  We propose a simple tweak to a recently developed regularisation scheme for
particle methods. This allows us to chose the particle spacing $h$ proportional
to the regularisation length $\sigma$ and achieve optimal error bounds of the
form $\mathcal{O}(\sigma^n)$, $n\in\mathbb{N}$, without any need of remeshing.
We prove this result for the linear advection equation but also carry out
high-order experiments on the full Navier--Stokes equations. In our experiments
the particle methods proved to be highly accurate, long-term stable, and
competitive with discontinuous Galerkin methods.
