Bound-Preserving Discontinuous Galerkin Methods with Modified Patankar Time Integrations for Chemical Reacting Flows

In this paper,we develop bound-preserving discontinuous Galerkin(DG)methods for chemical reactive flows.There are several difficulties in constructing suitable numerical schemes.First of all,the density and internal energy are positive,and the mass fraction of each species is between 0 and 1.Second,due to the rapid reaction rate,the system may contain stiff sources,and the strong-stability-preserving explicit Runge-Kutta method may result in limited time-step sizes.To obtain physically relevant numerical approximations,we apply the bound-preserving technique to the DG methods.Though traditional positivity-preserving techniques can successfully yield positive density,internal energy,and mass fractions,they may not enforce the upper bound 1 of the mass fractions.To solve this problem,we need to(i)make sure the numerical fluxes in the equations of the mass fractions are consistent with that in the equation of the density;(ii)choose conservative time integrations,such that the summation of the mass fractions is preserved.With the above two conditions,the positive mass fractions have summation 1,and then,they are all between 0 and 1.For time discretization,we apply the modified Runge-Kutta/multi-step Patankar methods,which are explicit for the flux while implicit for the source.Such methods can handle stiff sources with relatively large time steps,preserve the positivity of the target variables,and keep the summation of the mass fractions to be 1.Finally,it is not straightforward to combine the bound-preserving DG methods and the Patankar time integrations.The positivity-preserving technique for DG methods requires positive numerical approximations at the cell interfaces,while Patankar methods can keep the positivity of the pre-selected point values of the target variables.To match the degree of freedom,we use polynomials on rectangular meshes for problems in two space dimensions.To evolve in time,we first read the polynomials at the Gaussian points.Then,suitable slope limiters can be applied to enforce the positivity of the solutions at those points,which can be preserved by the Patankar methods,leading to positive updated numerical cell averages.In addition,we use another slope limiter to get positive solutions used for the bound-preserving technique for the flux.Numerical examples are given to demonstrate the good performance of the proposed schemes.

ZERO DISSIPATION LIMIT TO A RAREFACTION WAVE WITH A VACUUM FOR A COMPRESSIBLE,HEAT CONDUCTING REACTING MIXTURE

In this paper,we study the zero dissipation limit with a vacuum for the reacting mixture Navier-Stokes equations.For proper smooth initial data that the initial density tends to zero as the relevant physical coefficients tend to zero,we demonstrate that the solution tends to a rarefaction wave connected to a vacuum on the left side coupled with a zero mass fraction of reactant.What is more,the uniform convergence rate is obtained.

NONLINEAR STABILITY OF RAREFACTION WAVES TO THE COMPRESSIBLE NAVIER-STOKES EQUATIONS FOR A REACTING MIXTURE WITH ZERO HEAT CONDUCTIVITY

In this paper,we study the time-asymptotically nonlinear stability of rarefaction waves for the Cauchy problem of the compressible Navier-Stokes equations for a reacting mixture with zero heat conductivity in one dimension.If the corresponding Riemann problem for the compressible Euler system admits the solutions consisting of rarefaction waves only,it is shown that its Cauchy problem has a unique global solution which tends time-asymptotically towards the rarefaction waves,while the initial perturbation and the strength of rarefaction waves are suitably small.

LARGE-EDDY SIMULATION OF TWO-PHASE REACTING FLOW IN MODEL COMBUSTOR

The gas-droplet two-phase reacting flow in a model combustor with the V-gutter flame holder is studied by an Eulerian-Lagrangian large-eddy simulation (LES) approach. The k-equation subgrid-scale model is used to simulate the subgrid eddy viscosity, and the eddy-break-up (EBU) combustion subgrid-scale model is used to determine the chemical reaction rate. A two-step turbulent combustion subgrid-scale model is employed for calculating carbon monoxide CO concentration, and the NO subgrid-scale pollutant formation model for the evaluation of the rate of NO formation. The heat flux model is applied to the prediction of radiant heat transfer. The gas phase is solved with the SIMPLE algorithm and a hybrid scheme in the staggered grid system. The liquid phase equations are solved in a Lagrangian frame in reference of the particle-source-in-cell (PSIC) algorithm. From simulation results, the exchange of mass, moment and energy between gas and particle fields for the reacting flow in the afterburner with a V-gutter flame holder can be obtained. By the comparison of experimental and simulation results, profile temperature and pollutant of the outlet are quite in agreement with experimental data. Results show that the LES approach for predicting the two-phase instantaneous reacting flow and pollutant emissions in the afterburner is feasible.

Critical temperatures and pressures of reacting mixture in synthesis of dimethyl carbonate with methanol and carbon dioxide

Critical temperatures and pressures of nominal reacting mixture in synthesis of dimethyl carbonate （DMC） from methanol and carbon dioxide （quaternary mixture of carbon dioxide ＋ methanol ＋ water ＋ DMC） were measured using a high-pressure view cell. The results suggested that the critical properties of the reacting mixture depended on the reaction extent as well as its initial composition （initial ratio of carbon dioxide to methanol）. Such information is essential for determining the reaction conditions when one intends to carry out the synthesis of DMC with CO2 and methanol under supercritical conditions.

THE NONLINEAR STABILITY OF TRAVELLING WAVE SOLUTIONS FOR A REACTING FLOW MODEL WITH SOURCE TERM

In this paper, author considers a 3 x 3 system for a reacting flow model propesed by [9]. Since this model has source term, it can be considered as a relaxation approximation to 2 x 2 systems of conservation laws, which include the well-known p-system. From this viewpoint, the author establishes the global existence and the nonlinear stability of travelling wave solutions by L-2 energy method.

High-order discontinuous Galerkin method for applications to multicomponent and chemically reacting flows

This article focuses on the development of a discontinuous Galerkin (DG) method for simulations of multicomponent and chemically reacting flows. Compared to aerodynamic flow applications, in which DG methods have been successfully employed, DG simulations of chemically reacting flows introduce challenges that arise from flow unsteadiness, combustion, heat release, compressibility effects, shocks, and variations in thermodynamic properties. To address these challenges, algorithms are developed, including an entropy-bounded DG method, an entropy-residual shock indicator, and a new formulation of artificial viscosity. The performance and capabilities of the resulting DG method are demonstrated in several relevant applications, including shock/bubble interaction, turbulent combustion, and detonation. It is concluded that the developed DG method shows promising performance in application to multicomponent reacting flows. The paper concludes with a discussion of further research needs to enable the application of DG methods to more complex reacting flows.

Efficient Stochastic Simulation Algorithm for Chemically Reacting Systems Based on Support Vector Regression

The stochastic simulation algorithm （SSA） accurately depicts spatially homogeneous wellstirred chemically reacting systems with small populations of chemical species and properly represents noise, but it is often abandoned when modeling larger systems because of its computational complexity. In this work, a twin support vector regression based stochastic simulations algorithm （TS^3A） is proposed by combining the twin support vector regression and SSA, the former is a well-known robust regression method in machine learning. Numerical results indicate that this proposed algorithm can be applied to a wide range of chemically reacting systems and obtain significant improvements on efficiency and accuracy with fewer simulating runs over the existing methods.

L-leap:accelerating the stochastic simulation of chemically reacting systems

Presented here is an L-leap method for accelerating stochastic simulation of well-stirred chemically reacting systems, in which the number of reactions occurring in a reaction channel with the largest propensity function is calculated from the leap condition and the number of reactions occurring in the other reaction channels are generated by using binomial random variables during a leap. The L-leap method can better satisfy the leap condition. Numerical simulation results indicate that the L-leap method can obtain better performance than established methods.

NUMERICAL SIMULATION OF SUPERSONIC REACTING MIXING LAYER

In this paper, the supersonic chemically reacting mixing layer is simulated with the third order ENN scheme, based on the Navier-Stokes equations, containing transport equations of all species. The numerical results show that the thickness of mixing layer increases gradually along the flow direction, and that the Kelvin-Helmholtz, instabilities may not exist in mixing layer flows.

Validation of the RANS-SOM Combustion Model Using Direct Numerical Simulation of Incompressible Turbulent Reacting Flows

The second-order moment combustion model, proposed by the authors is validated using the direct numerical simulation （DNS） of incompressible turbulent reacting channel flows. The instantaneous DNS results show the near-wall strip structures of concentration and temperature fluctuations. The DNS statistical results give the budget of the terms in the correlation equations, showing that the production and dissipation terms are most important. The DNS statistical data are used to validate the closure model in RANS second-order moment （SOM） combustion model. It is found that the simulated diffusion and production terms are in agreement with the DNS data in most flow regions, except in the near-wall region, where the near-wall modification should be made, and the closure model for the dissipation term needs further improvement. The algebraic second-order moment （ASOM） combustion model is well validated by DNS.

EXISTENCE OF ENTROPY SOLUTIONS TO TWO-DIMENSIONAL STEADY EXOTHERMICALLY REACTING EULER EQUATIONS

We are concerned with the global existence of entropy solutions of the two-dimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate function φ（T ） is assumed to have a positive lower bound. We first consider the Cauchy problem （the initial value problem）, that is, seek a supersonic downstream reacting flow when the incoming flow is supersonic, and establish the global existence of entropy solutions when the total variation of the initial data is sufficiently small. Then we analyze the problem of steady supersonic, exothermically reacting Euler flow past a Lipschitz wedge, generating an ad-ditional detonation wave attached to the wedge vertex, which can be then formulated as an initial-boundary value problem. We establish the global existence of entropy solutions containing the additional detonation wave （weak or strong, determined by the wedge angle at the wedge vertex） when the total variation of both the slope of the wedge boundary and the incoming flow is suitably small. The downstream asymptotic behavior of the global solutions is also obtained.

GLOBAL EXISTENCE AND LARGE TIME BEHAVIOR OF SOLUTION TO REACTING FLOW MODEL WITH BOUNDARY EFFECT

The initial boundary value problem (IBVP) for the 3×3 hyperbolic system of reacting flow with source term proposed by R.J.LeVeque and others (see [8]) is considered.It is shown, in the present paper, that if the initial data are a suitable perturbation of a shiftcd shock profile which is suitably away from the boundary, then there exists a unique smooth solution in R2+ to the IBVP of the 3×3 hyperbolic system, which tends to another shifted shock profile of this system as t →∞.

ASYMPTOTIC STABILITY OF A VISCOUS CONTACT WAVE FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS FOR A REACTING MIXTURE

We consider the large time behavior of solutions of the Cauchy problem for the one-dimensional compressible Navier-Stokes equations for a reacting mixture.When the corresponding Riemann problem for the Euler system admits a contact discontinuity wave,it is shown that the viscous contact wave which corresponds to the contact discontinuity is asymptotically stable,provided the strength of contact discontinuity and the initial perturbation are suitably small.We apply the approach introduced in Huang,Li and Matsumura(2010)[1]and the elemen tary L2-energy met hods.

Turbulence Characteristics of Swirling Reacting Flow in a Combustor with Staged Air Injection

This paper presents an experimental investigation of the turbulent reacting flow in a swirl combustor with staged air injection. The air injected into the combustor is composed of the primary swirling jet and the secon-dary non-swirling jet. A three dimension-laser particle dynamic analyzer (PDA) was employed to measure the in-stantaneous gas velocity. The probability density functions (PDF) for the instantaneous gas axial and tangential ve-locities at each measuring location, as well as the radial profiles of the root mean square of fluctuating gas axial and tangential velocities and the second-order moment for the fluctuating gas axial and tangential velocities are ob-tained. The measured results delineate the turbulence properties of the swirling reacting flow under the conditions of staged combustion.

NUMERICAL CALCULATIONS OF GASEOUS REACTING FLOWS IN A MODEL OF GAS TURBINE COMBUSTORS

This paper describes the numerical calculations of gaseous reaction flows in a model of gas turbine combustors. The profiles of hydrodynamic and thermodynamic patterns in a three-dimensional combustor model are obtained by solving the governing differential transport equations. The well-established numerical prediction algorithm SIMPLE, the modified k-ε turbulence model and k-ε-g turbulent diffusion flame model have been adopted in computations. The β function has been selected as probability density function. The effect of combustion process on flow patterns has been investigated. The calculated results have been verified by experiments. They are in remarkably good agreement.

Regulation of the Reacted Layer Thickness in a Gas-Solid Reacting System

A mathematical model for the analysis of a gas-solid reacting system is presented. This model is an alternative to the classical shrinking-core model. The model has a structure that can be easily transformed into a canonical control form, which is proper for controller synthesis. Analytical solution of the model to describe the open-loop behavior is expressed in terms of the Lambert function. The Lambert function is evaluated from aTaylorexpansion series. Besides, a controller is proposed to regulate the reacted layer thickness using initially the diffusion coefficient as control input. The control law is synthesized employing the feedback linearization technique. Main contributions of this work are the synthesis of the layer thickness controller, and the employment of the process temperature as substitute of the diffusion coefficient as the control input.

融合ReAct模式的图书馆大语言模型知识服务系统构建

文章聚焦大语言模型时代图书馆知识服务,以家谱知识内容为实验对象,探索融合ReAct模式的图书馆大语言模型知识服务系统构建路径。实验通过将RDF数据转化为自然语言文本构建数据集,运用ReAct模式推动大语言模型执行数据查询、多语种查询、资源检索、资源推荐和资源解读等任务,展现融合ReAct模式下大语言模型在自然语言处理和上下文理解方面的能力,实验也揭示了包括多语种问题理解上的挑战、模糊查询结果一致性、背景知识补充方面的改进空间等问题。文章对大语言模型时代图书馆知识服务的创新发展提出新视角,通过整合ReAct模式下智能系统的推理和行动能力,探索图书馆提升知识服务效能和个性化服务的新模式。

基于React的电商网站构建与实现

为了满足电商网站所需的各项功能和要求,基于React框架和Node.js进行了电商网站的前后端分离式开发,并设计了关键模块,如用户认证、商品展示、购物车管理及订单处理等。采用了React的组件化开发理念,有效提升了代码的可维护性和可重用性。通过系统测试和性能调优,网站性能和稳定性得到显著提升,包括页面加载时间缩短、数据库查询速度优化以及系统响应性能改善。

基于MVVM模式SpringBoot框架的高校信息化项目管理系统

传统的Java EE应用以Spring MVC、Mybatis、FreeMarker为核心,具有架构分层不清晰、前后端代码耦合性高、不易扩展等缺点。为提高轻量级Java EE应用的开发效率,提出一种基于Ant Design、React、SpringBoot、Apache Cayenne框架的Java EE应用架构。其基于MVVM模式,以SpringBoot为核心向上集成Ant Design和React为前端,向下集成Apache Cayenne为后端,集成后的架构通过Ant Design和React实现表示层,通过SpringBoot实现控制层和业务逻辑层,通过Apache Cayenne实现数据持久层。基于此开发的高校信息化项目管理系统,架构层次清晰,前后端代码彻底分离,可供高校信息化项目管理部门使用和推广。