Implicit Molecular Stresses in Weakly-Compressible Particle-Based Discretization Methods for Fluid Flow

TL;DR

This paper investigates the implicit molecular stresses in weakly-compressible particle-based fluid simulation methods, revealing a molecular stress tensor that explains some of the challenges faced in these techniques.

Contribution

It introduces a molecular stress tensor derived via NEMD analysis, providing new insights into the behavior of kernel-based fluid elements in particle methods.

Findings

Identification of a molecular stress tensor in particle methods

Explanation of volume partition errors affecting particle behavior

Insights into the limitations of pseudo-Lagrangian assumptions

Abstract

Weakly-compressible particle-based discretization methods, utilized for the solution of the subsonic Navier-Stokes equation, are gaining increasing popularity in the fluid dynamics community. One of the most popular among these methods is the weakly-compressible smoothed particle hydrodynamics (WCSPH). Since the dynamics of a single numerical particle is determined by fluid dynamic transport equations, the particle per definition should represent a homogeneous fluid element. However, it can be easily argued that a single particle behaves only pseudo-Lagrangian as it is affected by volume partition errors and can hardly adapt its shape to the actual fluid flow. Therefore, we will assume that the kernel support provides a better representative of an actual fluid element. By means of non-equilibrium molecular dynamics (NEMD) analysis, we derive isothermal transport equations for a kernel-based fluid element. The main discovery of the NEMD analysis is a molecular stress tensor which may serve to explain current problems encountered in applications of weakly-compressible particle-based discretization methods.