Variance consistent mean shift particle model for treating differential molecular diffusion in transported PDF methods for turbulent reactive flows

The mean shift (MS) particle model (McDermott and Pope, Journal of Computational Physics, 2007, 226, 947-993) was introduced to ensure consistent DNS limit for scalar variance production/dissipation and to incorporate the spatial differential molecular diffusion effect in the transported PDF method. Two significant issues are raised about the MS model in this work. First, the MS model misses molecular diffusion for the scalar variance transport and causes an inconsistent model behavior. Second, a correction algorithm is needed to ensure that the particle scalars remain bounded. The effect of this boundedness correction on the accuracy, consistency, and convergence of the MS model has not been fully examined. This work aims to address these two issues by developing a fully variance consistent mean shift (VCMS) model and by developing and examining correction algorithms for boundedness violation of particle scalars. A turbulent mixing layer problem is employed to validate the VCMS model and the boundedness correction algorithms.