Resolution of subgrid microscale interactions enhances the discretisation of nonautonomous partial differential equations

作者：

Highlights：

• We consider a general method for the macroscale modelling of nonlinear, nonautomomous partial differential equations or difference equations.

• Our method is able to resolve the complex fluctuations which arise in nonliner, nonautonomous systems.

• These fluctuations are not accounted for by popular multiscale averaging procedures and homogenization.

• Our method is illustrated with the example of a forced Burgers’ equation.

摘要

•We consider a general method for the macroscale modelling of nonlinear, nonautomomous partial differential equations or difference equations.•Our method is able to resolve the complex fluctuations which arise in nonliner, nonautonomous systems.•These fluctuations are not accounted for by popular multiscale averaging procedures and homogenization.•Our method is illustrated with the example of a forced Burgers’ equation.

论文关键词：Nonlinear nonautonomous PDEs,Spatial discretisation,Nonautonomous slow manifold,Multiscale modelling,Closure,Coarse graining

论文评审过程：Received 7 May 2015, Revised 16 December 2016, Accepted 23 January 2017, Available online 14 February 2017, Version of Record 14 February 2017.

论文官网地址：https://doi.org/10.1016/j.amc.2017.01.056