Multiscale overlap coupling for hybrid computations

A class of multiscale overlap coupling methods is proposed for hybrid computations which supplement partially-resolved simulations using low-frequency solutions. In this class of methods, the largest resolved scales of the partially-resolved simulation are forced to resemble low-frequency solutions in overlapping near-boundary regions. Simultaneously, the higher-frequency resolved scales are allowed to develop freely. The latter feature addresses a basic deficiency which has been encountered in the development of hybrid methods, that of poorly-excited high-wavenumber scales at interfaces between partially-resolved simulations and low-frequency solutions. The methods are embedded within the variational-multiscale framework and are elaborated for the case of a randomly-forced Burgers equation. Examples are given to illustrate their performance.