Meshless methods alleviate the overhead of mesh generation, particularly in complex geometries.

Eulerian meshless collocation schemes, however, face robustness issues in complex geometries.

We show that using DC PSE discretization for spatial differential operators improves the robustness.

This leads to an Eulerian meshless collocation solver that robustly converges even in cases where MLS fails.

We validate the method on benchmark problems and illustrate its robustness in complex 2D geometries.