Reduced Numerical Modeling of Turbulent Flow with Fully Resolved Time Advancement. Part 1. Theory and Physical Interpretation

Abstract

A multiscale modeling concept for numerical simulation of multiphysics turbulent flow utilizing map-based advection is described. The approach is outlined with emphasis on its theoretical foundations and physical interpretations in order to establish the context for subsequent presentation of the associated numerical algorithms and the results of validation studies. The model formulation is a synthesis of existing methods, modified and extended in order to obtain a qualitatively new capability. The salient feature of the approach is that time advancement of the flow is fully resolved both spatially and temporally, albeit with modeled advancement processes restricted to one spatial dimension. This one-dimensional advancement is the basis of a bottom-up modeling approach in which three-dimensional space is discretized into under-resolved mesh cells, each of which contains an instantiation of the modeled one-dimensional advancement. Filtering is performed only to provide inputs to a pressure correction that enforces continuity and to obtain mesh-scale-filtered outputs if desired. The one-dimensional advancement, the pressure correction, and coupling of one-dimensional instantiations using a Lagrangian implementation of mesh-resolved volume fluxes is sufficient to advance the three-dimensional flow without time advancing coarse-grained equations, a feature that motivates the designation of the approach as autonomous microscale evolution (AME). In this sense, the one-dimensional treatment is not a closure because there are no unclosed terms to evaluate. However, the approach is additionally suitable for use as a subgrid-scale closure of existing large-eddy-simulation methods. The potential capabilities and limitations of both of these implementations of the approach are assessed conceptually and with reference to demonstrated capabilities of related methods.