Equation-free multi-scale simulation method in chemical reaction diffusion

Abstract

The invention discloses an equation-free multi-scale simulation method in chemical reaction diffusion. The method comprises the following steps of: establishing a small-scale model, i.e. a lattice Boltzmann model, on the basis of mesoscopic scale, wherein the small-scale model can truly approach reaction diffusion systems; respectively constructing coarse-grained time steps to the reaction diffusion systems of Schlogl and Selkov; and coupling an Euler method in a traditional numerical technology and the coarse-grained time steps of the reaction diffusion systems of Schlogl and Selkov into the coarse-grained projection integration of the reaction diffusion systems of Schlogl and Selkov so as to realize the multi-scale simulation of concentrations in constant steady states with different projection durations and evolution durations, and comparing with direct lattice Boltzmann simulation, wherein the concentration value of a macro system is fitted by adopting a least square method. The invention successfully avoids the procedure of acquiring a reaction diffusion model equation from the small-scale model and improves the operational efficiency of the direct lattice Boltzmann simulation, thereby providing a new idea for reaction diffusion simulation research which has difficulty in equation resolution on a macroscopic scale and has gigantic calculated amount of direct simulation on a small scale.

Description

technical field [0001] The invention relates to a novel complex system multi-scale simulation framework - an equation-free (Equation-free) method, in particular to an equation-free multi-scale simulation method in chemical reaction diffusion problems. It belongs to the technical field of multi-scale simulation of complex systems. Background technique [0002] The reaction-diffusion system is a typical complex system in nature, and its application range covers many disciplines, such as the predator-prey model in the ecosystem, the gas discharge model in the physical system, and the public opinion propagation model, etc. Chemical reaction is a typical reaction-diffusion system. With different control parameters, the system can exhibit different spatiotemporal behaviors, such as bistability, chemical wave, non-uniform steady state, chemical oscillation and other complex phenomena. It has something in common with the orderly structure of organisms and the law of self-organizati...

AI Technical Summary

Problems solved by technology

[0006] The purpose of the present invention is to overcome the essential defects of traditional direct simulation methods in obtaining complex system characteristics, and apply the coarse-grained projective integration (coarse projective integration) in the equation-free method for the Schlogl and Selkov two types of reaction-diffusion problems respectively The multi-scale simulation of the steady state of the concentration lays a solid foundation for the study of a new type of multi-component reaction-diffusion system with a huge amount of computation and more complex

Images