Method for efficiently solving steady-state microdynamics equation set based on automatic combination of time integration and Newton method

Abstract

The invention discloses a method for efficiently solving a steady-state microdynamics equation set based on automatic combination of time integration and a Newton method. The method comprises the following steps of carrying out time integration on the initial value by adopting a time integration method based on a low-precision numerical value, automatically integrating to obtain a coarse-precisionsteady-state coverage degree by combining coverage degree sensitivity, and obtaining the steady-state coverage degree by combining with a high-precision numerical value Newton method; if single solving fails, randomly initializing the coverage in the exponential space to carry out a new round of solving, which is used for automatically solving the microcosmic kinetic equation set of the catalystsurface chemical reaction network. The method provided by the invention has higher success rate, speed and precision for solving a steady-state microdynamics equation set; meanwhile, the method is high in automation degree, automatic iterative solving can be achieved only by setting initial parameters, man-machine interaction is not needed in the process, and the algorithm process is simple and easy to master.

Description

technical field [0001] The invention belongs to the research field of microcosmic dynamics analysis of heterogeneous catalytic reactions, and specifically relates to a method for automatically and efficiently solving steady-state microcosmic kinetic equations based on time integral and Newton's method, which can be used for complex catalyst surface reaction network microcosmic kinetic equations High-precision, fast and automatic solution. Background technique [0002] Heterogeneous catalysis plays an indispensable role in modern chemistry, especially in the fields of energy conversion and the environment, where catalysts play a key role. Today, the scientific design of efficient catalysts has become an important goal for researchers, but it is also a challenging problem. Compared with the relatively inefficient trial-and-error method in traditional experiments, the development of density functional theory (DFT) and micro-kinetic analysis in the past two decades can prompt r...

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Problems solved by technology

Therefore, this method can only obtain accurate values ​​quickly by selecting a reasonable initial value, otherwise it is difficult to converge to a high-precision solution or an effective solution (with physical meaning); In order to ensure the validity and accuracy of its iterative direction (Jacobian matrix), the Newton method iteration usually consumes a lot of computer memory and computing time, especially when the Newton method fails to solve

In addition, microscopic dynamics simulation programs such as Cantera and MKMCXX use high-precision numerical time integration to a sufficiently long time scale as a steady-state solution. Although the high-precision numerical time-integration method can achieve a relatively stable solution through iteration, the It usually requires a large time step and computer memory, and repeated iterations lead to a long solution time; although the time integration method of low-precision numerical values ​​is faster, it usually can only obtain the approximate distribution trend of the coverage, and its order of magnitude is comparable to that of high-precision Numerical results vary considerably, especially at higher degrees of stiffness

If simply combining time integration and Newton's method for alternate iterations, although it is possible to realize the possibility of combining the characteristics of the two methods, using the coverage that has not reached a steady state as the initial value of the Newton's method will lead to a high probability of failure in the solution result. Simultaneous multiple iterations of the Newton method require longer solution time. Therefore, in practical applications, this method still has problems such as long solution time, low efficiency and frequent failures.

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