Proper orthogonal decomposition of atomistic flow simulations

An adaptive proper orthogonal decomposition based on time windows (WPOD) for analysis of velocity fields from atomistic simulations is presented. The method effectively separates the field into ensemble average and fluctuation components, and can be applied to both stationary and non-stationary flows in simple and complex geometries. The criteria to distinguish POD modes representing ensemble average and fluctuation components are based on adaptive examination of eigenvalue decomposition, specifically on the rate of decay of POD eigenvalues and analysis of POD eigenvectors. The WPOD method is efficient and its superior accuracy leads to smooth field gradients that can be used effectively in multiscale formulations. The method has been applied in molecular dynamics and dissipative particle dynamics simulations. We demonstrate the method for several cases including steady and unsteady flow and red blood cell flow, but the same approach can be used in atomistic simulations of materials.