Continuing Investigations of Nonlocality in Rayleigh-Taylor Instability Using the Macroscopic Forcing Method

In our past work, we used the Macroscopic Forcing Method (MFM) to assess the importance of higher-order spatio-temporal moments of the eddy diffusivity kernel for 2D Rayleigh-Taylor Instability (RTI) and concluded that nonlocality should not be neglected when constructing models for RTI. In the present work, we continue our investigation of nonlocality in RTI in two areas: 1) we apply a method for accelerated statistical convergence of MFM results; 2) we examine the importance of higher-order moments of eddy diffusivity in 3D RTI. Accelerated statistical convergence is achieved by reformulating the MFM equations such that propagation of statistical errors from one moment equation to another moment equation is substantially suppressed. New MFM receiver equations are presented, and a desirable level of statistical convergence is achieved in nearly one tenth of the number of simulations needed in the original method. This accelerated method allows us to obtain statistically-well-converged MFM measurements for 3D RTI with fewer high-fidelity simulations than in the original method, when MFM for 3D RTI would have otherwise been quite costly. We present MFM measurements of eddy diffusivity moments for 3D RTI using this accelerated method.