Upstream monotonic interpolation for scalar transport with application to complex turbulent flows

Abstract

Abstract A new monotonic scheme for the approximation of steady scalar transport is formulated and implemented within a collocated finite‐volume/pressure‐correction algorithm for general turbulent flows in complex geometries. The scheme is essentially a monotonic implementation of the quadratic QUICK interpolation and uses a continuous and compact limiter to secure monotonicity. The principal purpose is to allow an accurate and fully bounded, hence stable, approximation of turbulence convection in the context of two‐equation eddy viscosity and Reynolds stress transport modelling of two‐ and three‐dimensional flows, both subsonic and transonic. Among other benefits, this capability permits an assessment to be made of the adequacy of approximating turbulence convection with first‐order upwind schemes in conjunction with higher‐order formulations for mean‐flow properties—a widespread practice. The performance characteristics of the bounded scheme are illustrated by reference to computations for scalar transport, for a transonic flow in a Laval nozzle, for one separated laminar flow and for two separated turbulent flows computed with a non‐linear RNG model and full Reynolds stress closure.