameters and intravoxel dephasing due to flow disturbances. These results were in good agreement with those obtained using the Lagrangian approach with a sufficient particle density. The feasibility of the Eulerian approach to PC-MRI modeling was successfully demonstrated.

Multiple Time Scales and Normal Form of Hopf Bifurcation in a Delayed Reaction–Diffusion–Advection System

In the reaction–diffusion systems, the Laplacian is usually a self-adjoint operator. Incorporating advection terms generally destroys this and yields a quite complicated decomposition of phase space in the Center Manifold Reduction (CMR) method. Considering that the Multiple Time Scales (MTS) method can be directly applied to bifurcation analysis and normal form derivation based on algebraic operations, and the computational process is relatively universal, we apply the MTS method to analyze the Hopf bifurcation problem of reaction–diffusion–advection systems with time delay. First, we introduce the MTS method for the system with a specific boundary condition, which is used to derive the normal form of Hopf bifurcation. Calculating the normal form using the MTS method can be summarized as determining the bifurcation parameters, conducting Taylor expansion based on the MTS idea, and eliminating secular terms. Then, the key coefficients in the normal form are explicitly given, which are also compared with the results obtained by the CMR method, and both methods lead to the same bifurcation results. Finally, we use the MTS method to calculate the normal form of Hopf bifurcation for a predator–prey model with mixed boundary conditions. We find that the spatially nonhomogeneous periodic solutions appear near the equilibrium in the system when the time delay exceeds the critical value, and the theoretical results are illustrated by numerical simulations.

Performance Evaluation of TGFS Typhoon Track Forecasts over the Western North Pacific with Sensitivity Tests on Cumulus Parameterization

This study employed the new generation Taiwan global forecast system (TGFS) to focus on its performance in forecasting the tracks of western North Pacific typhoons during 2022–2023. TGFS demonstrated better forecasting performance in typhoon track compared to central weather administration (CWA) GFS. For forecasts with large track errors by TGFS at the 120th h, it was found that most of them originated during the early stages of typhoon development when the typhoons were of mild intensity. The tracks deviated predominantly towards the northeast and occasionally towards the southwest, which were speculated to be due to inadequate environmental steering guidance resulting from the failure to capture synoptic environmental features. The tracks could be corrected by replacing the original new simplified Arakawa–Schubert (NSAS) scheme with the new Tiedtke (NTDK) scheme to change the synoptic environmental field, not only for Typhoon Khanun, which occurred in the typhoon season of 2023, but also for Typhoon Bolaven, which occurred after the typhoon season, in October 2023, under atypical circulation characteristics over the western Pacific. The diagnosis of vorticity budget primarily analyzed the periods where divergence in typhoon tracks between control (CTRL) and NTDK experiments occurred. The different synoptic environmental fields in the NTDK experiment affected the wavenumber-1 vorticity distribution in the horizontal advection term, thereby enhancing the accuracy of typhoon translation velocity forecasts. This preliminary study suggests that utilizing the NTDK scheme might improve the forecasting skill of TGFS for typhoon tracks. To gain a more comprehensive understanding of the impact of NTDK on typhoon tracks, further examination for more typhoons is still in need.

Discrete strong extremum principles for finite element solutions of advection‐diffusion problems with nonlinear corrections

AbstractA nonlinear correction technique for finite element methods of advection‐diffusion problems on general triangular meshes is introduced. The classic linear finite element method is modified, and the resulting scheme satisfies discrete strong extremum principle unconditionally, which means that it is unnecessary to impose the well‐known restrictions on diffusion coefficients and geometry of mesh‐cell (e.g., “acute angle” condition), and we need not to perform upwind treatment on the advection term separately. Moreover, numerical example shows that when a discrete scheme does not satisfy the strong extremum principle, even if it maintains the global physical bound, non‐physical numerical oscillations may still occur within local regions where no numerical result is beyond the physical bound. Thus, it is worth to point out that our new nonlinear finite element scheme can avoid non‐physical oscillations around sharp layers in advection‐dominate regions, due to maintaining discrete strong extremum principle. Convergence rates are verified by numerical tests for both diffusion‐dominate and advection‐dominate problems.

Mixed-precision computing in the GRIST dynamical core for weather and climate modelling

Abstract. Atmosphere modelling applications are becoming increasingly memory-bound due to the inconsistent development rates between processor speeds and memory bandwidth. In this study, we mitigate memory bottlenecks and reduce the computational load of the Global–Regional Integrated Forecast System (GRIST) dynamical core by adopting a mixed-precision computing strategy. Guided by an application of the iterative development principle, we identify the coded equation terms that are precision insensitive and modify them from double to single precision. The results show that most precision-sensitive terms are predominantly linked to pressure gradient and gravity terms, while most precision-insensitive terms are advective terms. Without using more computing resources, computational time can be saved, and the physical performance of the model is largely kept. In the standard computational test, the reference runtime of the model's dry hydrostatic core, dry nonhydrostatic core, and the tracer transport module is reduced by 24 %, 27 %, and 44 %, respectively. A series of idealized tests, real-world weather and climate modelling tests, was performed to assess the optimized model performance qualitatively and quantitatively. In particular, in the long-term coarse-resolution climate simulation, the precision-induced sensitivity can manifest at the large scale, while in the kilometre-scale weather forecast simulation, the model's sensitivity to the precision level is mainly limited to small-scale features, and the wall-clock time is reduced by 25.5 % from the double- to mixed-precision full-model simulations.

Shifted Legendre Gauss‐Lobatto collocation scheme for solving nonlinear coupled space‐time fractional reaction‐advection diffusion equations

AbstractThis work aims to develop and apply an algorithm for solving space‐time fractional reaction‐advection diffusion (STFRAD) nonlinear coupled equations with specified initial and boundary conditions by employing a Shifted Legendre Gauss‐Lobatto collocation (SLGLC) scheme. The fractional derivatives of time and space are defined in Caputo sense. The approximate solutions have been constructed with the help of shifted Legendre polynomials. The proposed numerical scheme reduces the coupled fractional order differential equations into a system of algebraic equations which can then be easily solved. The error analysis through the two test problems is carried out to validate the efficiency and efficacy of the method. The effect of advection and reaction terms, and various space‐time fractional order derivatives on the solution profiles have been studied and are shown graphically for different particular cases. It has been observed that the species whose transport is simulated using STFRADE shows higher concentration at a specific distance in porous media in case of integer order differential equations as compared to fractional order equations demonstrating overestimation of its impact in case of integer order differential equation. This is extremely important observation with respect to applications in the field of groundwater pollution management. The salient feature of the article is the stability and convergence analyses of the proposed scheme on the concerned model, which demonstrates the effectiveness and capabilities of the developed method.

Characteristics and Mechanisms of Spring Tidal Mixing and Sediment Transport in a Microtidal Funnel-Shaped Estuary

Information about estuarine mixing and its control of sediment transport is crucial to elucidating the dynamics and evolution of estuaries. Here, the microtidal and funnel-shaped Zhenhai Estuary, located in the southwestern Pearl River Delta of China, is used to investigate the characteristics and mechanisms of water mixing and sediment transport based on observations from three spring tides. The results reveal that the studied estuary remains well mixed during spring tides from 2013–2022 despite its microtidal regime. Tidal stirring, which is enhanced by tidal energy convergence and benefits from the funnel-shaped geometry and shallow bathymetry, favors vertical mixing, contributing to the formation of strong mixing in the estuary. Due to the well-mixed regime, sediment transport in the estuary is dominated by the advective term, followed by a moderate tidal pumping term and minor estuarine circulation term. Accordingly, sediments within the estuary tend to be transported landward owing to the regulation of the funnel-shaped geometry, and a gradual but slow infilling trend is predictable. This paper deepens our understanding of hydrodynamics and sediment transport in microtidal estuaries.

Modeling the electro-chemo-mechanical failure at the lithium-solid electrolyte interface: Void evolution and lithium penetration

The solid-solid contact interface is crucial for the reliability of solid-state energy storage systems. The contact condition becomes more complicated when lithium (Li) metal is used as the anode. The contact between solid electrolyte (SE) and Li metal is inferior compared to the liquid/solid interface in conventional Li-ion batteries. Experimental evidence has shown that improper operating conditions of solid-state batteries can lead to electro-chemo-mechanical failures at the Li/SE interface, including the formation of voids and the penetration of Li. In this study, a unified phase-field model is developed to investigate these two mechanisms. The model considers the coupled electro-chemo-mechanical processes including void diffusion, lattice annihilation, stripping and plating reactions, and plastic deformation of Li metal. The study begins with a revisit of the deformation-mechanism map for Li metal under a wide range of temperatures, stress, and deformation rates. This map serves as the basis for the mechanical characterization in the phase-field model. The large inelastic deformation of Li is considered by introducing an advection term into the Allen-Cahn equation, which is used to describe the dynamic evolution of the Li and void phases. The effects of current density and stack pressure on void evolution and Li penetration are studied based on the model predictions. By combining the simulation results with the experimental data from publications, we obtain the stable operation zone of stack pressure and applied current density. In this zone, the Li/SE interface can enable stable stripping and plating of Li metal. The same phase-field modeling framework is transferred to investigate the Li-Mg alloy/SE interface considering Li-Mg alloy is also used as the anode. The fundamental difference between Li/SE and Li-Mg/SE is analyzed accordingly. This study provides a useful tool for the design, manufacturing, and management of next-generation batteries by providing important scientific insights into the electro-chemo-mechanical processes of different anode materials under various operational conditions.

Classification of spatial dynamics of a vector–host epidemic model in advective heterogeneous environment

AbstractIn this paper, we propose and analyze a reaction–diffusion vector–host disease model with advection effect in an one‐dimensional domain. We introduce the basic reproduction number (BRN) and establish the threshold dynamics of the model in terms of . When there are no advection terms, we revisit the asymptotic behavior of w.r.t. diffusion rate and the monotonicity of under certain conditions. Furthermore, we obtain the asymptotic behavior of under the influence of advection effects. Our results indicate that when the advection rate is large enough relative to the diffusion rate, tends to be the value of local basic reproduction number (LBRN) at the downstream end, which enriches the asymptotic behavior results of the BRN in nonadvection heterogeneous environments. In addition, we explore the level set classification of , that is, there exists a unique critical surface indicating that the disease‐free equilibrium is globally asymptotically stable on one side of the surface, while it is unstable on the other side. Our results also reveal that the aggregation phenomenon will occur, namely, when the ratio of advection rate to diffusion rate is large enough, infected individuals will gather at the downstream end.

Analytical and Numerical Conceptions of Flame Propagation in Porous Media with a Generalization in Diffusion and Reaction Modeling

ABSTRACT In this paper, we expand on previous studies to further describe the flame propagation dynamics in porous media. We develop a model that incorporates a p-Laplacian operator to represent both fast and slow diffusion effects. Additionally, we include an advection term and a modified reaction term to address a broader range of chemical reactions related to flame spread. Based on analytical assessments, we first ascertain fundamental properties of the model’s solutions, such as regularity, boundedness, and uniqueness. We also examine stationary solutions, deriving their approximate analytical forms using regular perturbation methods and analyzing them within a Hamiltonian framework. Finally, we compare these analytical solutions with numerical ones to determine the spatial region where the approximate analytical solutions are valid within acceptable levels of error.