Stress evaluation in combined immersed boundary lattice Boltzmann simulations
The recovery of the stress tensor in computer simulations is not as straight-forward as it may appear at first view. The reason is that usually not the stress tensor σ itself enters the macroscopic equations. Rather, its divergence, \( \nabla \cdot \sigma \) appears. Even if this divergence is known, it is generally not possible to uniquely reconstruct the stress tensor from it since the equation system is underdetermined1. It has already been mentioned in section 5.2 that the full fluid stress tensor is known at each point within the lattice Boltzmann method (LBM). The situation is different for the particle stress. If, however, averages of some kind are sufficient (e.g., over time, volume, or a coordinate plane), different approaches are available to recover the particle stress tensor or some of its components.