Higher-order moments in macrotransport processes

A novel moment-gradient expansion scheme, expressing the microscale probability density P as an infinite sum of global-space gradients of its corresponding macroscale density P̄ multiplied by coefficients formed from its local and total moments, is employed to derive an asymptotic long-time macrotransport equation from its more detailed microtransport predecessor. Particular emphasis is paid to third- and higher-order gradient terms in the expansion. These are shown to result in non-Gaussian behavior of the macroscale probability density P̄ governing convective–diffusive transport processes.