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 e...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.展开更多
Chemical process optimization can be described as large-scale nonlinear constrained minimization. The modified augmented Lagrange multiplier methods (MALMM) for large-scale nonlinear constrained minimization are studi...Chemical process optimization can be described as large-scale nonlinear constrained minimization. The modified augmented Lagrange multiplier methods (MALMM) for large-scale nonlinear constrained minimization are studied in this paper. The Lagrange function contains the penalty terms on equality and inequality constraints and the methods can be applied to solve a series of bound constrained sub-problems instead of a series of unconstrained sub-problems. The steps of the methods are examined in full detail. Numerical experiments are made for a variety of problems, from small to very large-scale, which show the stability and effectiveness of the methods in large-scale problems.展开更多
To accelerate the kinetics of the oxygen reduction reaction(ORR)in proton exchange membrane fuel cells,ultrafine Pt nanoparticles modified with trace amounts of cobalt were fabricated and decorated on carbon black thr...To accelerate the kinetics of the oxygen reduction reaction(ORR)in proton exchange membrane fuel cells,ultrafine Pt nanoparticles modified with trace amounts of cobalt were fabricated and decorated on carbon black through a strategy involving modified glycol reduction and chemical etching.The obtained Pt36Co/C catalyst exhibits a much larger electrochemical surface area(ECSA)and an improved ORR electrocatalytic activity compared to commercial Pt/C.Moreover,an electrode prepared with Pt36Co/C was further evaluated under H2-air single cell test conditions,and exhibited a maximum specific power density of 10.27 W mgPt^-1,which is 1.61 times higher than that of a conventional Pt/C electrode and also competitive with most state-of-the-art Pt-based architectures.In addition,the changes in ECSA,power density,and reacting resistance during the accelerated degradation process further demonstrate the enhanced durability of the Pt36Co/C electrode.The superior performance observed in this work can be attributed to the synergy between the ultrasmall size and homogeneous distribution of catalyst nanoparticles,bimetallic ligand and electronic effects,and the dissolution of unstable Co with the rearrangement of surface structure brought about by acid etching.Furthermore,the accessible raw materials and simplified operating procedures involved in the fabrication process would result in great cost-effectiveness for practical applications of PEMFCs.展开更多
基金supported by the NSF under Grant DMS-1818467Simons Foundation under Grant 961585.
文摘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.
文摘Chemical process optimization can be described as large-scale nonlinear constrained minimization. The modified augmented Lagrange multiplier methods (MALMM) for large-scale nonlinear constrained minimization are studied in this paper. The Lagrange function contains the penalty terms on equality and inequality constraints and the methods can be applied to solve a series of bound constrained sub-problems instead of a series of unconstrained sub-problems. The steps of the methods are examined in full detail. Numerical experiments are made for a variety of problems, from small to very large-scale, which show the stability and effectiveness of the methods in large-scale problems.
基金supported by the National Major Research Project(2016YFB0101208)the National Natural Science Foundation of China(21576257)+1 种基金the Natural Science Foundation-Liaoning United Fund(U1508202)the Strategic Priority Research Program of the Chinese Academy of Sciences(XDB06050303)~~
文摘To accelerate the kinetics of the oxygen reduction reaction(ORR)in proton exchange membrane fuel cells,ultrafine Pt nanoparticles modified with trace amounts of cobalt were fabricated and decorated on carbon black through a strategy involving modified glycol reduction and chemical etching.The obtained Pt36Co/C catalyst exhibits a much larger electrochemical surface area(ECSA)and an improved ORR electrocatalytic activity compared to commercial Pt/C.Moreover,an electrode prepared with Pt36Co/C was further evaluated under H2-air single cell test conditions,and exhibited a maximum specific power density of 10.27 W mgPt^-1,which is 1.61 times higher than that of a conventional Pt/C electrode and also competitive with most state-of-the-art Pt-based architectures.In addition,the changes in ECSA,power density,and reacting resistance during the accelerated degradation process further demonstrate the enhanced durability of the Pt36Co/C electrode.The superior performance observed in this work can be attributed to the synergy between the ultrasmall size and homogeneous distribution of catalyst nanoparticles,bimetallic ligand and electronic effects,and the dissolution of unstable Co with the rearrangement of surface structure brought about by acid etching.Furthermore,the accessible raw materials and simplified operating procedures involved in the fabrication process would result in great cost-effectiveness for practical applications of PEMFCs.
