In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-depe...In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-dependent problems.We use the convex splitting method,the variant energy quadratization method,and the scalar auxiliary variable method coupled with the LDG method to construct first-order temporal accurate schemes based on the gradient flow structure of the models.These semi-implicit schemes are decoupled,energy stable,and can be extended to high accuracy schemes using the semi-implicit spectral deferred correction method.Many bound preserving DG discretizations are only worked on explicit time integration methods and are difficult to get high-order accuracy.To overcome these difficulties,we use the Lagrange multipliers to enforce the implicit or semi-implicit LDG schemes to satisfy the bound constraints at each time step.This bound preserving limiter results in the Karush-Kuhn-Tucker condition,which can be solved by an efficient active set semi-smooth Newton method.Various numerical experiments illustrate the high-order accuracy and the effect of bound preserving.展开更多
By introducing the dimensional splitting(DS)method into the multiscale interpolating element-free Galerkin(VMIEFG)method,a dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method is propose...By introducing the dimensional splitting(DS)method into the multiscale interpolating element-free Galerkin(VMIEFG)method,a dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method is proposed for three-dimensional(3D)singular perturbed convection-diffusion(SPCD)problems.In the DSVMIEFG method,the 3D problem is decomposed into a series of 2D problems by the DS method,and the discrete equations on the 2D splitting surface are obtained by the VMIEFG method.The improved interpolation-type moving least squares(IIMLS)method is used to construct shape functions in the weak form and to combine 2D discrete equations into a global system of discrete equations for the three-dimensional SPCD problems.The solved numerical example verifies the effectiveness of the method in this paper for the 3D SPCD problems.The numerical solution will gradually converge to the analytical solution with the increase in the number of nodes.For extremely small singular diffusion coefficients,the numerical solution will avoid numerical oscillation and has high computational stability.展开更多
Economical water electrolysis requires highly active non-noble electrocatalysts to overcome the sluggish kinetics of the two half-cell reactions,oxygen evolution reaction,and hydrogen evolution reaction.Although inten...Economical water electrolysis requires highly active non-noble electrocatalysts to overcome the sluggish kinetics of the two half-cell reactions,oxygen evolution reaction,and hydrogen evolution reaction.Although intensive efforts have been committed to achieve a hydrogen economy,the expensive noble metal-based catalysts remain under consideration.Therefore,the engineering of self-supported electrocatalysts prepared using a direct growth strategy on three-dimensional(3D)nickel foam(NF)as a conductive substrate has garnered significant interest.This is due to the large active surface area and 3D porous network offered by these electrocatalysts,which can enhance the synergistic eff ect between the catalyst and the substrate,as well as improve electrocatalytic performance.Hydrothermal-assisted growth,microwave heating,electrodeposition,and other physical methods(i.e.,chemical vapor deposition and plasma treatment)have been applied to NF to fabricate competitive electrocatalysts with low overpotential and high stability.In this review,recent advancements in the development of self-supported electrocatalysts on 3D NF are described.Finally,we provide future perspectives of self-supported electrode platforms in electrochemical water splitting.展开更多
文摘In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-dependent problems.We use the convex splitting method,the variant energy quadratization method,and the scalar auxiliary variable method coupled with the LDG method to construct first-order temporal accurate schemes based on the gradient flow structure of the models.These semi-implicit schemes are decoupled,energy stable,and can be extended to high accuracy schemes using the semi-implicit spectral deferred correction method.Many bound preserving DG discretizations are only worked on explicit time integration methods and are difficult to get high-order accuracy.To overcome these difficulties,we use the Lagrange multipliers to enforce the implicit or semi-implicit LDG schemes to satisfy the bound constraints at each time step.This bound preserving limiter results in the Karush-Kuhn-Tucker condition,which can be solved by an efficient active set semi-smooth Newton method.Various numerical experiments illustrate the high-order accuracy and the effect of bound preserving.
基金supported by the Natural Science Foundation of Zhejiang Province,China(Grant Nos.LY20A010021,LY19A010002,LY20G030025)the Natural Science Founda-tion of Ningbo City,China(Grant Nos.2021J147,2021J235).
文摘By introducing the dimensional splitting(DS)method into the multiscale interpolating element-free Galerkin(VMIEFG)method,a dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method is proposed for three-dimensional(3D)singular perturbed convection-diffusion(SPCD)problems.In the DSVMIEFG method,the 3D problem is decomposed into a series of 2D problems by the DS method,and the discrete equations on the 2D splitting surface are obtained by the VMIEFG method.The improved interpolation-type moving least squares(IIMLS)method is used to construct shape functions in the weak form and to combine 2D discrete equations into a global system of discrete equations for the three-dimensional SPCD problems.The solved numerical example verifies the effectiveness of the method in this paper for the 3D SPCD problems.The numerical solution will gradually converge to the analytical solution with the increase in the number of nodes.For extremely small singular diffusion coefficients,the numerical solution will avoid numerical oscillation and has high computational stability.
基金supported by The Chinese Academy of Sciences (CAS) President’s International Fellowship Initiative (No. 2023VCB0014)The National Natural Science Foundation of China (No. 52203284)Shenzhen Science and Technology Program (Nos. GJHZ20220913143801003 and RCBS20221008093057026)
文摘Economical water electrolysis requires highly active non-noble electrocatalysts to overcome the sluggish kinetics of the two half-cell reactions,oxygen evolution reaction,and hydrogen evolution reaction.Although intensive efforts have been committed to achieve a hydrogen economy,the expensive noble metal-based catalysts remain under consideration.Therefore,the engineering of self-supported electrocatalysts prepared using a direct growth strategy on three-dimensional(3D)nickel foam(NF)as a conductive substrate has garnered significant interest.This is due to the large active surface area and 3D porous network offered by these electrocatalysts,which can enhance the synergistic eff ect between the catalyst and the substrate,as well as improve electrocatalytic performance.Hydrothermal-assisted growth,microwave heating,electrodeposition,and other physical methods(i.e.,chemical vapor deposition and plasma treatment)have been applied to NF to fabricate competitive electrocatalysts with low overpotential and high stability.In this review,recent advancements in the development of self-supported electrocatalysts on 3D NF are described.Finally,we provide future perspectives of self-supported electrode platforms in electrochemical water splitting.
