Economical Turbulence Simulation Using Map-Based Advection
Lagrangian numerical advection schemes typically involve displacements of mesh-cell boundaries that can be viewed as property-conserving maps applied to the discretized flow domain. The representation of advective motion as a suitably constrained map motivates reduced modeling of turbulent flow that involves a stochastic time sequence of maps, where the map definition and the spatiotemporal distribution of maps embody turbulence phenomenology. This nonlocal, time-discontinuous advection treatment is not deduced from the Navier-Stokes equation but its conservation properties are analogous to those of Navier-Stokes flow. This framework enables turbulent flow simulation on a one-dimensional (1D) spatial domain. The resulting computational efficiency allows fully resolved time advancement of both advection and concurrent microphysical processes (viscous transport, scalar micromixing, chemical reactions, multiphase phenomena, etc.) in highly turbulent flows. Several representative formulations within this framework are described. Applications include free shear flows, boundary layers, particle clustering and coagulation, chemically reacting flows, thermohaline staircases, and shock-turbulence interactions. Various subgrid-scale closure formulations are in use or under development.
