From discrete elements to continuum fields: Extension to bidisperse systems

TL;DR

This paper introduces an advanced coarse-graining method for converting discrete two-component flow data into continuum fields, effectively handling boundary interactions and constituent-specific forces without ensemble averaging.

Contribution

The paper extends micro-macro transition methods to unsteady two-component flows, enabling consistent continuum field construction from discrete data with boundary and constituent-specific force considerations.

Findings

Consistent continuum fields including boundary interactions are obtained.

The method works with any discrete data, including experiments and simulations.

No ensemble averaging required, suitable for static and dynamic flows.

Abstract

To develop, calibrate and/or validate continuum models from experimental or numerical data, micro-macro transition methods are required. These methods are used to obtain the continuum fields (such as density, momentum, stress) from the discrete data (positions, velocities, forces). This is especially challenging for non-uniform and dynamic situations in the presence of multiple components. Here, we present a general method to perform this micro-macro transition, but for simplicity we restrict our attention to two-component scenarios, e.g. particulate mixtures containing two types of particles. We present an extension to the micro-macro transition method, called \emph{coarse-graining}, for unsteady two-component flows. By construction, this novel averaging method is advantageous, e.g. when compared to binning methods, because the obtained macroscopic fields are consistent with the continuum equations of mass, momentum, and energy balance. Additionally, boundary interaction forces can be taken into account in a self-consistent way and thus allow for the construction of continuous stress fields even within one particle radius of the boundaries. Similarly, stress and drag forces can also be determined for individual constituents of a multi-component mixture, which is essential for several continuum applications, \textit{e.g.} mixture theory segregation models. Moreover, the method does not require ensemble-averaging and thus can be efficiently exploited to investigate static, steady, and time-dependent flows. The method presented in this paper is valid for any discrete data, \textit{e.g.} particle simulations, molecular dynamics, experimental data, etc.