Critical Quenching Exponents for Heat Equations Coupled with Nonlinear Boundary Flux

We discuss the quenching phenomena for a system of heat equations coupled with nonlinear boundary flux. We determine a critical value for the exponents in the boundary flux, such that only in the super critical case the simultaneous quenching can happen for any solution.

GLOBAL EXISTENCE AND NONEXISTENCE FOR A DOUBLY DEGENERATE PARABOLIC SYSTEM COUPLED VIA NONLINEAR BOUNDARY FLUX

This article deals with the degenerate parabolic system with nonlinear boundary flux. By constructing the self-similar supersolution and subsolution, we obtain the critical global existence curve and the critical Fujita curve for the problem. Especially for the blow-up case, it is rather technical. It comes from the construction of the so-called Zel＇dovich-Kompaneetz-Barenblatt profile

Real-Time Traffic State and Boundary Flux Estimation with Distributed Speed Detecting Networks

The rapid development of 5G mobile communication and portable traffic detection technologies enhances highway transportation systems in detail and at a vehicle level. Besides the advantage of no disturbance to the regular traffic operation, these ubiquitous sensing technologies have the potential for unprecedented data collection at any temporal and spatial position. While as a typical distributed parameter system, the freeway traffic dynamics are determined by the current system states and the boundary traffic demand-supply. Using the three-step extended Kalman filtering, this paper simultaneously estimates the real-time traffic state and the boundary flux of freeway traffic with the distributed speed detector networks organized at any location of interest. In order to assess the effectiveness of the proposed approach, a freeway segment from Interstate 80 East (I-80E) in Alameda, Emeryville, and Northern California is selected. Experimental results show that the proposed method has the potential of using only speed detecting data to monitor the state of urban freeway transportation systems without access to the traditional measurement data, such as the boundary flows.

PROPERTIES OF THE BOUNDARY FLUX OF A SINGULAR DIFFUSION PROCESS

The authors study the singular diffusion equationwhere Ω(?)Rn is a bounded domain with appropriately smooth boundary δΩ, ρ(x) = dist(x,δΩ), and prove that if α≥p-1, the equation admits a unique solution subject only to a given initial datum without any boundary value condition, while if 0 <α< p - 1, for a given initial datum, the equation admits different solutions for different boundary value conditions.

A Reaction-diffusion System with Nonlinear Absorption Terms and Boundary Flux

This paper deals with a reaction-diffusion system with nonlinear absorption terms and boundary flux. As results of interactions among the six nonlinear terms in the system, some sufficient conditions on global existence and finite time blow-up of the solutions are described via all the six nonlinear exponents appearing in the six nonlinear terms. In addition, we also show the influence of the coefficients of the absorption terms as well as the geometry of the domain to the global existence and finite time blow-up of the solutions for some cases. At last, some numerical results are given.

Quenching rates for heat equations with coupled singular nonlinear boundary flux

We study finite time quenching for heat equations coupled via singular nonlinear boundary flux. A criterion is proposed to identify the simultaneous and non-simultaneous quenchings. In particular, three kinds of simultaneous quenching rates are obtained for different nonlinear exponent regions and appropriate initial data. This extends an original work by Pablo, Quirós and Rossi for a heat system with coupled inner absorption terms subject to homogeneous Neumann boundary conditions.

A Nonlinear Diffusion System with Coupled Nonlinear Boundary Flux

This paper studies a nonlinear diffusion system with coupled nonlinear boundary flux and two kinds of inner sources （positive for the first and negative for the second）, where the four nonlinear mechanisms are described by eight nonlinear parameters. The critical exponent of the system is determined by a complete classification of the eight nonlinear parameters, which is represented via the characteristic algebraic system introduced to the problem.

STEFAN PROBLEM WITH NONLINEAR BOUNDARY FLUX AND INTERNAL CONVECTION OF A MATERIAL

A Stefan problem with nonlinear boundary flux and internal convection of a material are considered. The existence, uniqueness and continuous dependence of globally weak solution of this problem are obtained. This paper extends the results of Fahuai Yi and T.M.Shih, relaxes restrictions that does not be to accord with reality very much on internal convection and boundary conditions in their articles.

Generalized boundary dilatation flux on a flexible wall

In this paper,by applying theoretical method to the governing equations of compressible viscous flow,we derive the theoretical formula of the boundary dilatation flux(BDF)on a flexible wall,which generalizes the most recent work of Mao et al.(Acta Mechanica Sinica 38(2022)321583)for a stationary wall.Different boundary sources of dilatation are explicitly identified,revealing not only the boundary generation mechanisms of vortex sound and entropy sound,but also some additional sources due to the surface vorticity,surface angular velocity,surface acceleration and surface curvature.In particular,the generation mechanism of dilatation at boundary due to the coupled divergence terms is highlighted,namely,the product of the surface velocity divergence(▽_(■B)·U)and the vorticity-induced skin friction divergence(V_(■B)·τ_(ω)).The former is attributed to the surface flexibility while the latter characterizes the footprints of near-wall coherent structures.Therefore,by properly designing the surface velocity distribution,the dilatation generation at the boundary could be controlled for practical purpose in near-wall compressible viscous flows.

Non-simultaneous quenching for a slow diffusion system coupled at the boundary

This paper deals with the quenching behavior of positive solutions to the Newton filtration equations coupled with boundary singularities.We determine quenching rates for non-simultaneous quenching at first,and then establish the criteria to identify the simultaneous and non-simultaneous quenching in terms of the parameters involved.

Blow-up rate estimate for degenerate parabolic equation with nonlinear gradient term

Abstract In this paper, the blow-up rate is obtained for a porous medium equation with a nonlinear gradient term and a nonlinear boundary flux. By using a scaling method and regularity estimates of parabolic equations, the blow-up rate determined by the interaction between the diffusion and the boundary flux is obtained. Compared with previous results, the gradient term, whose exponent does not exceed two, does not affect the blow-up rate of the solutions.

Numerical Study on Impact of the Boundary Layer Fluxes over Wetland on Sustention and Rainfall of Landfalling Tropical Cyclones

Numerical studies have been carried out to investigate the sustention and intensification of Typhoon Nina （7503）, and the impacts of saturated wetland on the sustention and rainfall of tropical cyclone （TC） over land through sensitivity experiments, using the PSU/NCAR non-hydrostatic mesoscale model MM5v3 and its TC bogus scheme. The results show that the vertical transfer of fluxes in the boundary layer over saturated wetland has significant influence on the intensity, structure, and rainfall of a landfalling TC. The latent heating flux and the sensible heating flux are both favourable for TC sustaining and intensification on which the latent heating transfer is more favourable than the sensible heating transfer. They are also favourable for the maintenance of the spiral structure, and have an evident effect on the distribution of TC rainfall. The momentum flux weakens the TC vortex wind fields significantly, and is the dominant factor to dissipate and fill in a low pressure system, while it increases the local precipitation induced by a typhoon.

Optimization design of multiphase pump impeller based on combined genetic algorithm and boundary vortex flux diagnosis

A novel optimization design method for the multiphase pump impeller is proposed through combining the quasi-3D hydraulic design（Q3DHD）, the boundary vortex flux（BVF） diagnosis, and the genetic algorithm（GA）. The BVF diagnosis based on the Q3DHD is used to evaluate the objection function. Numerical simulations and hydraulic performance tests are carried out to compare the impeller designed only by the Q3DHD method and that optimized by the presented method. The comparisons of both the flow fields simulated under the same condition show that（1） the pressure distribution in the optimized impeller is more reasonable and the gas-liquid separation is more efficiently inhibited,（2） the scales of the gas pocket and the vortex decrease remarkably for the optimized impeller,（3） the unevenness of the BVF distributions near the shroud of the original impeller is effectively eliminated in the optimized impeller. The experimental results show that the differential pressure and the maximum efficiency of the optimized impeller are increased by 4% and 2.5%, respectively. Overall, the study indicates that the optimization design method proposed in this paper is feasible.

Boundary Vorticity Flux and Engineering Flow Management

To improve the performance of complex viscous engineering flows,the focus should be on local dynamics(local processes and structures)measured by the space-time derivatives of the primary-variable fields,rather than these fields themselves.In the context of optimal flow management such as optimal configuration design and flow control,the local fluid dynamics on solid wall is of most direct relevance.For large Reynolds-number flows,we show that the on-wall local dynamics is highlighted by the balance between tangential pressure gradient and vorticity creation rate at the wall(boundary vorticity flux,BVF),namely the on-wall coupling of the compressing and shearing processes.This basic concept is demonstrated by previously unpublished and newly obtained numerical examples for external and internal flows,including the role of BVF as a faithful marker of the local appearance of boundary-layer separation and wall curvature discontinuity,and the use of BVF-based formulas to optimize the integrated performance of airfoil and compressor rotor blade.

Causal mechanism behind the stall delay by airfoil's pitching-up motion

Why the stall of an airfoil can be significantly delayed by its pitching-up motion？ Various attempts have been proposed to answer this question over the past half century, but none is satisfactory. In this letter we prove that a chain of vorticity-dynamics processes at accelerating boundary is fully responsible for the causal mechanism underlying this peculiar phenomenon. The local flow behavior is explained by a simple potential-flow model.

GROUNDWATER MASS TRANSPORT AND HOMOGENEOUS EQUILIBRIUM CHEMISTRY IN THE PRESENCE OF FLUX BOUNDARY CONDITIONS

Considering a solute transport problem deseribed by some algebraic and partial differentialequations with the presence of flux boundary conditions, we reduce the problem to a fixed point oneand use a priori estimates to prove the existence and uniqueness of the global solutions.

Effects of different freshwater flux representations in an ocean general circulation model of the tropical Pacific

Freshwater flux(FWF) is a major forcing that affects the ocean through several processes. The effects of FWF may be represented in ocean modeling as real freshwater flux(RFF) formulations and virtual salt flux(VSF) methods. RFF formulations have been implemented in the Geophysical Fluid Dynamics Laboratory(GFDL) Modular Ocean Model version 5(MOM5) as a replacement for the non-physical VSF method, which is primarily used in state-of-the-art ocean models. Here, we systematically evaluated the effects of RFF-related processes on the GFDL MOM5-based simulations in the tropical Pacific.When the FWF was treated as the natural boundary condition(NBC), it directly decreased the local temperature and the salinity by changing the volume of the top model layer, and it increased the temperature in the eastern Pacific by triggering an eastward Goldsbrough–Stommel circulation in the subsurface.Moreover, the heat content induced by the FWF tended to counteract the decreasing effects of the NBC on sea surface temperatures(SSTs) in the western-central tropical Pacific. The relationships between SST perturbations and the FWF representation in ocean modeling are also discussed.

Analysis on capabilities of density-based solvers within OpenFOAM to distinguish aerothermal variables in difusion boundary layer

Open source feld operation and manipulation（OpenFOAM）is one of the most prevalent open source computational fluid dynamics（CFD）software.It is very convenient for researchers to develop their own codes based on the class library toolbox within OpenFOAM.In recent years,several density-based solvers within OpenFOAM for supersonic/hypersonic compressible flow are coming up.Although the capabilities of these solvers to capture shock wave have already been verifed by some researchers,these solvers still need to be validated comprehensively as commercial CFD software.In boundary layer where diffusion is the dominant transportation manner,the convective discrete schemes＇capability to capture aerothermal variables,such as temperature and heat flux,is different from each other due to their own numerical dissipative characteristics and from viewpoint of this capability,these compressible solvers within OpenFOAM can be validated further.In this paper,frstly,the organizational architecture of density-based solvers within OpenFOAM is analyzed.Then,from the viewpoint of the capability to capture aerothermal variables,the numerical results of several typical geometrical felds predicted by these solvers are compared with both the outcome obtained from the commercial software Fastran and the experimental data.During the computing process,the Roe,AUSM＋（Advection Upstream Splitting Method）,and HLLC（Harten-Lax-van Leer-Contact）convective discrete schemes of which the spatial accuracy is 1st and 2nd order are utilized,respectively.The compared results show that the aerothermal variables are in agreement with results generated by Fastran and the experimental data even if the1st order spatial precision is implemented.Overall,the accuracy of these density-based solvers can meet the requirement of engineering and scientifc problems to capture aerothermal variables in diffusion boundary layer.

Diagnosis and Design Improvement of the Internal Flow Field in an Automotive Cooling Fan Based on Boundary Vorticity Dynamics, Part Ⅰ: Blade Profile Scaling and Rotation

To optimize the aerodynamic performance of the automobile cooling fan(ACF), the internal flow field of the original fan was numerically simulated. According to the theory of boundary vorticity dynamics(BVD), the distribution laws of the boundary vorticity flux(BVF) on the blade surface and the circumferential vorticity(CV) at the wake plane of the fan were analyzed, and the underlying various negative factors, such as vortex shedding, separated flow and complicated secondary flow, on the fan blade surface and its dynamic source were diagnosed. Combined with the velocity triangle theory, the mathematical relationship between the BVF diagnosis and the geometrical characteristics of the blade profile(hereinafter referred to as profile) is used to guide the design improvement of the blade. The analysis found that at the same speed, the extension and rotation of the profile could match a smaller input torque at the same flow rate and pressure rise, thereby improving the efficiency of the fan. The test results confirmed the above conclusion. The peak efficiency of the improved fan has been increased by 2.3%, and the aerodynamic performance in the low-flow-rate has been improved. The conclusion of the study shows the applicability of the BVD theory in the diagnosis and design improvement of ACF internal flow.

Evolutionary understanding of airfoil lift

This review attempts to elucidate the physical origin of aerodynamic lift of an airfoil using simple formulations and notations,particularly focusing on the critical effect of the fluid viscosity.The evolutionary development of the lift problem of a flat-plate airfoil is reviewed as a canonical case from the classical inviscid circulation theory to the viscous-flow model.In particular,the physical aspects of the analytical expressions for the lift coefficient of the plate-plate airfoil are discussed,including Newton’s sine-squared law,Rayleigh’s lift formula,thin-airfoil theory and viscous-flow lift formula.The vortex-force theory is described to provide a solid foundation for consistent treatment of lift,form drag,Kutta condition,and downwash.The formation of the circulation and generation of lift are discussed based on numerical simulations of a viscous starting flow over an airfoil,and the evolution of the flow topology near the trailing edge is well correlated with the realization of the Kutta condition.The presented contents are valuable for the pedagogical purposes in aerodynamics and fluid mechanics.