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

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