In this paper we propose an accurate, and computationally efficient method
for incorporating adaptive spatial resolution into weakly-compressible Smoothed
Particle Hydrodynamics (SPH) schemes. Particles are adaptively split and merged
in an accurate manner while ensuring that the number of particles is not large
for a given resolution. Critically, the method ensures that the number of
neighbors of each particle is optimal, leading to an efficient algorithm. A set
of background particles is used to specify either geometry-based spatial
resolution or solution-based adaptive resolution. This allows us to simulate
problems using particles having length variations of the order of 1:250 with
much fewer particles than currently reported with other techniques. The method
is designed to automatically adapt when any solid bodies move. The algorithms
employed are fully parallel. We consider a suite of benchmark problems to
demonstrate the accuracy of the approach. We then consider the classic problem
of the flow past a circular cylinder at a range of Reynolds numbers and show
that the proposed method produces accurate results with a significantly reduced
number of particles. We provide an open source implementation and a fully
reproducible manuscript.Comment: 44 pages, 32 figures, 3 table