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A Hybrid backward euler Control Volume Method to Solve the Concentration-Dependent Solid-State Diffusion Problem in Battery Modeling

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Journal of Applied Mathematics and Physics 2020年第6期8卷 1066-1080页

作者： Kudakwashe Chayambuka Grietus Mulder Dmitri L. Danilov Peter H. L. Notten VITO Mol Belgium EnergyVille Genk Belgium Eindhoven University of Technology Eindhoven Netherlands Forschungszentrum Jülich Fundamental Electrochemistry (IEK-9) Jülich Germany University of Technology Sydney Broadway Sydney NSW Australia

Several efficient analytical methods have been developed to solve the solid-state diffusion problem, for constant diffusion coefficient problems. However, these methods cannot be applied for concentration-dependent diffusion coefficient problems and numerical methods are used instead. Herein, grid-based numerical methods derived from the control volume discretization are presented to resolve the characteristic nonlinear system of partial differential equations. A novel hybrid backward euler control volume (HBECV) method is presented which requires only one iteration to reach an implicit solution. The HBECV results are shown to be stable and accurate for a moderate number of grid points. The computational speed and accuracy of the HBECV, justify its use in battery simulations, in which the solid-state diffusion coefficient is a strong function of the concentration.

关键词： Solid-State Diffusion Implicit Methods backward euler

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Alternating Direction Implicit Galerkin Finite Element Method for the Two-Dimensional Time Fractional Evolution Equation

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Numerical Mathematics(Theory,Methods and Applications) 2014年第1期7卷 41-57页

作者： Limei Li Da Xu College of Mathematics and Computer Science Hunan Normal UniversityChangsha 410081China Department of Mathematics Hunan Institute of Science and TechnologyYueyang 414000China

New numerical techniques are presented for the solution of the twodimensional time fractional evolution equation in the unit *** these methods,Galerkin finite element is used for the spatial discretization,and,for the time stepping,new alternating direction implicit(ADI)method based on the backward euler method combined with the first order convolution quadrature approximating the integral term are *** ADI Galerkin finite element method is proved to be convergent in time and in the L2 norm in *** convergence order is O(k|ln k|+h^(r)),where k is the temporal grid size and h is spatial grid size in the x and y directions,*** results are presented to support our theoretical analysis.

关键词： Fractional evolution equation alternating direction implicit method Galerkin finite element method backward euler

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