Using DC PSE operator discretization in Eulerian meshless collocation methods improves their robustness in complex geometries

Many fluid-dynamics applications require solutions in complex geometries. In these cases, mesh generation can be a difficult and computationally expensive task for mesh-based methods. This is alleviated in meshless methods by relaxing the neighborhood relations between nodes. Meshless methods, however, often face issues computing numerically robust local operators, especially for the irregular node configurations required to effectively resolve complex geometries. Here we address this issue by using Discretization-Corrected Particle Strength Exchange (DC PSE) operator discretization in a strong-form Eulerian collocation meshless solver. We use the solver to compute steady-state solutions of incompressible, laminar flow problems in standard benchmarks and multiple complex-geometry problems in 2D with a velocity-correction method in the Eulerian framework. We verify that the solver produces stable and accurate results across all benchmark problems. We find that DC PSE operator discretization is more robust to varying node configurations than Moving Least Squares (MLS). In addition, we find that in more challenging complex geometries, the solver using MLS operator discretization fails to converge, whereas DC PSE operators provide robust solutions without node adjustment.